Técnicas Dinámicas para Teledetección Empleando Imágenes

Técnicas Dinámicas para Teledetección Empleando Imágenes SAR, Ópticas y Vehículos

Aéreos no Tripulado

Caleb G. De Bernardis

www.ua.es

www.eltallerdigital.com

Técnicas Dinámicas para Teledetección Empleando Imágenes SAR, Ópticas y Vehículos

Aéreos no Tripulado

DOCTOR POR LA UNIVERSIDAD DE ALICANTE

INSTITUTO UNIVERSITARIO DE INVESTIGACIÓN INFORMÁTICA

Caleb G. De Bernardis

Tesis presentada para aspirar al grado de

Programa de Doctorado en Informática

Dr. Tomás Martínez Marín

Dirigida por:

Agradecimientos

A Dios que me ha dado la vida. A mi amada esposa que siempre ha estado a mi

lado y que sin ella este logro no hubiera sido posible. A mis padres y hermanos de

quienes he aprendido las cosas mas importante de la vida. A mı tutor Dr. Tomas

Martınez Marın y a Dr. Juan Manuel Lopez por guiarme y volcar en mi todo lo

necesario para poder llevar a cabo esta tesis. A mis companeros de trabajo, amigos,

y familiares que siempre han estado a mi lado.

Gracias.

2

Indice general

Agradecimientos 2

1. Sıntesis 9

1.1. Introduccion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2. Objetivos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.3. Resultados . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.4. Contribucion aportada . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.5. Conclusiones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2. Trabajo Publicado 27

2.1. Estimation of Key Dates and Stages in Rice Crops Using Dual-Polarization

SAR Time Series and a Particle Filtering Approach . . . . . . . . . . 29

2.2. Particle Filter Approach for Real-Time Estimation of Crop Phenological

States Using Time Series of NDVI Images . . . . . . . . . . . . . . . 41

2.3. Contribution to Real-Time Estimation of Crop Phenological States in

a Dynamical Framework Based on NDVI Time Series: Data Fusion

With SAR and Temperature . . . . . . . . . . . . . . . . . . . . . . . 61

3. Trabajo no publicado 75

3

Indice general 4

3.1. Modelos de estimacion fenologica basados en observaciones RADAR

Sentinel-1 y datos de temperatura . . . . . . . . . . . . . . . . . . . . 76

3.1.1. Introduccion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

3.1.2. Metodologıa desarrollada . . . . . . . . . . . . . . . . . . . . . 78

3.1.3. Filtro de Partıculas . . . . . . . . . . . . . . . . . . . . . . . . 80

3.1.4. Filtrado . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

3.1.5. Conjunto de datos . . . . . . . . . . . . . . . . . . . . . . . . 92

3.1.6. Resultados . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

3.1.7. Discusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

3.1.8. Conclusiones y futuras lıneas de trabajo . . . . . . . . . . . . 102

3.2. Estudio de medidas utilizando sensores embarcados en UAV . . . . . 104

3.2.1. Introduccion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

3.2.2. Objetivo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

3.2.3. Pruebas y medidas . . . . . . . . . . . . . . . . . . . . . . . . 106

3.2.4. Elaboracion de un sistema de medidas de campo sobre cultivos

de arroz empleando los sensores que se utilizaran en el UAV . 109

3.2.5. Analisis de los datos . . . . . . . . . . . . . . . . . . . . . . . 115

3.2.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

4. Conclusiones 123

A. Publicaciones en congresos 127

Bibliografıa 129

Indice de figuras

3.1. Evolucion multitemporal promedio de las variables VH, VV a lo largo

de las distintas etapas fenologicas en cultivos de arroz. . . . . . . . . 83

3.2. Evolucion multitemporal promedio de las variables VH, VV y CGDd

a lo largo de las distintas etapas fenologicas en cultivos de arroz. . . . 84

3.3. Probabilidad de transicion VV y VH cuando el estado origen es X =

−13,5dB,−19,5, 1020. . . . . . . . . . . . . . . . . . . . . . . . . . . 86

3.4. Proyeccion VV contra CGDd de la probabilidad de transicion cuando

el estado origen es X = −13,5dB,−19,5, 1020. . . . . . . . . . . . . . 87

3.5. Proyeccion VH contra CGDd de la probabilidad de transicion cuando

el estado origen es X = −13,5dB,−19,5, 1020. . . . . . . . . . . . . . 87

3.6. Estimacion fenologica medida en BBCH y medidas de campo para

los cultivos estudiados en 2016. Las medidas de campo se dan en

valores maximos (lınea continua) y mınimos (lınea discontinua). Las

estimaciones se marcan con un cırculo negro. . . . . . . . . . . . . . 95

5

Indice de figuras 6

3.7. Estimacion fenologica medida en BBCH y medidas de campo para

los cultivos estudiados en 2017. Las medidas de campo se dan en

valores maximos (lınea continua) y mınimos (lınea discontinua). Las

estimaciones se marcan con un cırculo negro. . . . . . . . . . . . . . 99

3.8. Imagen pancromatica del recinto donde se realizaron las primeras

pruebas de los sensores de medida embarcados en el UAV. . . . . . . 107

3.9. Imagen pancromatica del recinto donde se realizaron las primeras

pruebas de los sensores de medida embarcados en el UAV. . . . . . . 108

3.10. Esquema de interconexion de los elementos de captura de datos . . . 111

3.11. Vista interna de los elementos de captura de datos . . . . . . . . . . . 112

3.12. Sensor optico y laser utilizados. . . . . . . . . . . . . . . . . . . . . . 113

3.13. Sistema de medidas instalado en arrozal. . . . . . . . . . . . . . . . . 114

3.14. Imagenes captadas con camara Parrot Sequoia para distintas fechas. . 116

3.15. Imagenes NDVI captadas con camara Parrot Sequoia para distintas

fechas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

3.16. Evolucion temporal promedio y desviacion del NDVI para los datos

captados con la camara Parrot Sequoia (en rojo) . . . . . . . . . . . . 118


captados con la camara Parrot Sequoia (en rojo) y con el Sentinel-2

(en azul) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119


captados con la camara Parrot Sequoia (en rojo) y con el Sentinel-2

(en azul) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

Indice de cuadros

1.1. RMSE y MAE obtenidos para la estimacion de la fecha de EoS usando

TIMESAT y la metodologıa propuesta. . . . . . . . . . . . . . . . . . 19

1.2. Resultado usando combinaciones diferentes de los datos en el proceso

de estimacion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.1. Error cometido en las estimaciones para la campana 2016 . . . . . . . 94

3.2. Matriz de confusion para la estimacion fenologica en la campana 2016 97

3.3. Error cometido en las estimaciones para la campana 2017 . . . . . . . 98

3.4. Matriz de confusion para la estimacion fenologica en la campana 2017 100

7

Indice de cuadros 8

Capıtulo 1

Sıntesis

1.1. Introduccion

La agricultura es una de las practicas humanas que nos hace unicos como especie.

Comenzo hace mas de 11000 anos y ha permitido el desarrollo y la subsistencia

de millones de personas a lo largo de nuestra historia. En todo este tiempo los

metodos y tecnicas utilizados han ido evolucionando y mejorando para sacar un

mayor rendimiento de los cultivos. Por ejemplo, el diseno de canales y uso de herramientas

como el cigonal, permitieron el desarrollo economico de uno de los imperios mas

grandes y poderosos de la tierra, el antiguo Egipto. Si bien esta tendencia por mejorar

las practicas ha sido una constante hasta hoy en dıa, se debe ser consciente de que

vivimos en un mundo donde los recursos de los que disponemos son limitados. Este

hecho choca con la tendencia del numero de habitantes en el planeta, que sigue

aumentando ano tras ano, a un ritmo de 75 millones de habitantes por ano.

Segun la FAO en la campana de 2017 el planeta ha conseguido generar un total de

759.6 millones de toneladas de arroz (503.9 millones de toneladas de arroz elaborado)

9

Capıtulo 1. Sıntesis 10

lo que supone un incremento del 0,6 % respecto a la campana anterior, segun Food

Agriculture Oragnization. Mientras que la poblacion mundial se incremento un 1,2 %

en 2017, ver pob. El enfrentarnos a este desajuste supone todo un desafıo para la

agricultura global. El presidente de la FAO mostro su preocupacion en este aspecto,

recalcando que, si seguimos manteniendo las mismas practicas agrıcolas actuales,

ineficientes, para 2050 no habra alimento para todos, y en 2025 paıses con bajo

desarrollo iban a tener serios problemas para acceder a agua potable dado que su

mayorıa se usa para la agricultura, Food Agriculture Oragnization. Es por esta razon,

que surge la necesidad de crear herramientas que nos permitan ayudar y mejorar las

practicas agrıcolas.

En ultimo siglo ha surgido un elemento tecnologico que nos ha permitido obtener

grandes avances como sociedad, hablamos del lanzamiento y funcionamiento de

constelaciones de satelites, que nos han dotado de una nueva perspectiva de nuestro

planeta. Han surgido para dar solucion a muchas aplicaciones diferentes, Joshi et al.,

siendo una de ellas la agricultura. Dadas las extensiones y ubicacion de las zonas

agrıcolas, el uso de teledeteccion es uno de los medios mas apropiados para su

monitorizacion, proporcionando a los agricultores una vision mas amplia de lo que

ocurre en sus parcelas, pudiendo ası actuar en consecuencia y ser eficientes, con el fin

de maximizar la produccion y minimizar el uso de recursos. Ademas, la teledeteccion

no solo permite la inspeccion de grandes areas en un mismo instante de tiempo, sino

que, al disponer de multiples sensores, es sensible a informacion que el ojo humano

no es capaz de detectar, ver Mulla.

Desde el lanzamiento de los primeros satelites hasta hoy en dıa, es importante

destacar el avance en el numero de constelaciones que estan constantemente orbitando


alrededor de la tierra. Esto provoca que aparezca un nuevo evento en el marco de la

teledeteccion y es el hecho de disponer de series multitemporales de alta frecuencia.

Es decir, surge la posibilidad de disponer de informacion con periodos temporales

muy cortos, por ejemplo, de 3-6 dıas como es el caso de Sentinel-1 y 2-5 dıas Sentinel-2

en Europa. En este aspecto, se ha abierto una lınea de investigacion en los ultimos

anos para poder evaluar el potencial de tener secuencias de datos con tan corto

periodo de revisita Estel et al., Joao et al., Schuster et al.. En otros campos, el

enfoque dinamico se ha presentado como la mejor solucion para trabajar con series

temporales. Su utilizacion se plantea como una herramienta eficaz, en la explotacion

de los datos de observacion remota, para monitorizar el estado de los cultivos.

La teorıa de sistemas dinamicos surge como una herramienta matematica que

nos permite estudiar el comportamiento o evolucion de un sistema. En este sentido,

un sistema es aquel que queda definido por la interaccion de los elementos que lo

conforman. Esta interaccion en un determinado instante de tiempo define lo que se

conoce como estado del sistema. Por ejemplo, un ser vivo es un sistema, donde la

interaccion de sus componentes (organos, celula, etc) definen el estado del ser vivo.

Si esta interaccion cambia con el tiempo, el estado del sistema tambien cambia. Si

hacemos uso de una representacion espacial de esos cambios, donde cada uno de los

ejes esta definido por cada uno de los elementos que definen el sistema, podremos

ver las trayectorias que surgen de dichas interacciones. A este tipo de representacion

se la conoce como espacio de estados y a las trayectorias que surgen a medida que

el sistema evoluciona se las conoce como modelo de comportamiento.

Este nuevo marco de trabajo nos permite abordar la estimacion del estado de

un cultivo de forma mucho mas eficiente y precisa. Se trata de aprender o conocer


el modelo de comportamiento a partir del estudio previo de un sistema. Conocido

el estado del sistema en un determinado instante de tiempo, podemos intuir gracias a

nuestro modelo hacia donde evolucionara cada uno de los elementos que lo conforman.

En concreto, el proceso de estimacion, de cualquier variable de interes, se basa en la

combinacion de dos etapas, una primera etapa conocida como etapa de prediccion y

una segunda etapa conocida como etapa de observacion. En la etapa de prediccion

utilizamos las trayectorias conocidas de nuestro espacio de estados para dar una

primera estimacion de la transicion de estados del sistema transcurrido un determinado

tiempo. La etapa de observacion consiste en observar el sistema una vez ha transitado

de estado. Si el sistema fuera directamente observable y no hubiera incertidumbre en

la observacion, la etapa de prediccion no serıa necesaria, pero en la realidad ningun

metodo de observacion es infalible. De esta forma reducimos la incertidumbre y ruido

presentes en la propia observacion.

Hay diferentes formas y metodos de combinar el estado dado por cada una de las

etapas. Uno de los filtros mas utilizados para combinar ambas fuentes de informacion

ha sido el filtro de Kalman Vicente-Guijalba et al.. Este filtro es optimo y el que mejor

combina tanto los datos de prediccion como de observacion, cuando las funciones de

densidad de probabilidad (pdf) de ambos son distribuciones normales. Ademas, el

sistema bajo observacion debe ser un sistema lineal. Uno de los filtros que surge

para mitigar estos problemas es el conocido como Filtro de Partıculas, Arulampalam

et al.. Este filtro permite trabajar con funciones con densidad de probabilidad no

definidas por una ecuacion conocida, dado que, se basa en aproximar su forma por

medio de un conjunto de estados muestreados denominadas partıculas. Cada una de

estas partıculas atravesara dos etapas; prediccion y actualizacion. Representan un


estado posible dentro de nuestro espacio de estados, con una probabilidad de ser el

estado correcto denominada peso.

1.2. Objetivos

Nace como objetivo de esta tesis evaluar la posibilidad de aprovechar la informacion

proporcionada por la teledeteccion para inferir parametros biofısicos en los cultivos.

En concreto se plantea la cuestion de evaluar el potencial de las series temporales

satelitales para poder monitorizar y detectar los cambios sufridos en el desarrollo de

los cultivos, que desde un punto de vista de analisis, se comporta como un sistema

dinamico (que evoluciona con el tiempo). Ante este marco de trabajo se plantea el

uso de herramientas dinamicas para abordar una cuestion tan ıntimamente ligada

a cambios temporales, tanto en los elementos de observacion como en los elementos

observados.

Para ello, se procedera a desarrollar las herramientas de filtrado necesarias para

poder inferir a partir de series temporales satelitales, los parametros que miden el

crecimiento de los cultivos. En concreto, se inferira la fenologıa, un variable que marca

en que etapa de su desarrollo (floracion, madurez, entre otros) se encuentra el cultivo,

Meier. Por otro lado, se buscara la forma de combinar observaciones satelitales de

distinta naturaleza, procedentes de sensores RADAR y sensores opticos, para abordar

la misma problematica. El objetivo es tener una herramienta que permita explotar

las ventajas de cada uno de los sensores en la tarea de monitorizacion fenologica.

Ademas, dado que recientemente se puso a disposicion de los usuarios datos de

acceso libre y gratuito del sentinel-1B, se desarrollara una herramienta que permita

utilizar estas series temporales de alta frecuencia de revisita. Estas imagenes estan


disponibles con un periodo de entre 3 y 6 dıas desde 2017 en Europa. Se evaluara

la mejora de reducir el tiempo de revisita a la mitad y su capacidad para inferir el

estado de los cultivos.

Por otro lado, dado que en los ultimos anos los Vehıculos Aereos no Tripulados

o Unmanned Aerial Vehicle (UAV) estan teniendo cada vez mayor protagonismo, se

evaluara la posibilidad de aplicar la metodologıa a los sensores embarcados en estos

medios. Se busca la posibilidad de estimar la fenologıa con este tipo de vehıculo en

un marco de trabajo que permita su compatibilidad con las observaciones satelitales.

1.3. Resultados

Como punto de partida de esta tesis se implemento el filtro conocido como

filtro de partıculas. Este filtro permite trabajar con distribuciones de probabilidad

multimodales. Dada la naturaleza del sistema bajo observacion y de las propias

senales de observacion es importante contar con una herramienta que nos permita

combinar probabilidades multimodales y modelos no lineales. En esta tesis se presentaran

un total de 5 trabajos, 3 han sido ya publicados, uno sera enviado para su posterior

publicacion y otro de resultados de experimentales en campo. En esta seccion se

resumiran los resultados de los trabajos publicados. Los trabajos no publicados se

detallan en la seccion de trabajos no publicados 3.

En el primer trabajo se disena e implementa el filtro de partıculas para trabajar

con imagenes RADAR captadas por el TerraSAR-x con el fin de inferir el estado

fenologico en cultivos de arroz. Se utilizaron un conjunto de 11 imagenes polarimetricas

en banda X captadas en el ano 2009 a 30o de inclinacion. En este caso, como

modelo de prediccion se utilizo el modelo descrito en Vicente-Guijalba et al.. El filtro


nos permitio combinar la estimacion dada por el modelo y la informacion inferida

directamente de las observaciones, cada vez que estaban disponibles.

Los resultados obtenidos se compararon con los obtenidos mediante el uso del

filtro Filtro extendido de Kalman (EKF) Vicente-Guijalba et al.. Para cada uno de

los metodos se presento la matriz de confusion resultante. Esta matriz nos permite

obtener una medida de la fiabilidad de un metodo para estimar o detectar un

determinado estado. En el caso de las estimaciones obtenidas con el EKF se alcanza

una precision total del 58,2 % y un factor Kappa = 0,5393 mientras que utilizando

la metodologıa presentada en este trabajo se alcanzo una precision total del 81,81 %

y un factor Kappa de 0,7874.

Por otro lado, se aprovecho el desarrollo de los modelos para inferir el dıa en el

que se produjeron o produciran ciertos aspectos claves del cultivo. En concreto, una

vez conocido el estado actual se trata de inferir en que dıa ocurrieron estos eventos.

El primero hace referencia a un evento pasado, como es el dıa de la siembra. Este dato

es de gran interes para productores o asociaciones que no son directamente quienes

realizan las tareas de cultivo pero sı quienes financian o pagan su produccion. De

esta forma se puede detectar si se esta cumpliendo con lo pactado. El otro evento

hace referencia a un evento futuro, como es el caso de en que dıa el cultivo alcanzara

el estado de iniciacion de la panıcula (BBCH 30). En los cultivos de arroz conocer

el momento en el que se alcanza el estado BBCH-30 es crucial, dado que marca el

momento exacto en el que se debe aplicar nitrogeno para maximizar la produccion.

Si se aplica en etapas muy tempranas el cultivo no aprovechara de forma optima el

total de lo aplicado con lo que se estarıan desperdiciando insumos. Por otro lado, si

se aplica demasiado tarde se esta favoreciendo la aparicion de plagas.


Para el caso de la estimacion de fecha de siembra se emplearon un total de 786

parcelas. El analisis mostro un error inferior a ± 10 dıas en el 75 % de los casos, unas

590 parcelas aproximadamente. De ese 75 % el 50 %, en torno a unas 393 parcelas,

presentaban un error que era incluso inferior a ± 5 dıas. Por otro lado, con el fin

de evaluar el potencial de la metodologıa para predecir el momento exacto en el que

nuestro cultivo alcanzara el estado 30 en la escala BBCH se utilizaron un total de 6

parcelas de las que se disponıa informacion. En este caso se observo como a medida

que incorporamos observaciones llegamos a poder predecir la fecha cometiendo un

error promedio de 3 dıas, unos 40 dıas antes de que el evento se produzca.

En un segundo trabajo, se estudio la posibilidad de inferir el estado de los cultivos

mediante el uso de series temporales opticas. En este aspecto, hay un mayor numero

de investigaciones que han presentado resultados utilizado la curva que describe el

Indice de Vegetacion Diferencial Normalizado, NDVI de sus siglas en ingles, para

intentar determinar el momento en el que el cultivo alcanzaba determinados estados,

como la etapa de floracion o la etapa de maduracion. La mayorıa de estos metodos

requieren los datos de la campana en su totalidad, dado que se basan en el ajuste

de los valores de NDVI empleando una curva ya conocida. Estos metodos no solo

tienen el inconveniente de que discriminan pocos estados, sino que como se expone en

White y Nemani, no son aptos para dar estimaciones en tiempo real (cada vez que una

observacion este disponible). Surgieron algunas otras soluciones para poder trabajar

en tiempo real pseudo tiempo real,como Suwannachatkul et al., White y Nemani

pero seguıan siendo pocos los estados detectados. Gracias al enfoque dinamico, se

pueden solventar ambos problemas.

En primer lugar, se diseno un modelo que nos permitiera predecir cual va a


ser el estado fenologico del cultivo transcurrido un determinado instante de tiempo

y conocido el estado fenologico anterior. A este modelo se lo denomino modelo de

prediccion. Por otro lado, tambien se diseno el modelo de observacion que nos permite

relacionar las observaciones opticas con el estado del sistema. De todas las bandas

de las que disponen los sensores opticos, se hace uso de dos de ellas, la banda roja

y la banda infrarroja cercana. Con estas dos bandas se puede obtener el NDVI, ver

ecuacion 3.8. Se ha demostrado que este ındice es un buen indicador de cultivo y de

la salud de este. El modelo de observacion nos permite relacionar la curva NDVI con

los estados fenologicos, es decir, nos permite inferir que estado o en que etapa del

cultivo genera unos determinados valores de NDVI.

NDV I =NIR−REDNIR +RED

(1.1)

En este trabajo se procedio a estimar la fenologıa de 54 parcelas repartidas en un

total de 5 anos. Para separar el conjunto de datos utilizado en la obtencion de los

modelos y el conjunto utilizado en la evaluacion, se empleo el metodo denominado

metodo de validacion cruzada. Este metodo consiste en generar los modelos con el

total de datos disponibles excepto el que se usara en la evaluacion.

En total se obtuvieron 379 estimaciones y se logro alcanzar un factor de correlacion

de R2 = 0,93 y un error cuadratico medio de RSME = 6,6 estados. Por otro lado,

se evaluo la posibilidad del metodo de trabajar sobre otros tipos de arroz que tienen

tiempos de desarrollo diferentes. En concreto, se propuso compararlo con arroz de

ciclo mas corto (120 dıas) frente al de 150 dıas que se utilizo para la generacion de los

modelos. Dado que no se disponıa de datos reales, se procedio a su simulacion. Para

conseguirlo se comprimio el tiempo de desarrollo de los datos de campo un 20 %. De


esta forma lograbamos que su ciclo completo de desarrollo se acortara a los 120 dıas.

En este caso para un total de 379 estimaciones se obtuvo un factor de determinacion

de R2 = 0,9 y un RSME = 11,2 estados con un error maximo de 36 estados.

Otro de los objetivos del estudio fue comparar la metodologıa propuesta con

otros metodos que tienen un uso mas extendido en la literatura. Estos se encuentran

implementados en un software conocido como TIMESAT, Jonsson y Eklundh. El

objetivo es comparar la estimacion, empleando cada uno de los metodos, de la etapa

conocida como End Of Season (EoS) que marca el comienzo de la maduracion del

cultivo. En concreto, se comparo la fecha en la que se produjo este evento con la

obtenida por tres metodos basados en ajuste: asimetrica Gaussiana, funcion doble

logıstica y el filtro adaptativo Savitzky-Goalay y por el obtenido con la metodologıa

desarrollada.

Para este analisis, del total de parcelas, se descartaron 12 por no tener datos

de campo de cuando se alcanzaba la etapa EoS. En la tabla 1.1 se presetan los

factores de determinacion y RSME obtenidos para cada uno de los metodos. El

mejor resultado que se obtiene utilizando el TIMESAT es de R2 = 0,639 empleando

el ajuste Savistzky-Golay. Si comparamos estos resultados con los obtenidos por el

filtro de partıculas observamos una mejora de un 20 % los resultados.

Una de las desventajas de las estimaciones basadas en ajustes de los datos es que

requieren una serie de datos con un muestreo uniforme y dada la problematica de los

datos opticos a la presencia de nubes, hace que se requieran metodos de interpolacion

previos afectando a la precision de los mismos. En la metodologıa propuesta, al contar

con una etapa de prediccion, no es necesario aplicar ninguna interpolacion a los datos

si hay ausencia debido a nubes.


Cuadro 1.1: RMSE y MAE obtenidos para la estimacion de la fecha de EoS usandoTIMESAT y la metodologıa propuesta.

Metodo R2 RSME

asymmetric Gaussian 0.406 14.0

Double-logistic 0.508 12.8

Savistzky-Golay 0.639 10.3

Filtro de Partıculas 0.773 8.0

A modo de conclusion, en este trabajo se presento un metodo novedoso para

la estimacion de parametros biofısicos y de eventos claves utilizando observaciones

opticas. Se compararon los resultados obtenidos con nuestro metodo con otros metodos

mas extendidos obteniendo claras ventajas. Una de ellas es la mayor robustez ante

la perdida de imagenes debido a las nubes y la posibilidad de trabajar en tiempo

real, dando una nueva estimacion cada vez que una nueva imagen esta disponible.

Ademas, se demostro la posibilidad de generalizar el metodo para otros tipos de

cultivos u otra zonas geograficas.

Demostrado el potencial que radica en el uso de series temporales SAR u opticas

en la estimacion del estado fenologico, se planteo el tercer trabajo con el objetivo de

combinar ambas observaciones en el proceso de estimacion. De esta forma logramos

las siguientes mejoras: disminuir el tiempo entre estimaciones, aumentar el numero

de las mismas y sumar informacion de naturaleza independiente que sera sensible

a fenomenos distintos. Otro factor nuevo es la inclusion de informacion externa


en la etapa de prediccion. Se anadio la temperatura como elemento clave en el

comportamiento de los cultivos, dado que numerosos estudios demostraron la dependencia

de su desarrollo con la temperatura. La acumulacion de mayor o menor temperatura

hace que los cambios de estados sean mas rapidos o mas lentos.

Utilizando los datos de temperatura acumulada y datos de campo de 5 anos se

desarrollo un modelo de prediccion que utiliza como variable de control la cantidad de

grados acumulados entre dos observaciones para proveer una estimacion de cuanto

ha cambiado la fenologıa. En cuanto a los modelos de observacion, se utilizo el

modelo presentado en el artıculo anterior para las observaciones opticas y se diseno

un nuevo modelo de observacion que describe la relacion entre el ratio HH/VV y el

estado fenologico para las observaciones RADAR.

Para el analisis de los resultados se utilizaron dos campanas, 2008 con nueve

parcelas y 2009 con 10 parcelas, todas localizadas en Sevilla, Espana. La informacion

de temperatura se obtuvo de una estacion meteorologica cercana, La Puebla del Rio II

que perteneciente al Sistema de Informacion Agroclimatica para el Regadıo (SIAR).

Las imagenes opticas utilizadas son las captadas por el satelite Landsat-7 y para las

observaciones SAR se utilizo el satelite TerraSAR-X.

Con el fin de evaluar las mejoras obtenidas en el contexto de fusion de datos se

evaluaron las estimaciones realizando las siguientes combinaciones:

1) Utilizando solo optico

2) Utilizando SAR+ optico

3) Utilizando SAR+optico+temperatura

Para cada uno de los casos se obtuvo el factor de correlacion R2, la raız del


error cuadratico medio y el maximo error que se comete. Los resultado se presentan

en la tabla 1.2. En la primera fila no se incorpora informacion de temperatura en

la etapa de prediccion, mientras que en la segunda fila sı es tenida en cuenta. La

primera columna muestra los resultados cuando en observacion solo contemplamos

observaciones opticas y la segunda columna es la fusion SAR-optico.

En el caso de utilizar solo datos opticos nos encontramos con el problema ya

mencionado en un estudio previo y es la dependencia de los datos a la presencia de

nubes. La falta de datos en la observacion es suplida por las estimaciones dadas por

la prediccion, pero si esta ausencia se mantiene de forma prolongada hace que el error

que se acumula en la etapa de prediccion sea cada vez mas elevado, empeorando el

resultado en las estimaciones.

Cuando realizamos la fusion de datos SAR-opticos se mejora en la estimacion.

Esta mejora se debe en parte al incremento del numero de observaciones disponibles

y a la reduccion del tiempo entre predicciones. Sin embargo, una de las mejoras mas

destacadas que se puede observar se da en aquellas estimaciones que transcurren

cuando el cultivo se encuentra en el rango fenologico 40-80. En estas etapas el

ındice optico NDVI se encuentra en un estado de saturacion y la observacion no

nos proporciona informacion relativa al estado en el que se encuentra el arroz. Algo

que no ocurre en las observaciones SAR, que sı aporta variaciones en dichos estados.

Este es un beneficio directo de combinar informacion proveniente de distintas fuentes

de observacion.

Finalmente se vuelve a realizar la misma comparacion, pero esta vez se emplea

en la etapa de prediccion informacion referente a la temperatura acumulada. A

diferencia de antes, para el caso de estimar usando solo datos opticos, esta vez se


dispone de un modelo de prediccion basado en la temperatura acumulada. Esto hace

que el error acumulado en prediccion cuando no tenemos datos debido a las nubes sea

menor, dado que sigue estando presente una fuente de informacion, la temperatura.

Cuadro 1.2: Resultado usando combinaciones diferentes de los datos en el procesode estimacion.

NDVI NDVI-SAR

RMSE R2 MAE RMSE R2 MAE

Sin modelo de temperatura 6.36 0.94 25 4.40 0.96 19

Con modelo de temperatura 5.83 0.95 19 3.90 0.97 16

En este trabajo se demostro la versatilidad de la metodologıa para poder combinar

fuentes de informacion distinta y con distintos tiempos de adquisicion. Empleando

el filtro de partıculas y los modelos disenados se combina informacion de distintas

fuentes, SAR, optico y temperatura, para proporcionar una estimacion mas precisa

del estado de los cultivos. Este concepto permite mejorar los metodos de estimacion

dotando al sistema de menor tiempo de actualizacion y una mayor robustez ante

fenomenos meteorologicos, ası como la capacidad de detectar eventos que con un

solo sensor no son detectables.

1.4. Contribucion aportada

Si bien a lo largo de este trabajo se detallan las aportaciones de esta tesis, a

continuacion se presenta un resumen de las mismas:

- Se ha disenado un marco de trabajo para explotar el uso de series temporales de


teledeteccion en un contexto dinamico. Esto ha permitido estimar el estado fenologico

del arroz en tiempo real, es decir, cada vez que una imagen esta disponible.

- Se ha demostrado que el uso de modelos dinamicos permite determinar en que

momento ocurren determinados eventos agrıcolas, sean pasados o futuros. Ademas,

se ha logrado incrementar considerablemente el numero de estados que se pueden

detectar mediante observacion remota.

- Se ha mostrado como para la monitorizacion de cultivos, los filtros basados en

simulaciones de Monte Carlo dan mejores resultados que los metodos basados en

ajustes de datos o el mismo filtro extendido de Kalman (EKF).

- Se ha propuesto un metodo novedoso para la fusion de datos sensoriales. Como

ejemplo, se ha estimado el estado fenologico combinando datos opticos, RADAR y

de temperatura. La fusion nos ha permitido alcanzar estimaciones mas precisas que

cuando se utilizan datos de un unico sensor.

- Se ha disenado un espacio de estado de 3 dimensiones para complementar los

datos del satelite Sentinel-1 con la informacion de temperatura. Esto, junto con el

enfoque dinamico, nos ha permitido compensar la ausencia de las polarizaciones HH

y HV (mas sensibles a los cambios estructurales en cultivos) con el bajo tiempo de

revisita del sensor. Es decir, sin cambiar el sensor, un aumento en la frecuencia de

revisita nos permite aumentar la precision en las estimaciones.

1.5. Conclusiones

Esta investigacion ha permitido el desarrollo de una serie de herramientas nuevas

en el marco de la teledeteccion. Se ha disenado un marco de trabajo para explotar

el uso de series temporales en la estimacion de eventos y parametros biofısicos en


los cultivos de arroz. Se obtuvo la estimacion fenologica empleando observaciones

satelitales. Este enfoque nos permitio obtener resultados con mayor resolucion en la

estimacion de lo que se conseguıa con los metodos actuales. Se desarrollaron distintos

algoritmos los cuales nos permitıan realizar las estimaciones empleando sensores

activos (RADAR), pasivos (opticos) e incluso combinando ambos para dar una unica

estimacion.

En el primer trabajo se demostro la eficacia de la metodologıa frente a otro

tipo de tecnicas mas convencionales o incluso metodos similares como el filtro EKF.

Demostrando ser un metodo mucho mas robusto ante el ruido y evoluciones no

lineales. Ademas de proporcionar el estado fenologico se logro dar estimacion de dos

eventos claves en las practicas agrıcolas, como son la determinacion de en que dıa se

alcanza la etapa 30 o el dıa en el que se produjo la siembra.

En un segundo trabajo, se diseno un conjunto de modelos opticos que nos permiten

mejorar las tecnicas existentes para la determinacion de etapas claves en el desarrollo

natural de los cultivos. Hemos evaluado y comparado la metodologıa con los resultados

obtenidos al emplear el software de uso extendido TIMESAT que implementa una

serie de metodos basados en ajustes. Los resultados demostraron la robustez del

enfoque ante la perdida de datos debido a las nubes.

Finalmente se hizo uso de las herramientas desarrolladas para combinar informacion

de fuente diversa: Temperatura, optica y RADAR. Se demostro que la posibilidad

de usar diversos canales de datos mejora las estimaciones finales. Estas mejoras se

deben en parte al aumento de datos en observacion que reduce el tiempo entre las

actualizaciones de las predicciones y a que son sensores complementarios, dado que

son sensibles a informacion diferente. Esto hace que la incertidumbre asociada a


ciertas etapas del desarrollo se vea reducida. Ademas, el disponer de un modelo de

prediccion basado en actualizaciones de informacion diaria, como es la temperatura,

permite obtener predicciones con menor incertidumbre.


Capıtulo 2

Trabajo Publicado

En este capıtulo se presentan los trabajos publicados. A continuacion se datalla

los indicios de calidad de cada una de las revistas. Para los ındices de calidad se ha

consultado ISI Web of KnowledgeSM JCR y el numero de citas ha sido consultado

Scopus a fecha 26 de julio de 2018.

En la seccion 2.1 se presenta el artıculo Estimation of Key Dates and Stages

in Rice Crops Using Dual-Polarization SAR Time Series and a Particle Filtering

Approach. Este trabajo ha sido publicado por la revista IEEE Journal of Selected

Topics in Applied Earth Observations and Remote Sensing. Esta revista alcanzo

un ındice de impacto de 2.145 (Engineering, Electrical & Electronic) en 2015. Su

posicion fue 61 de 257 quedando en el primer cuartil (Q1). Este trabajo, a julio de

2018, alcanza un total de 18 citas.

En la seccion 2.2 se presenta el artıculo Particle Filter Approach for Real-Time

Estimation of Crop Phenological States Using Time Series of NDVI Images. Este

trabajo ha sido publicado por la revista Remote Sensing, la cual alcanzo en 2016 un

ındice de impacto de 3.244 (Remote Sensing) quedando en la posicion 7 de 29 (Q1).

27

Capıtulo 2. Trabajo Publicado 28

Este trabajo presenta un total de 3 citas.

En la seccion 2.3 se presenta el artıculo Contribution to Real-Time Estimation of

Crop Phenological States in a Dynamical Framework Based on NDVI Time Series:

Data Fusion With SAR and Temperature. Este trabajo ha sido publicado por la

revista IEEE Journal of Selected Topics in Applied Earth Observations and Remote

Sensing. En 2016 el ındice de impacto fue de 2.913 (Imaging, Science & Photographic

Technology) y su posicion 6 de 26 (Q1). El numero de citas que recibe es 5.


2.1. Estimation of Key Dates and Stages in Rice

Crops Using Dual-Polarization SAR Time Series

and a Particle Filtering Approach

1008 IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING, VOL. 8, NO. 3, MARCH 2015

Estimation of Key Dates and Stages in Rice CropsUsing Dual-Polarization SAR Time Series and

a Particle Filtering ApproachCaleb G. De Bernardis, Fernando Vicente-Guijalba, Tomas Martinez-Marin,

and Juan M. Lopez-Sanchez, Senior Member, IEEE

Abstract—Information of crop phenology is essential for eval-uating crop productivity. In a previous work, we determinedphenological stages with remote sensing data using a dynamic sys-tem framework and an extended Kalman filter (EKF) approach.In this paper, we demonstrate that the particle filter is a morereliable method to infer any phenological stage compared to theEKF. The improvements achieved with this approach are dis-cussed. In addition, this methodology enables the estimation ofkey cultivation dates, thus providing a practical product for manyapplications. The dates of some important stages, as the sowingdate and the day when the crop reaches the panicle initiation stage,have been chosen to show the potential of this technique.

Index Terms—Agriculture, multitemporal, particle filter,phenology, polarimetry, rice, synthetic aperture radar (SAR).

I. INTRODUCTION

R ICE is one of the most important sources of food in theworld, Asia being the largest producer with increasing

importance in Africa and Latin America as well as pockets ofproduction in Australia, Europe, and the U.S. To ensure a max-imum yield, it is necessary to keep a continuous monitoringover fields. This would allow producers to have an accurateknowledge on the crop status and to apply a correct treatmentat the precise moments. Phenology represents a measurementof crop evolution and it can be used as a control variable bythe farmers [1], [2]. Traditionally, it is measured by means ofvisual inspection on ground but, due to clear limitations, differ-ent alternative ways of monitoring appear, such as those basedon remote sensing satellite images [2]–[4].

In [5], the phenological stage estimation problem was treatedin a dynamic context. A sequence of synthetic aperture radar(SAR) images, acquired by the German TerraSAR-X sensorat X-band, was used as input data to deduce the phenologi-cal stage. The methodology consisted of: 1) the generation of

Manuscript received April 02, 2014; revised September 12, 2014; acceptedNovember 13, 2014. Date of publication December 09, 2014; date of currentversion March 27, 2015. This work was supported in part by the SpanishMinistry of Economy and Competitiveness (MINECO) and EU FEDER underProject TEC2011-28201-C02-02, and in part by the Generalitat Valencianaunder Project ACOMP/2014/136. All SAR images have been provided by DLRin the framework of projects LAN0021 and LAN0234 of the prelaunch AO ofTerraSAR-X.

The authors are with the Institute for Computing Research (IUII),University of Alicante, E-03080 Alicante, Spain (e-mail: [email protected]; [email protected]; [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSTARS.2014.2372898

a transition model of the phenological evolution and 2) theapplication of the extended Kalman filter (EKF) [6] approachto combine the observations and the derived model for estima-tion purposes. This filtering method uses a linearization of thetransitions and assumes that the probability density function(pdf) of both observation and transition models are describedby a Gaussian distribution in order to provide optimal esti-mations. However, the model is strongly nonlinear and theobservations do not exhibit exactly a Gaussian distribution. Forthese reasons, another filtering method able to work under theseconditions needs to be considered. The particle filtering (PF)approach [7] is proposed here because the estimation proce-dure is not affected by these limitations. It is a sequential MonteCarlo [8], [9] method based on approximating the posterior pdfof the state vector, based on all available information, by a setof samples (or “particles”). When a new input data is avail-able the pdf given by the model is combined with the pdf ofthe observation to estimate the most likely state. Hence, the PFis proposed here as a convenient method for obtaining moreaccurate estimations of phenological stages than the EKF.

From the application point of view, different works inthe literature are based on the analysis of normalized differ-ence vegetation index (NDVI) curves. Phenological parametersare derived in correspondence to inflection points or localminimum/maximum points of the temporal signal [10], [11].Despite the reduced observation space (only one observable),the time coordinate is exploited to estimate some stages, suchas vegetation green-up or start of season, end of season, beginof brown-down, and end of brown-down. In our work, the tran-sition model is presented in a state space defined by a set ofvariables (a detailed explanation is given in Section III) pro-viding a continuous representation for the phenological stages.Therefore, the estimation of any date is feasible with thismethodology.

This approach enables estimating the date of critical stagesthat are strongly related with the productivity, as the panicle ini-tiation stage or the sowing date [12]. A tight control of nutrientinputs, especially nitrogen (N) fertilizer [13], is one of the keyaspects in the improvement of yields in the world. While N fer-tilization maximizes grain yield, an overuse may actually havethe opposite effect [14], [15]. For this reason, N fertilization isstopped at panicle initiation stage. The accurate prediction of aparticular crop reaching this stage will enable to optimize pro-duction and reduce the impacts on the environment, which isbecoming a serious issue as it happens in Asia [16]. Moreover,

1939-1404 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

DE BERNARDIS et al.: ESTIMATION OF KEY DATES AND STAGES IN RICE CROPS 1009

the access to an accurate sowing date estimate will provide therequired information to governments or relevant agencies toreduce the increase in pests and soil damages. Pests affect thecrop yield and force farmers to use toxic products to combat theproblem, and it can be dangerous to consumers. For instance,an alternative technique for breaking the life cycle of the insectpest is presented in [17]. The goal is to synchronize the plant-ing date of crops in large areas. However, this study concludeswith the need of a legislation control in the cycle of sowing tomake it effective. On the other hand, dependence of yield withthe sowing date is shown in [12] and [18], so the knowledge ofsowing dates can be used to establish when is the optimum dateto plant in certain area.

In this paper, the estimation of the current phenological stageof rice crops is addressed first, showing the improvementsachieved by the PF instead of the EKF. In second place, thismethod provides a solution to predict or estimate any key dateof the cultivation cycle. Due to their relevance, as describedin the previous paragraph, the sowing date and the panicleinitiation stage date have been chosen to test it.

An introduction on the PF theory is described in Section II,followed by the description of the methodology proposed forthis particular problem in Section III. Then, results are pre-sented in Section IV. Finally, conclusion and a discussion areaddressed in Section V.

II. THEORY OF PARTICLE FILTER

Particle filter is a method based on Monte Carlo [8], [9]and recursive Bayesian sequential estimation [19], [20] that isvery suitable for nonlinear and/or non-Gaussian applications[21]–[23].

Systems that have a dynamic behavior can be describedmathematically by a set of inputs, outputs, and variables, usingwhat is known as a state space [24]. The state-space approachis convenient when the process is nonlinear and non-Gaussianinstead of using traditional time-series techniques [25]. The rel-evant information about a dynamic process is represented in anN-dimensional space. The state vector defines the position inthe state space of the process at a precise moment. For exam-ple, in navigation tracking problems, the information could bedefined by the distances to the boundaries and the orientationangle. Data acquired by noisy measurements define the result-ing state vector and introduce an uncertainty, forcing us to workin statistical terms. Therefore, filtering techniques are necessaryto obtain the optimal estimation.

The goal of Bayesian sequential estimation is to construct theposterior pdf, to know which is the most likely state, in a recur-sive way, by separating the process in two stages: predictionand update.

Prediction: The Chapman–Kolmogorov integral equationcan be used to generate the prior pdf, if we have definedthe transition model p(Xk|Xk−1), which will be explained inSection III-A, and the posterior pdf p(Xk−1|Z1:k−1) is avail-able. The prior pdf defines the most likely state at time kwithout introducing the observation.

Update: When the observation Zk is available, the priorpdf is updated via Bayes’ rule to obtain the posterior pdf. Acomplete expression is shown in [26].

Fig. 1. Illustration of the stages of the PF algorithm for a pixel at 1-D.

Considering the Markovian assumption, the posteriorpdf p(Xk|Z1:k) can be obtained recursively from the pdfp(Xk−1|Z1:k−1) calculated at a previous state k − 1. In casethe initial distribution pdf p(X0|Z0) = p(x0) is unknown,a uniform distribution over the whole state space can beconsidered.

PF is used to approximate the posterior pdf with a set of Nsamples when the prediction and update steps are not analyti-cally tractable. Particles represent possible states over the statespace. Each particle is defined by a vector (position) and a prob-ability value (weight) based on the likelihood of an observation.In other words, the posterior pdf is represented by a set of Nparticles and their weights. In the initialization step, a set of Nparticles are distributed with an initial pdf that can be uniform(step 1). In the prediction step particles evolve in time accord-ing to the transition model p(Xk|Xk−1) to obtain the prior pdf.When an observation is available the update step is carried out,in which the weights of the particles are computed to gener-ate the posterior pdf using (1) and, being N sufficiently large, itapproximates the posterior pdf (step 3)

p(X0:k|Z1:k) ≈N∑

i=1

ωikδ(X0:k − Xi

0:k) (1)

where δ is the delta-Dirac function, p(X0:k|Z1:k) is the trueposterior pdf, Xi

0:k is the ith simulated sample (particle), andωi

k is the weight of ith simulated sample (particle).For a one-dimensional (1-D) process, a graphical evolution

of the samples at each state is shown in Fig. 1. The particlesare distributed over the horizontal axis represented by a circle,and the area indicates the weight of each one. At step k, theparticles evolve using the transition model to obtain the priorpdf. When a new observation is available, weights are updatedby the observation p(Zk−1|Xi

k−1) to obtain the posterior pdf.As k increases, only a few particles will keep a significant

weight, or in other words, the particles will degenerate withtime. In order to resolve the degeneracy problem, it is neces-sary to implement a resampling step. In the literature, we canfind a lot of resampling methods [27]. If the number of particles


Algorithm 1. RSR Method

Generate a random number U (0) ≈ U [0, 1M ]

for m = 1 to N doi(m) = (ω(m)

n − U (m−1)M + 1

U (m) = U (m−1) + i(m)

M − ω(m)n

end for

with high weight is below a threshold, resampling is employedto concentrate more particles where the posterior pdf is morelikely. To measure the degeneracy, an estimate of the effectivesample size is typically used as

Neff =1

∑Ni=1(ω

ik)2

. (2)

When Neff is smaller than a previously defined threshold,resampling is applied. A small Neff value means a large vari-ance for the weights, hence more degeneracy. The objective ofthe resampling is to concentrate more particles, where there arehigh weights and drop only a few where weights are low. In thiswork, the residual-systematic resampling (RSR) [28] is used forthis purpose. The pseudocode in Algorithm 1 shows the RSRalgorithm for N input and M output particles, where ωN

n is anarray of weights. The indicates a rounded down and U [0, 1

M ]represents the uniform distribution between 0 and 1

M .The resulting set of samples is in fact an independent

and identically distributed (i.i.d.) from the discrete posteriorpdf p(Xk|Z1:k). Therefore, the weights can now be reset toωi

k = 1/Ns. In Fig. 1, the resampling and normalization stepsare illustrated, showing the particles before and after beingresampled. In addition resampling enables the adaption of thecomputational cost, i.e., the number of particles can be variedat each step, and the minimum number of particles can be usedto keep the most important information from the pdf (hencereducing the computational cost), or it can be increased whennecessary. However, if we reduce sharply the number of parti-cles it is possible that the new acquisition pdf does not overlapthe pdf given by the transition mode, meaning that the predic-tion and the observation are incoherent. To solve this issue,a uniform redistribution of the particles is necessary. To pre-vent this, it is important to adapt the number of particles afterresampling.

The last step is the normalization of the weights before goingto the prediction step again. A summary of all stages involvedin the estimation process is shown in Table I.

III. METHODOLOGY

In this section, the methodology for our particular problem ispresented. Point A describes the transition model employed inthis work. In point B, the development of the PF in the frame-work of precision farming is shown, and finally, the approachto estimate different key dates and the phenological stage isexposed in Section III-C.

TABLE IPF SEQUENCE

A. Dynamic Model

A transition model, which characterizes the behavior over thestate space, is required to apply the prediction step in a filteringprocedure. It is a representation of the phenological evolutionfor any rice crop, and it can be employed by any dynamic filter-ing method. In this paper, the dynamic model defined in [5] isused.

From data provided by a polarimetric SAR sensor, it is pos-sible to derive a set of polarimetric observables. In our case,we have decomposed the available dual-polarization data intothree sets of polarimetric parameters: power terms, magnitude,and phase from the correlations between polarimetric chan-nels, and parameters derived from the eigen decomposition ofthe coherency matrix. In this particular scenario, a total of 13parameters are employed, as detailed in [5].

In order to reduce the number of these observables, but mini-mizing the loss of information, an orthogonal transformation ismade based on a principal component analysis (PCA) [29], anda 3-D state space is defined. A time series of dual-polarizationSAR images and the corresponding phenological ground truthare used to generate the dynamic model in the space state. Thecomplete procedure is explained more detail in [5]. In this work,the estimation process is based on the exploitation of this pre-viously generated model, but with a PF approach. In general,all parcels present a similar behavior, so for that reason theyare combined to create an average model (or signature). Such asignature describes the temporal evolution of crops that followthe same management practices. The model must be built withhomogeneous plots, since heterogeneities in the parcel meansthat some areas are not evolving correctly. In such cases, thesignature in the space state is different from the signature of


Fig. 2. Dynamic model applied to a particle at time k to obtain the new posi-tion at time k + 1. Black line represents signature of rice on state space. Bluepoint represents particle position at time k. Blue line represents signature of riceshifted to the particle position. (Red point) Position of particle at time k + 1without noise. Red circle represents zone of possible positions when noise isadded.

the model. This deviation can be used to alert the farmers of apossible problem in the crops.

It is important to remind that using a PCA transformationentails the loss of physical interpretation of the polarimetricdata in the new state space. However, this study is focused onthe final application (i.e., estimation of the current phenologicalstage) and not in the physical interpretation of the polarimetricdata. It should be noticed that the definition of the state spaceemploying such a tool provides us an effective mechanism toreduce the dimensions of the space while losing the minimumquantity of information.

Fig. 2 shows the phenological evolution of rice crops overthe state space. The model is used to define the evolution ofeach particle from time k − 1 to k. It is necessary to deter-mine the way to apply it, due to the absence of an analyticalmodel. First, each particle is projected to the closest state of themodel (hereafter referred as closest state). Once we have a cor-respondence between both, the model is shifted to the particleposition. Particles will evolve as their closest state would do.Therefore, the new position at time k is obtained by evolvingover the shifted model (this is illustrated in Fig. 2). In case thetemporal resolution of the model is in a daily basis, we have toincrement as many steps as days from the previous acquisitionto obtain the new state of the particle. The noise on the transi-tion model was defined by a covariance matrix that depends ofthe variance of the input data (used when the model was gener-ated). Once the new position is calculated, the state vector andthe covariance matrix are multiplied to obtain a new state vec-tor. The same process is applied to all particles to generate theirprior pdf.

B. Filtering Approach

Initially, particles are distributed uniformly because the ini-tial pdf is unknown. To generate the prior pdf the transition

model is applied for each particle, evolving to the new posi-tion k days later. When the observation is available the weightsof the particles are computed using (3)

ωik ∝ ωi

k−1

∑piδ(Zk − Zi

k) (3)

where p(Zk|Xik) =

∑piδ(Zk − Zi

k) represents the proba-bility of particle Xi

k to generate an observation Zk, andp(Xk|Xk−1) is used as proposal pdf [7]. In this case, the num-ber of particles used to provide the estimations was N = 1000.With N below 1000 the representation of the posterior pdf’sis deficient. In particular, some stages show a multimodal pdfwhich cannot be properly modeled due to the small number ofsamples, producing an incorrect estimation. If we increase Nto values much larger than 1000 the estimations do not presentany significant improvement but the computational burden isincreased considerably. Consequently, a set of 1000 particleswas selected as a good tradeoff.

The observations described in [5] are used in this work.However, instead of generating the covariance matrix employedin the EKF approach, the pdf is generated to characterize theobservation.

The projection of the 3-D pdf over each axis of the statespace is used to apply the methodology. Finally, when theposterior pdfs are available we can combine them to get thethree-dimensional pdf again. The result is a set of particleslocated in a particular zone of the state space. Each particle willhave an associated phenological stage which is determined bythe projection of the state vector over the model. The particlewith largest weight, i.e., the highest probability, shows the mostlikely phenological stage, and the standard deviation is given bythe projection of the other particles. If the posterior pdf in (1)has degeneracy, i.e., only a few particles have a significant valuewhereas the rest of them have a low weight, we have to make aresampling. Finally, a normalization of the weight is necessary,and the sequence is repeated from the prediction step.

C. Application of PF

Using the previously introduced model and a set of obser-vations, the PF method provides an estimation tool that can beapplied for different purposes. We focus on the retrieval of thecurrent phenological stage, the estimation of the sowing date,and prediction of the date at which the crop will reach thepanicle initiation stage.

To have a proper description of the crop evolution, thegeneral Biologische Bundesanstalt, Bundessortenamt, andChemical industry (BBCH) scale for cereals [1], [30] is consid-ered. The BBCH scale provides a numerical code to representevery growth stage along the life cycle of plants. This coderanges in a continuous way from 0 (associated with sowing)to 100 (associated with harvest). Therefore, every phenologicalstage along the cultivation period of cereals is associated witha BBCH code, which constitutes a convenient way to describenumerically the evolution of crops.

The evolution model contains all possible ranges of BBCH.The way to obtain the phenological stage from any state is byprojecting its position over the closest state in the model. Using


only one input image the result depends on the observationprecision. Instead, when a set of images is used, noise effectsare reduced, wherewith the state is better determined, and thefinal estimate is improved.

To track phenological changes, particles evolve according tothe transition model, generating a prior pdf. When a new obser-vation is available, the pdf can be updated to provide the newdistribution of particles. The projection of the new states overthe model generates a set of possible phenological values (onefor each particle). To provide a single solution, the maximum aposterior probability (MAP) estimate is used. The phenology iscalculated using the particle with highest weight, and the vari-ance is given by the estimates of the other particles. Each timea new observation is available, we can estimate the phenologyof the crop by repeating this procedure.

Furthermore, each state of the model has a temporal stampthat represents the position along the temporal evolution of thecrop over the state space. This temporal stamp information isexploited here to provide estimates of the date at which the cropreaches a specific stage. Due to their relevance in rice farming(explained in the Section I), we have chosen the date of sowingand the date of the panicle initiation stage for this study.

In order to know the time elapsed between two states, e.g.,from k − n to k, being k the state at the current observation,the difference between the two temporal stamps is calculated.Issues appear when k − n is an unknown state, for instancewhen the observations available are only of later states. In sucha case, the state is predicted from a signature (or trace) over thestate space from k − m to k, being k − m the state defined bythe first observation available and k − m > k − n. This trace isrepresented by a specific zone of the model.

To provide a solution for the sowing date, the model is usedto complete the trace to the initial state to find the starting point.The amount of model used gives the elapsed time. As new datafrom the time series are incorporated, the trace is more repre-sentative and the fitting of the model is more accurate. Thisprocedure allows us a more accurate estimation of the timeelapse than when only one observation is available.

The anticipation of future events enables farmers to organizecampaigns in an optimized way and maximize the yield. Oncethe current stage is identified in the transition model, it can beused to predict any future stages. Indirectly, this provides infor-mation about the time remaining before an event occurs. In suchan approach, the temporal prediction is made in “open loop,”so as new images are available they can be used to correct theestimation. Due to its importance for rice crops, an example ofthis procedure for the date of panicle initiation (BBCH 30) isconsidered here.

IV. RESULTS

This methodology was tested with rice crops located inSevilla (Spain), using a stack of 11 HH/VV dual-polarizationX-band images acquired by TerraSAR-X in 2009 at 30 of inci-dence angle, and with a resolution of 6.6 and 2.3 m in azimuthand ground range, respectively [4]. The dynamic model usedwas presented in [5] and is valid for this configuration modeand for the same crop management. In addition, ground truth

Fig. 3. BBCH estimates and ground truth values in the 2009 cultivationcampaign versus days from sowing. Black line represents BBCH estimation.Blue square represents ground truth. Blue line represents ground truth linearinterpolation.

data are available at parcel scale. First, current phenology isretrieved to show the advantages of employing a PF approachinstead of the EKF. Then, the estimation of the date for two keyevents, i.e., sowing and panicle initiation stage, are presented toshow the potential of this technique to be applied in precisionfarming.

A. Phenology Estimation

Fig. 3 shows the estimation results for one of the moni-tored parcels. The result is compared with the available groundtruth. At any date, the estimate is taken from the most likelyvalue of the posterior pdf defined in (1). There is a good agree-ment between estimates and ground data, but we can identifytwo zones in which estimates are clearly different from theground truth data. As aforementioned, the first step of theestimation consists of a uniform distribution of particles overthe state space (see initialization step in Table I), since priorinformation is not available. Consequently, the estimation dur-ing the first states presents larger errors. However, as soon asnew images are incorporated the accuracy of the estimationincreases, thanks to the convergence to the real value. Thesecond zone in which results differ from ground truth occursbetween BBCH 30 and 50. This phenological range presentsthe strongest nonlinear behavior in the model. At this point,after the posterior pdf’s have been obtained (step 3 in Table I),the most likely value is projected over the model to provide anestimation of the current phenological stage. The projection inthis zone of the model is more likely to provide an incorrectestimation because the stages before and after stage 4 are veryclose to each other (see Fig. 2).

To show the benefits involved when the PF approach isused, in contrast with the EKF method, both algorithms aretested for the phenological estimation process at all availableparcels. To get a measurable difference between them, a con-fusion matrix is also calculated considering the phenologyestimation as a classification problem. The confusion matrixshows the coincidences or agreements between the predic-tions (rows) and the ground truth values (columns) for a set


TABLE IISTATISTICS OF THE BBCH RESULTS WITH EIGHT PHENOLOGICAL INTERVALS USING PF

TABLE IIISTATISTICS OF THE BBCH RESULTS WITH EIGHT PHENOLOGICAL USING EKF

of phenological intervals. Along the main diagonal one findsthe correct estimations (the estimation and the ground truthare in the same stage), so high values in the main diagonalwith respect to off-diagonal positions mean that the estima-tion process is accurate. To interpret correctly the numbers inthese tables, we provide here an example. In Table II, a totalof 11 ground truth samples are in the BBCH range 0–15 (firstcolumn). Then, in the estimation process nine of them werecorrectly estimated (first row), and two were wrongly assignedto the next range of BBCH values (second row). To quantifythe validity of the results, two different accuracy values areusually defined: producer’s accuracy and user’s accuracy. Fora given set of samples in the ground truth data (a column),producer’s accuracy provides the percentage of them that wereclassified correctly. On the other hand, for a set of samples inthe estimates (a row) user’s accuracy yields the percentage ofthe correctly classified. Finally, the kappa index reflects the dif-ference between actual agreement and the agreement expectedby chance, so high values (close to 1) mean results better thanby chance alone (close to 0). Table II shows the results using thePF approach, and Table III the results using the EKF approach.In both cases, we use the same set of seven intervals of pheno-logical stages. In the case of the PF, the kappa value improves46% with respect to the value obtained with the EKF. This ismainly due to the zones in which the model is strongly nonlin-ear and a rapid trend change is present (i.e., around BBCH 40).

In such a situation, the linearization made by EKF techniqueis very poor to fit the evolution and cannot provide a goodestimation, hence the error increases. Note that a value ofkappa = 0.78 is regarded as a substantial agreement, whereaskappa = 0.53 corresponds to a moderate agreement [31].

In the approach presented here, as in [5], the observationnoise may not be completely modeled. To test the consequencesfor both approaches (EKF and PF), a simulation in which thenoise distribution was distorted in the input data has been car-ried out, generating a new set of simulated observations. Afterapplying the PCA the most likely state keeps the same value,but new zones acquire relevance by the noise effects. Fig. 4shows the projection of the observation pdf over one dimen-sion (a state variable) and the same pdf with the simulatedobservation noise. With these conditions the PF can provide amore reliable estimation than the EKF. The reason is that thePF can consider all the potential zones by drawing particles inall potential states, but the EKF cannot work with multimodalpdf’s. Fig. 5 shows the phenological estimation using the PF,the EKF, and the ground truth. When input data are noisy, andalso the model has a strong nonlinearity, like around BBCH 40,the EKF is unable to follow the evolution to provide a goodestimation.

Fig. 6 shows the estimation results at pixel level for a sin-gle parcel, using the BBCH ranges employed in the previousconfusion matrices. The first three images show a completely


Fig. 4. Projection of the pdf of one observation over one dimension of statespace. Blue line is the observation without noise added. Red line is theobservation with noise added.

homogeneous estimation, since stages 1–27 are contained ina wide zone over the transition model (from stage 0 to 3 inFig. 2). Afterward, there appear some heterogeneities, mean-ing that there exist pixels at diverse phenological stages withinthe same acquisition date. These pixels can evolve at differentrates but all of them follows the same signature. These evo-lution differences make the prediction step less accurate butthe observation step allows to minimize the impact over theestimation. In case the prediction is very inaccurate (a widerpdf), the estimation is limited by the observation accuracy. Thelast two phenological intervals, which dominate in the last fourimages, are the most mixed for the same date, as it was expectedfrom their proximity in the state space (see stages 6 and 7in Fig. 2).

Finally, in order to provide a visual insight of the potentialof this approach, the estimation approach was applied to a largeset of parcels (786 in total) for which information on the sow-ing date and harvest date was available. In Fig. 7, the valuesobtained at the time of the 11 acquisitions are represented inthe form of colour maps. Although there was not ground truthavailable over these parcels for validation, and the model gen-eration was carried out with information from only six parcels,this result shows a monotonic and spatially coherent evolutionover the whole area, hence confirming its potential.

B. Estimation of the Date of Key Events

1) Sowing Date: Tables IV and V show the absolute errors(in days) that are made on the sowing date estimation for twodifferent parcels. Series of up to 10 images are used to test thisapplication. The acquisition dates, relative to the date of sow-ing, i.e., days after the sowing date (DaS), are indicated in thefirst row. The row index refers to the first image used in the esti-mation process, and the column index represents the last imageused to compute the sowing date. For instance, for parcel A(Table IV) the element on row 1 and column 5 shows that theerror is 1 day when the estimation is made with image 5 com-bined with the past information, given by the last four images.The main diagonal contains the estimation error when previousinformation is not used, i.e., with a single acquisition. In this sit-uation, considering the results of both parcels, the error ranges

Fig. 5. Phenological estimation vs days regarding sowing when the observationhas large distortion. Black line represents ground truth. Blue line representsparticle filter estimation. Red line represents EKF estimation.

between 87 days in the worst scenario and 1 day in the best one(the closest state to the sowing day).

The noise of the observation is modeled by only taking intoaccount the polarimetric speckle noise. Hence, other sourcesof noise are being dismissed. Zones with non modeled noisemay produce larger deviations in the estimation, e.g., column 9.The PF allows us to reduce this effect significantly when a newimage with low noise is available, for example the transitionbetween column 9 and 10. Moreover, this improvement can beobserved between images 4 and 5 on row 3, or images 6 and 7on row 4 (Table IV). On the other hand, in some cases more thantwo images are necessary to guarantee an accurate estimation.The situation is shown in row 4. This is mainly due to the highnonlinearity and the large variance in this part of the model,and also because the observations exhibit their highest variancevalues. However, the results of parcel B (Table V) show muchbetter estimates. For instance, estimates with only two imagesare much better for this parcel.

In this example, we have not made any assumptionabout the stage of the crop before the first observa-tion is considered in the estimation. Therefore, in orderto know the current phenological stage, when the firstobservation arrives, the observation is directly pro-jected over the model (as explained in Section III-B).As aforementioned, these results, obtained by a direct projec-tion, are contained in the main diagonal of Tables IV and V.In most cases, the induced errors are large because only theprojection is used, so they depend on the accuracy of a singleobservation. Between DaS 65 and 88 (columns 5–7), the pro-jection over the model is very precise and the result is accurateenough with only one observation. Improving the estimationusing more observations is not possible due to the high varianceof the model in these areas. In consequence, in this range ofdays, observations present a high weight in the filtering pro-cess, producing similar results employing a single observation.On the other hand, it is possible to reach a situation for whichthe errors are so large that we cannot recover. For these twoparticular parcels, this situation is found at image 8, from whichthe estimated dates are no longer precise. The error cause is themethod employed to estimate the current phenological stage:


Fig. 6. Phenological estimation results obtained over the test parcel at pixel basis with the proposed methodology. The index indicates the images sequence. Thefirst was acquired 12 days after sowing. The time between images is 11 days.

Fig. 7. Maps with the phenological estimation computed over 786 parcels in the area at 11 acquisition dates. The time between images is 11 days. NS means thatthe parcel was not sown yet at that date.

the projection fails to distinguish between starting states (1 and2) and ending states (6 and 7) because they are very close in themodel (see Fig. 2). An incorrect projection causes that whenthe next image is available (image 9) the prior pdf given by thetransition model is not overlapped with the pdf given by theobservation. Consequently, the posterior pdf cannot be definedand an uniform redistribution of the particles is necessary (step1 in Table I). The same situation is repeated for images 9 and10. This is the reason why it is not possible to have a goodestimation when the first input data is after DaS 100. This issuecan be solved by simply dividing the model into two sectionsto apply the projection. The first section, for instance, could bedefined from state 0 to 3, and the second from state 4 to 7 (seeFig. 2). After projecting and applying the transition model,each section gives different prior pdf’s. Considering the case inwhich there is an overlap between prior and observation pdf’s,an accurate estimation starting at any image could be provided.

Finally, the improvement achieved in the estimation whena set of images is employed, instead of a single acquisition,can be observed by comparing elements of the main diagonal

TABLE IVERROR (IN DAYS) OF THE SOWING DATE ESTIMATION FOR PARCEL A

with off diagonal elements. Extremely noisy input data couldproduce inaccurate estimates, as e.g., at image 4 in Table IV.The error in the estimation is about 32 days (row 4, column 4)when previous information is unknown, but using the pro-posed methodology the error decreases down to 1 day (row 1,column 4).


TABLE VERROR (IN DAYS) OF THE SOWING DATE ESTIMATION FOR PARCEL B

Fig. 8. Map and histogram of the error in the estimation of the sowing day fora set of 786 parcels, obtained by using the first four SAR acquisitions.

To further evaluate the accuracy of the sowing date estima-tion process, the complete set of 786 parcels was also used forvalidation. The results are shown in Fig. 8. Date estimates areobtained by using the first four SAR images. Each color rep-resents a range of error in days and the percentages of parcelsin each range are presented also in the picture. Negative valuesmean that the estimated date is before the actual value, whereaspositive values mean it corresponds to later dates. It must beemphasized that we are estimating the sowing date of 786 plotsusing a model that was created with information from only sixplots [5]. Even so, we have obtained a very good accuracy: theabsolute error is less than 5 days for 50% of the parcels and lessthat 10 days for 85% of them. If the number of plots used tobuild the model were increased, it is expected that the accuracyin the estimation process would increase because the averagebehavior of them would be better defined. The fact that theseaccuracies are achieved with so few samples is an evidence ofthe potential of the methodology.

Fig. 9. Error (in days) in the estimation of the date in which rice reaches stageBBCH 30 (panicle initiation) for different parcels, represented by differentcolours. The vertical axis shows the estimation error in days, and the horizon-tal axis indicates the DoY when the acquisition was made. The vertical dashedlines represent the DoY in which each crop reaches BBCH 30 according to theground truth.

2) Date of Panicle Initiation Stage: The final set of resultscorresponds to the predictions of the date in which crops reachthe panicle initiation stage. Fig. 9 shows the results obtained forthe six individual parcels with ground data, represented withdifferent colours. The estimated error is depicted in the verti-cal axis and represents the difference in days between the dategiven by the ground truth and the estimated date. The horizontalaxis shows the day of year (DoY) in which the acquisitions (andhence the estimations) were made. The vertical dashed linesindicate the dates in which each parcel reaches the BBCH 30according to the ground truth. The first acquisitions available inthe data set are around 10 days after the sowing date. A totalof up to five images are employed to predict the moment inwhich stage 30 is reached. The first predicted dates (around 50days before) exhibit the worst values, as expected, with errorsgreater than 5 days in most cases. Each time a new image isincorporated (every 11 days) the error decreases, even in theparcel represented in black, for which the nonmodeled noisehas the strongest influence. All parcels show an improvementwhen temporal sequences are used in the estimation process.The results obtained from 40 days before the panicle initiationdate onward show differences of only 3 days in average, and notlarger than 5 days in most cases. Therefore, the estimation of thedate associated with the panicle initiation stage shows that thePF is a robust method to predict dates of future phenologicalstages.

V. CONCLUSION AND DISCUSSION

In this paper, the advantage of the particle filter, over otherfiltering techniques like the EKF, is demonstrated in estima-tion applications relative to precision farming. It is much morerobust to noisy measurements and nonlinear evolutions, mak-ing this method a better tool to obtain the required results. Twomain applications have been tested: retrieval of current pheno-logical stage and estimation of dates of particular crop events,like sowing and initiation of panicle. Phenology tracking hasbeen improved with this technique, and the contribution of timeseries of data has been studied.

The sowing date was estimated with an error that is less than1 day in parcels that are well characterized by the model. Theestimation was also carried out over 786 parcels using a model


that was created with the information of only six parcels. Inthis case, we achieve errors lower than 5 days in the estimationprocess for 50% of the parcels, and less than 10 days for 85%of them.

This technique also enables the prediction of the date offuture events. For instance, it has been shown that it is possi-ble to get a prediction 40 days before the panicle initiation datewith an error of only 3 days on average.

To ensure proper estimations, the model must be built withhomogeneous fields. Plots producing a signature very differentfrom the model can be identified, so this approach would pro-vide an indicator that the plot is not developing properly andwould help to alert farmers. According to our methodology, themodel characterizes crops with the same management practices.To apply this approach to crops with different farming practices,it would be necessary to build a new model representing eachtypical crop development in the site.

Ongoing work is addressed to test the methodology overother types of crops. Moreover, results have to be evaluatedas a function of the available revisit time. In case of exploit-ing polarimetric data, the influence of incidence angle and theavailable polarimetric space (i.e., dual-pol and compact-pol)will be analyzed. Such a study is of interest in view of thenext availability of data from new missions like Sentinel-1 andALOS-2. Finally, since the methodology allows us to combineinput data from different sources, another promising line ofresearch would consist in combining optical and SAR data inorder to generate more accurate estimations.

ACKNOWLEDGMENT

The authors would like to thank the Federacion de Arrocerosde Sevilla for providing the ground measurement data.

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Caleb G. De Bernardis was born in Mar del Plata,Buenos Aires, Argentina, in 1989. He received theIngeniero Tecnico (B.S.) degree (summa cum laude)in sound and image engineering from the Universityof Alicante, Alicante, Spain, in 2010, and theIngeniero (M.S.) degree in telecommunication engi-neering from the Technical University of Valencia(UPV), Valencia, Spain, in 2014. Currently, he ispursuing the Ph.D. degree at Signals, Systems andTelecommunications Group, University of Alicante.

He collaborated with the NanophotonicsTechnology Centre (NTC), Valencia, Spain, in 2013.


Fernando Vicente-Guijalba was born in Elche,Spain, in 1981. He received the Ingeniero Tecnico(B.S.) degree in telecommunication engineering andthe Ingeniero (M.S.) degree in sound and image engi-neering from the University of Alicante, Alicante,Spain, in 2006 and 2011, respectively.

Since 2011, he has been a Predoctoral Fellowwith the Signals, Systems, and TelecommunicationsGroup, University of Alicante. His research interestsinclude dynamical systems analysis with applicationsin polarimetric and interferometric SAR methods.

Tomas Martinez-Marin received the TechnicalEngineering (B.S.) degree from the University ofAlcalá (UAH), Madrid, Spain, in 1990, the M.S.and Ph.D. degrees in telecommunication engineer-ing from the Technical University of Madrid (UPM),Madrid, Spain, in 1995 and 1999, respectively.

In 1990, he joined the University of Alcaláas an Assistant Professor. In 1997, he joinedthe European University of Madrid (UEM) as anAssistant Professor. Since 2000, he has been withthe Department of Physics, System Engineering and

Signal Theory, University of Alicante (UA), Alicante, Spain, where he is cur-rently an Associate Professor. His research interests include reinforcementlearning, optimal control, intelligent vehicles, and SAR filtering algorithms.

Juan M. Lopez-Sanchez (S’94–M’00–SM’05) wasborn in Alicante, Spain, in 1972. He receivedthe Ingeniero (M.S). and Doctor Ingeniero (Ph.D.)degrees in telecommunication engineering from theTechnical University of Valencia (UPV), Valencia,Spain, in 1996 and 2000, respectively.

From 1998 to 1999, he worked as a PredoctoralGrantholder with the Space Applications Institute,Joint Research Centre of the European Commission,Ispra, Italy. Since 2000, he has been leading theSignals, Systems, and Telecommunication Group,

University of Alicante, Alicante, Spain, where he is a Full Professor sinceNovember 2011. He has coauthored more than 50 papers in refereed journalsand more than 90 papers and presentations in international conferences andsymposia. His research interests include microwave remote sensing for inver-sion of biophysical parameters, polarimetric and interferometric techniques,SAR imaging algorithms, and analytical and numerical models for multiplescattering problems.

Dr. Lopez-Sanchez was the Chair of the Spanish Chapter of the IEEEGeoscience and Remote Sensing Society, from 2006 to 2012. He was therecipient of the Indra Award for the best Ph.D. thesis about radar in Spain,in 2001.


2.2. Particle Filter Approach for Real-Time Estimation

of Crop Phenological States Using Time Series

of NDVI Images

remote sensing

Article

Particle Filter Approach for Real-Time Estimationof Crop Phenological States Using Time Series ofNDVI Images

Caleb De Bernardis *, Fernando Vicente-Guijalba, Tomas Martinez-Marinand Juan M. Lopez-Sanchez *

Signal Systems and Telecommunication Group, Institute for Computing Research (IUII), University of Alicante,P.O. Box 99, E-03080 Alicante, Spain; [email protected] (F.V.-G.); [email protected] (T.M.-M.)* Correspondence: [email protected] (C.D.B.); [email protected] (J.M.L.-S.); Tel.: +34-96-590-9597 (J.M.L.-S.)

Academic Editors: Sangram Ganguly, Compton Tucker, Clement Atzberger and Prasad S. ThenkabailReceived: 22 April 2016; Accepted: 13 July 2016; Published: 20 July 2016

Abstract: Knowing the current phenological state of an agricultural crop is a powerful tool forprecision farming applications. In the past, it has been estimated with remote sensing data byexploiting time series of Normalised Difference Vegetation Index (NDVI), but always at the end of thecampaign and only providing results for some key states. In this work, a new dynamical frameworkis proposed to provide real-time estimates in a continuous range of states, for which NDVI imagesare combined with a prediction model in an optimal way using a particle filter. The methodologyis tested over a set of 8 to 13 rice parcels during 2008–2013, achieving a high determination factorR2 = 0.93 (n = 379) for the complete phenological range. This method is also used to predict the endof season date, obtaining a high accuracy with an anticipation of around 40–60 days. Among thekey advantages of this approach, phenology is estimated each time a new observation is available,hence enabling the potential detection of anomalies in real-time during the cultivation. In addition,the estimation procedure is robust in the case of noisy observations, and it is not limited to a fewphenological stages.

Keywords: agriculture; phenology; time series; NDVI; state space formulation; particle filter

1. Introduction

Knowledge of the current state of an agricultural crop (i.e., its phenological state) is a powerfultool in the context of precision farming. It can be used to predict the future yield production by usingagronomical models, to assess irrigation requirements, to plan or trigger fertilisation activities, to detectanomalies due to pests, etc. Remote sensing represents a unique technology to measure vegetationstatus over large areas with short revisit periods. For this purpose, time series of vegetation indexes(VI) can be used to estimate different dates along the cultivation cycle, like Start of Season (SoS), Peak,and End of Season (EoS) [1–4].

The Normalised Difference Vegetation Index (NDVI) is one of the most employed VIs inprecision farming. With the goal of extracting seasonal stages from the NDVI data, some methodsare based on thresholds, which are used to separate different phenological states (greenup, maturity,senescence, etc.). In general, these thresholds are associated with changes in the curvature of thetypical NDVI time series. In threshold-based methods, it is common that noise causes incorrect stateestimates and false alarms. To minimise the influence of noise (independently of its source), sometype of smoothing or fitting can be used [2,5–10]. Fitting-based methods employ the parameters ofthe fitted functions (e.g., maximum or minimum rate of change in curvature) to derive particularphenological stages. However, as exposed in White and Nemani [11], all of these methods cannot

Remote Sens. 2016, 8, 610; doi:10.3390/rs8070610 www.mdpi.com/journal/remotesensing

Remote Sens. 2016, 8, 610 2 of 19

work in real-time applications because they require the whole time series to obtain the estimates ofdates and stages. Other methods propose a real-time or near real-time operation [11–14]. For example,in Suwannachatkul et al. [12] the Kalman filter (KF) is proposed as a real-time method to estimatethe current state of rice fields, but this method only provides a few particular stages, although theprocess being monitored is continuous. In White and Nemani [11], the authors present a land surfacephenology estimation and conclude that, in the case of crops or homogeneous regions, the use ofgrowth models combined with remote sensing observation provides better results. In our case, wepropose exploiting dynamic techniques that combine the information provided by a prediction modeland remote sensing data. This approach is employed in many fields, such as robotics [15] or targettracking [16], among others, for optimal estimation of noisy state variables.

In this study, a simple model is used to provide a prediction of the next phenological state.The prediction model takes into account the previous state and the elapsed time between the previousstate and the current time. This prediction is then combined with the value inferred by the NDVI data,thus providing a real-time estimation. From a farm manager perspective, it constitutes an interestingproduct for different uses, especially those requiring critical temporal sampling [17]. The informationprovided by prediction and observation can be combined by different types of estimators. One of themost used has been the Kalman filter, which obtains the optimal solution [18]. However, it is restrictedto linear models and processes described by Gaussian distributions. In order to avoid these limitations,the particle filter (PF) [19] has been selected here to estimate the phenological states.

In order to illustrate the potential of this technique, in this work, we show results, obtained overa set of rice plots, of two different applications: (1) estimation of the phenological state after everyacquisition; and (2) estimation of the date of End of Season (EoS).

The text is organised as follows. Section 2 describes the methodology, including the particlefilter theory and the particular implementation used here. The available data set and the test site areintroduced in Section 3. Results are presented in Section 4 and discussed in Section 5. Finally, Section 6summarises the main points.

2. Methodology

Systems that evolve over time are considered as dynamic systems and can be characterised by a setof differential equations employed to describe mathematically their physical behaviour. One or moretime dependent variables (x1(t), x2(t), ..., xn(t)) are direct or indirect characteristics that completelydescribe the system state at time t. Instead of regarding variables as functions of time, they can bethought as coordinates of points (states) in an n-dimensional domain. The space of all possible pointsfor the system is the state space. One of the most relevant aspects of the dynamical methods is thatthe future states are inherent to the model description. In other words, the next state of the system atinstant t + 1 could be inferred by the model from the state at instant t. Generally, a dynamical systemis described by the following equations:

xk+1 = f (xk) + vk, (1)

yk = h(xk) + ek, (2)

where Equation (1) describes the evolution of the state with time, and Equation (2) relates the (noisy)observation to the state. Function f () is known as the dynamic model or prediction model, i.e., arepresentation of the expected behaviour, linking xk and xk+1. In this notation, xk is the currentstate and xk+1 is the next state. The observation yk and the state are related by h(), which is knownas the observation model. Furthermore, vk and ek represent the model error and the measurementerror, respectively, which correspond to stochastic noises defined by their known probability densityfunctions (PDF) pvk and pek . In this case, functions f () and h() do not depend explicitly on time t,hence resulting in a time-invariant system. This means that we do not have to redefine the expressionsof f () and h() for future scenarios.

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Therefore, the estimation process is supported by the dynamics and not just by the experimentalmeasurements (observations) themselves. In this context, the phenological development of a particularfield can be regarded as a process of a dynamical system, i.e., the crop. The state space will be definedby one or more features that represent the state of the crop. For this work a one-dimensional statespace, using phenology as feature, is employed. Therefore, Equation (1) provides the prediction of thenext phenological value given the current value, and Equation (2) relates phenology (i.e., state) withthe remote sensing observations.

2.1. Particle Filter (PF) Theory

Prediction and observation models are used to infer the system state. Estimation algorithmsuse the relationship between both sources Equations (1) and (2) to provide a single estimate bytheir combination. The PF algorithm is selected because it is not constrained to work with linearmodels and Gaussian distributions.It is based on Monte Carlo methods [19,20] and recursive BayesianSequential Estimation [21,22] that provides the posterior PDF (p(Xk+1|Y1:k+1)) at instant k + 1,combining all the available information (prediction and observations). In order to provide the posteriorPDF, the process is separated in two steps: prediction (Equation (3)) and update (Equation (4)).

In the prediction step, the model is used to generate the prior PDF that defines the most likelystate at time k without introducing the observation:

p(Xk+1|Y1:k) =∫

p(Xk+1|Xk)p(Xk|Y1:k)dX, (3)

where p(Xk+1|Xk) represents the transition probability from state Xk to Xk+1 at time k + 1, andp(Xk|Y1:k) is the posterior PDF at time k. Finally, when the observation Yk+1 is available, the priorprobability density function (Equation (3)) is updated via Bayes’ rule:

p(Xk+1|Y1:k+1) =p(Yk+1|Xk+1)p(Xk+1|Y1:k)∫

p(Yk+1|Xk+1)p(Xk+1|Y1:k)dXk+1, (4)

where p(Yk+1|Xk+1) expresses the likelihood function that describes the measurement model, and∫p(Yk+1|Xk+1)p(Xk+1|Y1:k)dXk+1 is a normalisation constant. The state of the system is determined

by the most likely value of the posterior PDF. Considering the Markovian assumption, the posteriorPDF p(Xk+1|Y1:k+1) can be obtained recursively from the PDF p(Xk|Y1:k) calculated at previous state k.In case the initial distribution PDF p(X0|Y0) = p(x0) is unknown, a uniform distribution over the statespace can be considered.

The PF is used to approximate the posterior PDF (Equation (4)) with a set of N samples when it isnot analytically tractable. Each sample or particle represents a specific state of the system (Xi

k+1), andeach one has a probability value (named weight, ωi

k+1) given by the PDF. In other words, the PDF isrepresented by a set of N particles and their weights:

p(Xk+1|Yk+1) ≈N

∑i=1

ωik+1δ(Xk+1 − Xi

k+1), (5)

where p(Xk+1|Yk+1) is the true posterior PDF, Xik+1 is the i-th simulated sample (particle) and ωi

k+1 isthe weight of i-th simulated sample (particle). N represents the number of particles employed in thesimulation, and δ is the Dirac delta function. If N is sufficiently large, Equation (5) approximates thetrue posterior.

The whole procedure is described in Table 1 and Figure 1. The PDF evolves in time according tothe transition model p(Xk+1|Xk), which is applied to each particle generating a new distribution namedprior PDF. Once the observation is available, the prior PDF is updated to compute the posterior PDF.An important step in the PF is the principle of sequential importance sampling, used for selectingthe particle weights [23]. Generally, it is difficult or impossible to draw samples from the posterior

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PDF p(Xk+1|Y1:k+1). To avoid this difficulty, importance sampling generates particles xik+1 from

a function q(xk+1|yk+1) known as a proposal distribution (or importance density) and assigns theweights (importance weights) according to

ωik+1 ∝

p(Xik+1|Yk+1)

q(Xik+1|Yk+1)

, (6)

where q(Xik+1|Yk+1) is the proposal density. As presented in Arulampalam et al. [24], the proposal

distribution is factorised such that

q(Xk+1|Yk+1) = q(Xk+1|Xk, Yk+1)q(Xk|Yk). (7)

By substituting Equations (4) and (7) into Equation (6), the following equation is obtained

ωik+1 ∝ ωi

kp(Yk+1|Xi

k+1)p(Xk+1|Xk)

q(Xik+1|Yk+1)

, (8)

and the weight set satisfies:N

∑i=1

ωik+1 = 1. (9)

Equation (8) expresses the basic principle of the sequential importance sampling filter [24]. Finally,the most convenient and frequent is to choose the transition prior as proposal importance density(Equation (10)) to simplify the calculus in Equation (8) so that the weights derive on a recursive setgiven by Equation (11):

q(Xk+1|Yk+1) = p(Xk+1|Xik), (10)

ωik+1 ∝ ωi

k p(Yk+1|Xik+1). (11)

Table 1 and Figure 1 summarise the key steps to implement the PF algorithm. First, the particlesare distributed following the initial PDF p(x0). Afterwards, the iterative process starts in the predictionstep (point 2 in Table 1). The particles that approximate the posterior PDF at instant k go through theprediction model. It gives the new values of the state variables at instant k + 1 that represent the priorPDF p(xk+1|xk). In order to compute the likelihood function, the state variables are transformed tothe observation domain using the observation model in the measurement step, Equation (2). Giventhe observation, yk+1 and pek , the likelihood function is computed with the purpose of updatingthe weights of the particles. Finally, the weights are normalised to satisfy Equation (9). The resultis the new posterior PDF from which the estimation is inferred. This value can be determined indifferent ways, as the most likely value of the PDF (i.e., the mode), the median or the mean, amongothers. With the iterative process, the particles suffer a degeneration effect: the number of particleswith a representative weight tends to be low. A measure of the effective number of particles can beapproximated by Equation (12) introduced in Bergman [21]:

Ne f f =1

∑Ni=1 w2

i, (12)

with a small value indicating a severe degeneracy problem. In order to solve this problem, a techniqueknown as resampling is employed. Different resampling methods have been proposed, as presentedin [24,25]. In this work, the residual-systematic resampling (RSR) is implemented [26]. Its goal isduplicating the number of particles in the areas with high normalised weight and discarding theparticles with low normalised weight. In this step, N particles are redistributed over the areas wherethe particles present more weight. Finally, the weights are reset to uniform values (1/N). The iterativeprocess continues at point 2.

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Table 1. Particle Filter (PF) Sequence.

(1) Initialisation Generate N samples of x0 from the initial PDF p(x0) .

(2) Prediction Obtain the sample of xik from the transition PDF p(xk+1|xi

k).

(3) Measurement step Compute the likelihood function. p(yk+1|xik+1).

(4) Update Evaluate the importance weights from likelihood function.ωi

k+1 = ωik p(yk+1|xi

k+1).

(5) Normalisation Normalise the weights ωi =ωi

k+1

∑Ni=1 ωi

k+1.

(6) Resampling The effective number of particles (Ne f f ) provides a measure ofthe number of particles with significant weight representing theposterior PDF. If this number is lower than a provided threshold(Nthrd) they are redistributed where the PDF is more likely. Reset toωi = 1/N.

Model

p(xk | yk,uk)

vk+1

xk+1

p(xk+1 | xk,uk)

f(xk)

Observation eq.h(xk+1)

p(yk+1 | xk+1)

p(xk+1 | yk+1,uk+1)

Observationyk+1, pek+1

xkN xk+1

NxkN N

xk+1N

Estimation

Neff < Nthrd

if

No

Yes

2) Prediction Step

3) Measurement Step

Update &Normalisation

4)5)

Resampling6)

δ

Figure 1. Representation of the steps involved in the estimation algorithm based on the particle filter.The initialisation (step 1) is omitted because it is not part of the iterative procedure.

2.2. Particle Filter Implementation

Provided that agricultural crops are systems that evolve over time, they can be studied in thedynamical framework introduced in the previous subsection. Consequently, filtering techniques canbe applied to estimate the phenology of a crop [27,28]. The state space is naturally represented onthe Biologische Bundesanstalt, Bundessortenamt und CHemische Industrie (BBCH) scale, which definesthe growth states along the life cycle of many cultivated plants [29]. It uses a continuous code rangebetween states 0 and 100, where 0 is associated with sowing and 100 refers to the harvest. In addition,the states are grouped in 10 main intervals or stages, defined by the tens in this scale: germination(0–9), leaf development (10–19), tillering (20–29), stem elongation (30–39), booting (40–49), heading(50–59), flowering (60–69), development of fruit (70–79), ripening (80–89), and senescence (90–99).

This methodology should be applicable to any class of crop in any location defining thecorresponding prediction and observation models as shown in Figure 1. In this subsection, an exampleof the implementation is given for a particular class of rice.

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2.2.1. Crop Phenology Model

The first goal consists in finding a model valid for characterising the phenological evolution of rice.Since such a model will be used to provide an estimate of the next state reached by the crop whenthe current state is known, a mathematical approximation of the expected behaviour of a rice fieldhas to be obtained. As it was mentioned in the Introduction, changes in phenology of rice are mostlydriven by temperature evolutions [30], but here we propose a simplified model in which phenologicalchanges are a function of time and not of temperature. Consequently, this model is not the bestbecause temperature information is not taken into account, but it is improved with respect to the onesbased only on observations by the combination of prediction and observation during the estimationstep. Moreover, this framework would be also appropriate if temperature data were available, sincetemperature could be included in the prediction model as a control variable.

In order to provide a prediction model that represents the phenological development, a set ofground truth data is employed to fit a function. A detailed description of the ground truth data willbe presented in Section 3, but here we use them to illustrate this step. Considering all parcels and allground acquisitions between 2008 and 2013, we dispose of a total of 656 measures, which are all shownin Figure 2. Due to the fact that the parcels were sowed at different dates, it is impossible to fit thedata using the day of year (DoY) as time reference. In order to extract the common behaviour of thecrops, the time reference is fixed to the sowing date, and hence the ground data are represented usingthe day after sowing (DaS) instead of the DoY. Using this representation, all the parcels start at thesame time in the phenological state 0 (germination). In the early states, between leaf development andthe end of stem elongation phase (states 10–39), phenology increases at a constant rate. Then, at thebeginning of the booting phase (state 40) this rate of change increases until plants reach the ripeningphase (state 83). Finally, from ripening to senescence phase (state 90), phenology is characterised by asmall change rate. Such a temporal evolution can be represented mathematically by a linear trend upto state 40, followed by a sigmoid function, as proposed in the following expression:

x(t) =

mt + n t < tc

a + b1+exp(−r(t−t0))

t ≥ tc, (13)

where t is time measured in days after sowing; x(t) is the phenological state at time t; m and n are theslope and offset of the line, respectively; a + b is the maximum phenological value, being a the initialbackground value; t0 is the inflexion point and r the ratio of the logistic curve; tc is the day at whichthe function is switched.

20

40

60

80

100

00 20 40 60 80 100 120 140 160

Phe

nolo

gy

Ground Truth

Prediction Model

Day after sowing

Figure 2. Measurements of phenology (ground truth) for different parcels at different years, plottedagainst the day after sowing (black circles). The solid line corresponds to the model defined inEquation (13). m = 0.4458, n = 5, r = 0.0661, t0 = 97.6413, tc = 62, a = 26.2956 and b = 73.8626.

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In order to fit Equation (13) to the available data, all parameters are tuned simultaneously byminimising the mean square error (MSE). A graphical representation of the fitted function is shown inFigure 2 by a solid line.

Taking derivatives of Equation (13), one can characterise the system by a state-space formulation.After a few algebraic manipulations, the state equation becomes:

x =

m t < tc,

rb (x(t)− a) (b− x(t) + a) t ≥ tc,

(14)

To formulate a computational solution, a discrete-time model is required. The discrete version ofEquation (14) can be obtained easily by following the Euler method to approximate the derivative,considering small values for ∆t, yielding:

xk+1 =

xk + m∆t xk < xc

xk + r∆t(xk − a)(b− xk + a)/b xk ≥ xc,(15)

where tk = k∆t in which k takes integer values; xk is the phenological state at instant k∆t; xk+1 is thephenological state at the next instant; and xc is the phenological state at which the function is switched.

In Figure 2, we can also appreciate that there is a distribution of the ground truth data aroundthe model (fitted expression), which is just a representation of the average behaviour. The expectedvariation around the model is incorporated through vk in Equation (1). In order to characterise thePDF of the noise model (pvk ), the state transition variations are considered. Parcels starting at the samephenological state evolve to the same average state but with small differences. The distributions aftereach transition are employed to describe the transition noise itself. The expected value of the transition(mean) is obtained applying the evolution model to the phenological state (before the transition occurs).Both values are used to model pvk with a Gaussian distribution centred in the value given by the modeland the variance observed in the transitions.

2.2.2. Observation Model

Besides the availability of the model to make predictions of next states, producing accurateestimates requires the incorporation of observations provided by a sensor, e.g., a satellite acquiringimages, in the estimation process. As mentioned in Section 1, NDVI is strongly related with vegetationstatus, so it can be used as indicative of the phenological state. At this point, the observation model (2)will represent the relationship h() between the NDVI acquisitions, yk, and the state, xk, of the systemat a particular instant.

In order to find the expression of h(xk), all the available acquisitions for a set of rice fieldsfor several years (379 measurements in total) were considered. The NDVI values acquired by thesensor are represented as a function of phenological state in Figure 3. It is observed that, up to thetillering (around state 20), measurements exhibited low NDVI values, followed by a steep increase andsaturation around 0.8. Finally, they drop to low values again at states 70–80, approximately.

In some studies, it has been demonstrated that NDVI time series can be approximated byfitting double logistic curves [5,31–33] or asymmetric Gaussian model functions [6] to minimisethe measurements noise, or noise can be smoothed out using the Savitzky–Golay filter [34]. Here, wewill follow the approach based on fitting a double logistic curve, hence:

h(xk) = c + d[

11 + exp(−r1(xk − f1))

+1

1 + exp(−r2(xk − f2))− 1]

, (16)

where c is the minimum NDVI value and c + d the maximum NDVI value, r1 and f1 are parameters ofthe first logistic curve, and r2 and f2 correspond to the second logistic curve. As in the previous case,all parameters are fitted to optimise the MSE.

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The observation model (2) is completed by modelling the so-called observation noise ek. We haveseen in Figure 3 that a particular phenological state presents a range of NDVI values acquired by thesensor. The observation noise is modelled by a Gaussian distribution with zero mean and variancederived from the data dispersion with respect to the NDVI value given by Equation (15).

Phenology

1.0

NDVI data

Dynamic Model

ND

VI

0.8

0.6

0.4

0.2

00 10 20 30 40 50 60 70 80 90 100

Figure 3. Measurements of NDVI (observations) for different parcels at different years representedas a function of phenological state (black circles). The solid line corresponds to the observationmodel, i.e., the NDVI value for each phenological state given by Equation (16). r1 = 0.84, f1 = 21.07,r2 = −0.10, f2 = 95.40, c = 0.21, d = 0.65 and b = 73.8626 .

2.2.3. Estimation

To estimate phenological states, a uniform prior distribution is taken initially, p(x0), betweenstates 0 and 50; as in the first observation, the crop will not be in later states. Then, the first NDVIimage is incorporated and p(yk+1|xk+1) is calculated for every particular case using Equation (16).Next, Equation (11) is used to compute the probability a posteriori. The current state correspondsto the most probable value in the PDF. In the first estimation, the state is determined only with theobservation since the prior distribution is uniform. For the next observation, in the prediction step,particles evolve following the transition equation from the instant of the previous observation untilthe current one. Then, the process is repeated each time an observation is acquired. Regarding theestimation of the date of future states, the prediction model can be used at any time to estimate inwhich day a specific phenological state will be reached. In that case, additional observations are notincorporated since it is a future event.

In order to employ this methodology over other kind of crops, the next steps have to be followed.First, the state-space must be defined by a set of variables (xk) that characterises the system at anytime. In our case, a 1D space is used in which the state variable is phenology, but other physicalvariables such as leaf area index (LAI), biomass, etc. could be employed to derive a new state-space.The second step involves the definition of the prediction model. In order to provide function f (x),a set of phenological measurement for different parcels and different years are used. Using a fittingstrategy, the measured values are adjusted to provide the evolution model and the deviations of thedata define the noise process pv. The third step regards the observation sources. The evolution of thesystem is observed by a particular sensor given a set of measurements. Each state responds with acertain value to the observation. Given a set of measurement for different states of the system, theequation h(x) can be derived. The observation noise is defined considering this perturbation. Onceprediction and observation models are defined, the implementation of the particle filter is applied inthe same way that is explained in Section 2.1.

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3. Data Set and Test Site

This methodology has been tested with data acquired over rice fields located in Sevilla, southwestSW Spain (see Figure 4), during 2008–2013 (2012 is not included). In this area, rice is cultivated fromMay to October, with just one crop per year. The phenological information acquired during groundcampaign measurements have been provided by the local association of rice farmers (Federacion deArroceros de Sevilla) on a weekly basis over eight to 13 specific parcels, with areas ranging from 3 to17 ha, depending on the year (see Table 2). In addition, both sowing and harvest dates are knownfor each parcel. This information was used in the generation of the model and in the validation ofthe results.

4110000 4110000

4125000 4125000

215000

215000

230000

230000

Figure 4. Study area located in Sevilla, SW Spain. Coordinates are in Universal Transverse MercatorWorld Geodetic System 84 (UTM WGS)-84.

Table 2. Set of parcels with auxiliary phenological information available.

Year 2008 2009 2010 2011 2013

Number of Parcels 11 13 13 9 8Images per Parcel 15 16 15 14 6

Table 2 shows the total number of NDVI images available per parcel and per year, but only theimages during the campaign are used. The images were acquired by Landsat 5 and Landsat 7 with apixel size of 30× 30 m. All the images were already geometrically and radiometrically corrected [35,36].Some images were discarded due to excessive cloud cover, so the temporal basis (time gap betweensuccessive images) is not constant. In the best case, we can obtain an eight-day basis, combiningproducts of both sensors.

To validate the methodology, the set of parcels used to build the model has to be different fromthe set employed to obtain estimates. As the data set is small, a cross validation method has beenemployed in this analysis [37]. In this procedure, one case (i.e., all the data from a single parcel) iswithheld and models are generated with the remaining cases. Parameters of both Equations (15)and (16) are obtained applying the cross validation method. Therefore, they will be different for eachcase of study. Then, estimates are computed for the withdrawn parcel. This allows us to maximise theinformation used in the generation of the model.

4. Results

4.1. Phenological State Estimation

The first case study is focused on the estimation of the current phenological state each time NDVIinformation is available. For all the examples, the particle filter was implemented with a total of1000 particles.

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The estimation is carried out over the available parcels and images for the five years, resultingin a total of 379 estimates. Results are shown in Figure 5. A high determination factor (R2 = 0.93) isobtained, with an root mean square error (RMSE) of 6.6 states.

0 20 40 60 80 1000

20

40

60

80

100

Estimation

RMSE = 6.60R2 = 0.93

Phe

nolg

oy E

stim

ated

Ground truth

Figure 5. Phenological state estimates and ground truth for all parcels and available images.

In order to illustrate with an example the performance obtained by the proposed dynamic tool,the following evaluation is made for a single parcel (see Figure 6). Phenological states are computedemploying two different approaches. On the one hand, the proposed methodology is used to providethe estimation, and the results are shown with the blue line. On the other hand, the estimation isinferred using only observations (without taking into account the model predictions), showing theresults with the red line. In the latter case, the states are determined by the maximum values of thelikelihood PDF p(yk|xi

k) that are derived from Equation (2).

160 200 240 300180 220 260 280DoY

20

40

60

80

100

Phe

nolo

gy

Particle FilterGround Truth

Without model

Figure 6. Comparison for one parcel during one year campaign of phenological state estimates providedby the full particle filter approach (solid blue line) with estimates obtained without taking into accountthe prediction model (red squares). Ground truth data are represented with black circles.

4.2. Prediction of Key Dates

The second case study is focused on the estimation of the date named end of season (EoS), and italso serves as a comparison with other methods widely used in the literature. Regarding the othermethods, hereafter called fitting-based methods, the well-known TIMESAT software [38] was used toadjust the available time series in three different ways: with an asymmetric Gaussian curve, with adouble logistic function, and by applying the adaptive Savitzky–Golay filtering.

In the fitting-based methods, the estimation of the EoS is computed as the date in which the fittedcurve reaches a reference threshold. Instead of directly using the NDVI, these methods were appliedto the time series of the NDVIratio defined in Equation (17):

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NDVIratio =NDVI − NDVImin

NDVImax − NDVImin, (17)

where NDVImin and NDVImax are the minimum and maximum values of the NDVI time series,respectively. The transformation to NDVIratio allows us to fix a common threshold to estimate the EoS,independent from the specific land cover and geographical location [39]. The EoS was determined asthe day in which the NDVIratio reached 50% in a downwards direction.

The correct use of TIMESAT software to provide seasonal estimations employing NDVI timeseries requires a uniform time sampling of the input data. The presence of clouds forced us to discardsome images, so the NDVI was interpolated to provide an eight-day time basis. For some timeseries approaches, it must be noted that uniform sampling is a limiting factor for solving problemsdirectly in the time domain. In contrast, in a state-space approach, the most relevant information isthe behaviour projected in the state space, i.e., the trajectory. For this reason, such an approach isadvantageous for scenarios with a non-uniform sampling rate, as it often occurs within optical satellitedata. In addition, setting thresholds is not necessary in our approach. The only requirement is knowingthe correspondence of the EoS in the phenological scale. According to Meier [29], the EoS correspondsto the phenological state 92.

From the total set of available data, we did not consider in this test year 2013 because only a fewimages were available and, consequently, fitting-based methods can not provide a useful adjustmentto estimate the EoS. Moreover, in the 2011 campaign, only four rice fields reached state 92 during theground campaign. Therefore, a total of 42 cases (rice parcels monitored during whole campaigns) areused for this test.

In this evaluation, we employ only the first three NDVI images of the campaign to estimate thecrop state, and then the prediction model is used directly to provide the EoS estimate. This means thatthe forecast of EoS is given between 40 and 60 days before it occurs, i.e., it is for more than a month.

Figure 7 shows a comparison of the results obtained by using the four methods: (a) asymmetricGaussian curves, with a determination factor (R2) of 0.4; (b) double logistic functions, with R2 = 0.5;(c) adaptive Savitzky–Golay filtering, with R2 = 0.64; and (d) dynamical approach based on particlefilter, with R2 = 0.77.

To evaluate the accuracy of all methods for a reduced number of images, the following comparisonis done. For each parcel in 2009, the EoS is estimated using TIMESAT software and compared with theresults obtained by the dynamical framework. Due to the requirements of a uniform time sampling,the NDVI values are interpolated to provide a total of 38 input data with a constant sampling rate ofeight days. The RMSE and the maximum absolute error (MAE) are presented as measurements ofthe accuracy obtained with the different methods. Results obtained with TIMESAT are summarisedin Table 3. The first row shows the number of images used in the interpolation step. The resultsobtained when the whole set of images (16) is taken into account are shown in the first column. Theconsecutive columns show the results when one, two, three and four images are removed before theinterpolation step is applied. The process to estimate the EoS when the number of images decreasesis explained next. First, one image is removed randomly from the whole set and the remaining onesare interpolated to provided a constant sample rate, i.e., 38 NDVI input values. The EoS is estimatedusing the TIMESAT for each method. The process of removing and estimating is repeated a total of 30times, providing 30 different estimates for each parcel and method. With these values, the RMSE andthe MAE are computed. Then, the same approach is employed, removing two, three and four imagesfrom the original set. Table 4 shows the results obtained using the method proposed in this work. Forthis case, the interpolation step is not necessary. In order to provide the EoS, two steps are applied:first, three NDVI images are combined with the prediction to produce the estimation of the currentphenological state. Second, the prediction model is employed to compute the predicted EoS.

Remote Sens. 2016, 8, 610 12 of 19

260 270 280 290 300 310 320260

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260 270 280 290 300 310 320260

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Figure 7. Estimation of EoS using (a) asymmetric Gaussian functions; (b) double-logistic functions;(c) adaptive Savitzky–Golay filtering; and (d) methodology based on particle filter. Determinationfactor (R2) and RMSE are provided for each method. The number of cases is n = 42.

Table 3. RMSE and MAE obtained for the EoS estimation using TIMESAT.

Images Employed 16 15 14 13 12

asymmetric Gaussian RMSE 7.2 8.1 9.2 11.0 14.0MAE 13 21 35 35 43

Double-logistic RMSE 7.2 8.1 9.0 11.0 14.0MAE 13 21 37 39 43

Savistzky-Golay RMSE 10.2 11.0 12.4 14.0 17.7MAE 20 26 45 47 69

Table 4. RMSE and MAE obtained for the EoS estimation using a dynamical approach.

Images Employed 3

RMSE 8.3MAE 24

4.3. Estimation over Other Types of Rice

In this last example, we study the reliability of this methodology when a crop grows in a differentway from that expected (it grows faster or slower than usual). In such a case, our prediction modelcan not follow the changes because it does not include any other parameters (external information)except time. To evaluate this effect in the final estimates, we test the method over a crop with a fasterphenological evolution (120 days in total) since the model is designed for rice whose cycle is around150 days. As real data from a faster crop are not available, we simulate it by compressing the time scale.

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The proposed methodology is applied in the same way as before, without making any otherchanges, and results are compared with the estimates of the same crop without changes in the time scale.In Figure 8b, we show the estimation of the phenological states when time between acquisitions iscompressed by 20% and in Figure 8a without such a compression. Each time a new observation isavailable, two estimations are computed: the estimation given by the prediction (green triangle) andthe estimation given by the observation (red circle). The particle filter combines both estimations toprovide the final phenological state at each step.

0 20 40 60 80 100 120 1400

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Figure 8. Example of state estimations for a parcel with normal (a) and faster (b) development.The black solid line shows the ground truth measurements. Green triangles show the most likely valuegiven by the model at instant k + 1 (i.e., prediction). The red circles show the more likely value givenby p(yk+1|xk+1) at instant k + 1 (i.e., observation). The blue dashed line is the combination of bothprovided by the particle filter (i.e., estimation).

The same process is extended to the whole set of parcels providing a total of 379 estimations(see Figure 9). In this case, comparing with the results in Figure 5, the R2 is slightly reduced to 0.90,whereas the RMSE doubles (11.2).

0 20 40 60 80 1000

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Figure 9. Phenological state estimates and ground truth for all parcels and available images withdevelopment faster than normal (120 days cycle).

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5. Discussion

5.1. State Estimation and Prediction

The estimation of the current phenological state for a specific crop field describes one of the mainobjectives of this methodology. Hence, the first proposed evaluation is addressed to quantify the abilityof the algorithm to estimate such a variable. The importance of providing a real-time estimation has tobe remarked here. To be employed during the cultivation campaign, information has to be delivered assoon as possible to the final users so as to conduct the required actions. Although this feature has notbeen directly evaluated in a final application in precision farming, it represents a unique characteristicof this method and distinguishes it from alternative state-of-the-art techniques.

To test the quantitative performance, the state estimations have been compared with the referencedata provided by the on site campaign (see Figure 5). In general, the estimation accuracy improveswhen more observations are available. However, the performance is worse from state 40 to 60 than forthe rest. This is due to the lack of sensitivity of the observations (i.e., NDVI) to phenological changesin this interval (see Figure 3), so the estimation is mainly determined by prediction. It should beemphasised that observations alone would not be able to provide any different estimate in this interval,but the proposed methodology can cope with these conditions. Thanks to the model and the previousestimation, we can keep a good tracking between these states (see results between DoY 220 and 260).Finally, after state 60, the NDVI provides useful information again for updating the prediction andimproving the performance of the estimation. The results presented in Figure 5 demonstrate that thismethodology provides reliable information about the crop status all along the cultivation campaign.

Moreover, a comparison between the PF estimation and the direct inversion of the observationproves the ability of the approach to solve NDVI evolution ambiguities. An interesting feature ofthese results is the impossibility of estimating some phenological states using only NDVI observations.As it was mentioned, NDVI exhibits ambiguity between both initial and final states (both of themare characterised by low values), whereas the middle states present high constant NDVI values.Consequently, the third estimation in Figure 6 is totally incorrect. The likelihood PDF of an NDVI valuearound 0.5 (which is present both at the initial increase and the final decrease) is illustrated in Figure 10.The resulting bimodal distribution justifies the erroneous estimates provided by the observations alone.On the contrary, the particle filter can deal with bimodal distributions exploiting the prediction step toweigh with low values all improbable transitions, hence avoiding these unrealistic jumps. This is themain reason of using the particle filter instead of an extended Kalman filter (EKF) which only workswith Gaussian distributions.

0 10 20 30 40 50 60 70 80 90 1000

0.002

0.004

0.006

0.008

0.01

0.012

Phenology

Figure 10. Representation of the likelihood PDF of the observations for a value of NDVI close to 0.5.

An alternative, and useful in practice, output product from the algorithm is the estimated date ofarrival or prediction of key dates. These products are based on a reduced set of observations and theevolution model to infer at which date a specific state will be reached. A comparison in the precision

Remote Sens. 2016, 8, 610 15 of 19

provided by fitting-based methods and the proposed methodology has been conducted. The TIMESATsoftware has been selected to this aim providing predictions for the date of arrival using severalmethods, all of them based on curve fitting over the NDVI time series. The comparison strategyconsisted of estimating the date of the same state, in this case the end of season (EoS) was selected,with all methods.

This comparison shows the evident contribution of the proposed methodology, which outperformsthe other methods and is able to provide a good estimate of the EoS (RMSE = 8 days) with morethan 40 days of anticipation. The accuracy of the fitting-based methods is strongly related with thenumber of images employed, providing better results with a large number of data. The adaptiveSavitzky–Golay filtering presents the best results when all years are taken into account. The exceptionfor this case is 2009. This is because some parcels exhibited an increment of the NDVI during somemonths before the sowing date. Probably, it is an effect of natural vegetation growing in the location ofthe parcel that is removed before the sowing. The asymmetric Gaussian and double-logistic fitting areless sensitive to these perturbations. The method proposed here makes use of the prediction model toreduce the number of observations employed and the interpolation step is not necessary. In this case,using just three images, results are similar to the case of employing 15 images with the fitting-basedmethods (see Table 4).

5.2. Methodology Generalisation

This subsection provides a brief analysis on the generalisation process and the ways for it tobe applied. The presented applications were tested using the same set of crop fields both at themodelling and evaluation steps. However, the model is designed to be employed over alternative orfuture campaigns. Due to internal (type of rice) or external (temperature, soil characteristics, pests,etc.) conditions, the phenological development can be faster or slower with respect to their expectedbehaviour, i.e., the evolution model. For this reason, it is mandatory to evaluate how these factorsaffect the estimation process.

To perform such an analysis, a simulation of a faster development has been derived fromthe original set. Figure 8 shows the comparison between the original phenological evolution(150-days evolution) and the faster development (120-days evolution). In this case, there exists a generaltrend, caused by the evolution model, providing underestimated states. The prediction gives lowerphenological values due to the slower evolution of the model in contrast to the simulated 120-day rice.This delay is partially compensated in the prediction with the filter when incorporating observations.As expected, the results show that when using the wrong model, the estimations are worse. Thedeterioration is due to the low sensitivity of the NDVI between states 40 and 80 combined with a badprediction. This specific range of states accumulates most of the error based on the prediction since theobservation does not provide enough information to update the state correctly. However, we could useanother model for crops that evolve faster, and hence improve the prediction step. Another alternativeis to incorporate a control variable in the model that contains information about the velocity of thedevelopment of the crop to lead the prediction, for instance the accumulated temperature.

5.3. Summary of Advantages

The dynamical approach proposed in this work enables the use of a simple prediction model toestimate the phenological state. This model takes into account the previous state and the elapsed timebetween the previous state and the current time. It works properly when it is applied under similarconditions to those under which it was created (same crop, same location, etc.). This methodologyhas substantial advantages over conventional methods based on fitting or interpolation. The first oneis real-time evaluation, i.e., the estimation is provided each time an NDVI image is received, insteadof waiting until the whole set of images is available. Moreover, the estimation is not just based onobservation data, but it is optimally combined with the estimation predicted by the model. This derivesinto the second advantage: supplying a more robust system under persistently noisy observations if

Remote Sens. 2016, 8, 610 16 of 19

it is properly defined. The dynamics of the process can keep a satisfactory estimation performanceeven when the observation is highly noisy. The third advantage regards the continuity of the output.The model defines a wide set of phenological states instead of just a few of them. The fourth advantageis that the methodology can be used to provide future estimations. This opens a new set of differentapplications allowing the prediction of the day at which a crop reaches a specific state.

5.4. Perspectives and Future Research Lines

The potential of a dynamical approach based on the PF to provide real-time phenological statesand forecasts of state arrival dates has been introduced in this manuscript. In a future work, itwould be interesting to test the methodology over a bigger set of data and evaluate the scope of itsgeneralisation to other types of crops. Moreover, the proposed technique can be used in a more globalscale, for example in ecological studies. In this domain, there has been a significant growth of interestin phenology in the last few years due to shifts in the timing of different phenological phases in plantsconnected to climate change [40–43]. Due to the fact that phenology is affected by climatic conditions,it would be interesting to derive information about climate changes using the state estimated by theproposed methodology in a longer temporal study.

Currently, ongoing work is addressed to include complementary sources of information tocombine with NDVI, as images acquired with radar satellites, in order to improve the estimations andreduce the time between observations. Data fusion would benefit also from the diversity in sensitivityto the scene features. Moreover, air temperature has been found to be a dominant factor controllingthe timing of flowering and other phenological phases [44,45], so the incorporation of control variablesin the model (as the accumulated temperature, expressed in Cumulative Growing Degree Day, CGDD)is being studied to improve the prediction step.

The flexibility of the methodology allows us to consider alternatives for the prediction andobservation model. For instance, it can be interesting to evaluate the incorporation of a biologicalgrowth model to provide the prediction stage under the same estimation context. Although theevaluation of these sorts of models involves the consideration of a large number of parameters andvariables, the reliance on the output product could be significantly improved.

6. Conclusions

Dynamic tools have been demonstrated to be useful for providing accurate estimates of thephenological state of rice crops when time series of NDVI data are available. Thanks to theincorporation of a prediction model and an adequate combination of predictions and observations,carried out with a particle filter, this method outperforms other known methods in several aspects.First, the range of possible states to be estimated is made continuous, and not just a few particularstates of the cultivation cycles. Second, estimates are provided in real-time, as observations arrive, oreven with anticipation. This is in contrast to common methods, based on curve fitting and thresholds,which need to be employed at the end of the cycle.

In order to illustrate the performance of the proposed methodology, estimates along the wholephenological cycle have been obtained for a set of rice fields with NDVI satellite data acquired forfive years. A high correlation (R2 = 0.93, with n = 379) and low RMSE (6.6 states) is achieved.Moreover, estimates of the EoS have been produced with much better results (R2 = 0.77, n = 42,RMSE = 8 days) than common methods (provided by the TIMESAT software) and using just threeimages acquired at the beginning of the campaigns (i.e., with a 40–60 days anticipation). In addition,we have shown that despite the simplicity of the prediction model, thanks to the methodology, weare able to provide good estimations when anomalous behaviours (i.e., not covered by the predictionmodel) appear.

Acknowledgments: The authors would like to thank the support of the Federacion de Arroceros de Sevilla, forproviding the ground measurement data and for their helpful comments. All NDVI images employed in thiswork were derived from images acquired by satellites Landsat 5 and Landsat 7. Images were freely downloaded

Remote Sens. 2016, 8, 610 17 of 19

from the Servidor de imágenes Landsat y productos derivados de Doñana, a web server (http://mercurio.ebd.csic.es/imgs/) maintained and operated by the Laboratorio de Sistemas de Información Geográfica y Teledetección de laEstación Biológica de Doñana (LAST-EBD), Centro Superior de Investigaciones Científicas (CSIC), Spain. This work issupported by the Spanish Ministry of Economy and Competitiveness (MINECO) and EU FEDER under ProjectsTEC2011-28201-C02-02 and TIN2014-55413-C2-2-P.

Author Contributions: Caleb De Bernardis implemented and developed the proposed methodology.Fernando Vicente-Guijalba contributed to the design of the Particle Filter algorithm. Tomas Martinez-Maringuided the research from the perspective of the dynamical approach. Juan M. Lopez-Sanchez supervised thework and contributed some ideas. All of the authors contributed to the discussion of the results and to writingthe manuscript.

Conflicts of Interest: The authors declare no conflict of interest.

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2.3. Contribution to Real-Time Estimation of Crop

Phenological States in a Dynamical Framework

Based on NDVI Time Series: Data Fusion

With SAR and Temperature

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING 1

Contribution to Real-Time Estimation of CropPhenological States in a Dynamical Framework

Based on NDVI Time Series: Data FusionWith SAR and Temperature

Caleb De Bernardis, Fernando Vicente-Guijalba, Tomas Martinez-Marin,and Juan M. Lopez-Sanchez, Senior Member, IEEE

Abstract—In this study, a methodology based in a dynamicalframework is proposed to incorporate additional sources of infor-mation to normalized difference vegetation index (NDVI) timeseries of agricultural observations for a phenological state esti-mation application. The proposed implementation is based on theparticle filter (PF) scheme that is able to integrate multiple sourcesof data. Moreover, the dynamics-led design is able to conduct real-time (online) estimations, i.e., without requiring to wait until theend of the campaign. The evaluation of the algorithm is performedby estimating the phenological states over a set of rice fields inSeville (SW, Spain). A Landsat-5/7 NDVI series of images is com-plemented with two distinct sources of information: SAR imagesfrom the TerraSAR-X satellite and air temperature informationfrom a ground-based station. An improvement in the overall esti-mation accuracy is obtained, especially when the time series ofNDVI data is incomplete. Evaluations on the sensitivity to differ-ent development intervals and on the mitigation of discontinuitiesof the time series are also addressed in this work, demonstratingthe benefits of this data fusion approach based on the dynamicsystems.

Index Terms—Agriculture, data fusion, normalized differencevegetation index (NDVI), particle filter (PF), phenology, statespace, synthetic aperture radar (SAR), temperature, time series.

I. INTRODUCTION

R EMOTE sensing data represent a profitable complementto agricultural management. During the last years, dif-

ferent technologies have provided alternative products relatedsomehow to the biological status of crops. The knowledge ofthe current state of an agricultural land, updated with enoughrefresh rate and fine spatial resolution, is a powerful tool forpractical management. This information can be exploited for avariety of products related to crops: yield prediction, hydrolog-ical requirements, optimum fertilisation time, etc. Estimationof specific dates, with special attention to the relevant events

Manuscript received November 06, 2015; revised February 06, 2016;accepted February 29, 2016. This work was supported in part by SpanishMinistry of Economy and Competitiveness (MINECO) and in part by EUFEDER under Project TEC2011-28201-C02-02 and TIN2014-55413-C2-2-P.

The authors are with the Institute for Computing Research, IUII,University of Alicante, E-03080 Alicante, Spain (e-mail: [email protected]; [email protected]; [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSTARS.2016.2539498

from the agricultural point of view, has been proposed in [1]–[4]. In these studies, the normalized difference vegetation index(NDVI) is used to infer the phenological state of crops, and ameasure of the crop productivity was proposed by Sellers etal. [5] using the same index. The NDVI represents then a suit-able parameter in the estimation of the status of crops due toits relation with the biological process occurring in the plants.The index is defined as the ratio between the difference of thenear-infrared (NIR) and red bands and the sum of these bands.The correlation between this variable and the biological processis due to both the chlorophyll contained in the leaves, whichabsorbs energy in the red spectrum, and their structure, whichscatters the NIR components [6], [7].

Many satellite systems (e.g., LANDSAT, MODIS, orASTER) provide regularly multispectral images of these bandswith a large land coverage, thus making them suitable foragricultural purposes. The main difficulty of this observa-tion scheme is the loss of acquisitions, due to internal prob-lems, management considerations, maintenance, and otherexternal causes. For instance, the presence of clouds mightimpede, depending on the specific area and period of cul-tivation, the development of a real-time operational productfor phenological tracking. For this reason, relying on a sin-gle sensor technology does not guarantee the access to aregular time series of data. Accordingly, practical method-ologies should be developed to be unaffected by temporaldiscontinuities, or at least to minimize their effect over thefinal product. Moreover, there are no technologies sensitiveto every condition present in the crops along the wholephenological cycle. For example, multispectral optical sen-sors provide a good description on the radiation changesrelated to the plants’ chemical variations, but they do notperceive structural or morphological variations. Consideringother data from alternative technologies, as synthetic apertureradar (SAR) images, has a dual benefit: improving the sen-sitivity to the phenological development and increasing thetemporal sampling for tracking the dynamics of the growthevolution.

In this context, data fusion is a very promising strategy forcombining the information provided by different sources toimprove the exploitation of the data. In remote sensing, datafusion has shown to be very effective to get better results

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2 IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING

in diverse applications [8], such as multitemporal image pro-cessing [9], change detection in urban areas [10], [11], landcover classification [12], estimation of elevation models [13],and vegetation monitoring [14]. Statistics-based methods arecommonly used tools for implementing practical approachesfor data fusion [15]–[17]. The particle filter (PF), within thedynamical approaches, is a suitable method to combine dif-ferent information sources in statistical terms, with advantagesover other techniques [18]. For instance, it does not make anyassumption on the probability density function (pdf) of thesources. It also enables the integration of statistical informa-tion given by a physical or mathematical model that describesthe behavior of the scene, independently of its nature.

In previous works, it has been shown that the use of thedynamical approach to estimate the phenology of rice cropspresents high performance [19]–[21]. In the particular case ofcereals, the growth cycle is usually defined in three main stages,namely vegetative, reproductive, and maturation. However, thetemporal evolution along the different stages can be describedidentifying 10 main stages, which are subsequently divided intosecondary stages. As a result, the scale derives in a continuousnumerical scale of the plant development from 0 to 100, usingthe extended BBCH scale [22]. The description in terms of theBBCH scale is based on the actual characteristics of an indi-vidual plant. When the scale is used for the definition of thedevelopment stage of a plant stand or a parcel or a field, thedescription should apply to at least 50% of the plants inside theparcel. Therefore, a specific field or parcel will be consideredto reach a particular phenological stage when more than half ofits plants reach that stage.

In the dynamical framework, the estimates of phenologyare defined as state variables, evolving through a particulardynamical behavior characterized by a specific model calledprediction model. The phenological states can be observed indi-rectly by different sources, e.g., remote sensing sensors. For aparticular instant, the values predicted by the model and the val-ues inferred from the different sensors can be combined, henceproviding better results than if just one of them (model or obser-vations) was considered. Moreover, this approach is carried outonline or in real-time, i.e., an estimate is generated each timean observation is available. This is in contrast to other existingmethodologies which provide estimates only after the end ofthe campaign.

In agricultural crops, air temperature is considered a dom-inant factor controlling the timing of different phenologicalstates, and for that reason it has been widely used for predictingcrop status [23], [24]. In particular, it has been pointed out asone of the main variables driving the phenological developmentin rice cultivations [25]–[27]. In this study, we have analyzedthe incorporation of this information in the proposed dynami-cal methodology. The framework enables the integration of thetemperature in a straightforward way, since it can be included inthe prediction model as a control variable. In this manner, theparticular conditions of the campaign under observation, repre-sented by the accumulated temperature, are taken into accountin the prediction model. In fact, this procedure represents anonline improvement of the model as it is modified ad hoc forthe specific conditions of each campaign.

In summary, the specific objective of this work is the devel-opment of a methodology to improve the estimation of the phe-nological state of rice crops by exploiting a fusion of data fromtime series of NDVI, SAR, and temperature values. For this pur-pose, a previously proposed dynamical approach is enhancedunder a data fusion context. First, the observations given byNDVI are complemented by SAR acquisitions. Second, the pre-diction is also completed by a temperature driven model. Thetext is organized as follows. Section II describes the methodol-ogy, including the general theory and the particular aspects ofthe implementation used here. The available data set and the testsite are introduced in Section III. Results are presented and dis-cussed in Section IV. Finally, Section V summarizes the mainpoints and the conclusion of this work.

II. METHODOLOGY

A dynamical system is a definition for any system thatevolves over time. They are usually characterized by a set offirst-order differential equations, which describes mathemat-ically their physical behavior, as indicated in (1). The statevector (x) contains all the information related to the status ofthe system at a particular instant. All the possible states definethe state space that represents each and every condition the sys-tem can hold. Instead of regarding variables as functions oftime, they can be thought as coordinates of points (states) in then-dimensional domain the system is described in. One of themost relevant aspects of the dynamical methods relies on thefact that the future states are inherent to the model description

xk+1 = f(xk, uk) + vk+1 (1a)

yk+1 = h(xk+1) + ek+1. (1b)

where a one-dimensional system will be considered hereafter.Equation (1a) describes the evolution of the state with time. Inthis notation, xk and xk+1 represent the previous and the cur-rent (consecutive) states, respectively. Function f( ) is knownas the dynamic or prediction model, i.e., a representation of theexpected behavior, relating xk+1 with xk and the control vari-able uk. The prediction error or uncertainty is characterized bythe noise of the model vk+1.

Usually, xk+1 cannot be measured directly, but it can beinferred by external observations, e.g., using remote sen-sors. Equation (1b) relates the measured (noisy) observation(yk+1) to the current state (xk+1). Furthermore, ek+1 representsthe measurement error or uncertainty, which corresponds tostochastic noise process defined by its known pdf pek+1

. In thisformulation, functions f( ) and h( ) do not depend explicitly ontime t, hence resulting in a time-invariant system. Therefore,the estimation process is supported by the dynamics and notjust by the experimental measurements (observations) them-selves. In this context, all the noise sources are assumed tobe nonstationary processes, since their parameters are extractedindependently at each state during the modeling stage (see nextsections for details).

A. Data Fusion in a PF Context

In this section, a brief summary of the PF is made withspecial attention to the data fusion methodology. A whole


BERNARDIS et al.: CONTRIBUTION TO REAL-TIME ESTIMATION OF CROP PHENOLOGICAL STATES 3

TABLE IPF SEQUENCE

description of the theory in particle filtering is presented in [28]and [29]. The use of alternative filters, such as the extendedKalman filter, has not been considered for this work. Althoughthis filter is able to work under particular nonlinear models,the assumption of Gaussian noise process restricts its usage inour application, due to the multimodal nature of the observa-tions. For this reason and the ability to work with any kind ofnonlinear model, particle filtering provides a more appropriateframework [30].

PF is a sequential Monte Carlo method that approximatesthe posterior pdf with a set of particles, see (2). Particlesrepresent tentative states in the state space following the evo-lution model (1a) and concentrate around the most probablestate:

p (xk+1|yk+1, uk) ≈N∑

i=1

ωik+1δ

(xk+1 − xi

k+1

)(2)

where p (xk+1|yk+1, uk) is the true posterior pdf, xik+1 is

the ith simulated sample (particle), and ωik+1 is the weight

of ith simulated sample (particle). N represents the num-ber of particles employed in the simulation, and δ ( ) is theDirac delta function. If N is sufficiently large, (2) approxi-mates the true posterior pdf. The weights show the probabilityof each particle (state) at a particular instant k. The actualMonte Carlo simulation is applied over each one of the Nparticles. The evolution model is assessed over each one ofthem in an iterative manner, i.e., the integration between k andk + 1 is divided in 1-day steps. During the integration pro-cess, samples from the noise model distribution are includedin the differential increments. These are updated recursivelyeach time a new observation is acquired by the followingequation:

ωik+1 ∝ ωi

kp(yk+1|xi

k+1

)(3)

where p(yk+1|xik+1) expresses the likelihood function, and

yk+1 is the observation at instant k + 1. Particles and obser-vations are related by the observation equation (1b).

If more than one sensor is employed to provide measure-ments (observations) it is necessary to compute more than onelikelihood function p(yk+1|xi

k+1). Assuming that the observa-tion sources are statistically independent, (3) can be rewrittento incorporate all likelihood functions as

ωik+1 ∝ ωi

k

M∏

j=1

p(yj

k+1|xik+1

)(4)

where p(yjk+1|xi

k+1) expresses the likelihood function for theobservation given by the jth sensor, and M is the total numberof sensors.

Finally, the current state (xk+1) is obtained as a linearcombination of all particles

xk+1 =

N∑

i=1

ωik+1x

ik+1. (5)

A summary of each step involved in the algorithm is pre-sented in Table I. The iterative process goes from Step 2) to Step5), starting at Step 2) for each iteration. A complete descriptionof the algorithm was presented in [20], so it is not repeated hereto save space.

B. Prediction Model for Crops

In the case of rice crops, the model describing the evolutionof the particles (prediction step, 2 in Table I) was presentedin [21] and characterizes the phenological behavior of a par-ticular set of rice fields. It is represented mathematically by alinear trend followed by a sigmoid function. The expressionof the model using a discrete-time formulation is shown in thefollowing equation:

xk+1 =

xk + mΔt, xk < xc

xk + rΔt(xk − a)(b − xk + a)/b, xk ≥ xc

(6)



where Δt represents the integration time step, tk = kΔt inwhich k takes integer values; xk is the phenological state atinstant kΔt, and xk+1 is the phenological state at the nextinstant; and xc is the phenological state at which the functionis switched. Constants m, r, a, b, and xc are parameters of thefunction [21]. In this context, the current state can be calculatedas a function of the previous state and the elapsed time.

Such a framework is open to add information in the predic-tion step to improve the value of the final outcome. For instance,data of the air temperature are well suited to fit into the model,representing a supplementary level of data fusion. The growingdegree day (GDd) is a heat index that is usually employed as anindicator of the phenological development of crops [25], [31].The total or cumulated growing degree day (CGDd) representsthe integration over time of this variable during a growing sea-son and can be computed using expression (7). Unless cropsare extremely affected by droughts, pests or other unexpectedevents, the CGDd can be used to predict when a crop will reachmaturity

CGDd = CGDd−1 + GDd (7)

where

GDd = Ta − Tbase (8)

and

Ta =

⎧⎪⎨⎪⎩

Tbase, if Ta < Tbase

Tcutoff , if Ta > Tcutoff

Tavg, otherwise.

(9)

In this model, Ta (C) represents the daily average growingtemperature; and Tbase (C) and Tcutoff (C) are the mini-mum and maximum temperatures for physiologic crop growth,respectively. Tavg is the average of the daily temperature(Tavg = (Tmax + Tmin) /2), in which Tmax and Tmin are themaximum and minimum daily temperatures.

With the objective of including the information provided bythe temperature, the prediction model can be evaluated includ-ing a control variable (uk) as expressed in (1a). Therefore, themodel provides the evolution defined by f( ) but subject to thevariable uk, which represents the influence of CGDd in the pre-diction. In particular, the daily average temperature (Tavg) isconsidered as the control variable, i.e., the input for the pre-diction model. A continuous temperature time series is usedfor computing a prediction estimation in the same temporalsampling as the model.

The action of this variable governs the velocity of the phe-nological development in the prediction step. The phenologicalevolution model is determined by the combination of the aver-age model and the effects of the accumulated temperature. Inthis context, local variations on the control variable would affectdirectly the phenological evolution rate. To derive the modeldriven by CGDd, a particular set of reference parcels can beemployed to characterize the phenological behavior in termsof this variable. As illustrated in Fig. 1, the prediction modelin this case can be obtained after fitting a polynomial func-tion to the relation between the CGDd and the phenologicalinformation over the reference set.

Fig. 1. Relation between the cumulative growing degree days (CGDd) and thereference phenological values (dots) for 2008–2013 (except 2012 due to lack ofground data). The derived function is obtained from the fitting of a polynomialfunction (line) (degree = 4). The calibration parameters (Tbase, Tcutoff ) for theCGDd model are extracted from [26].

C. Observation Model

In this work, the observation of the scene is carried out bytwo different sensors (M = 2) at the same or different time:the first one provided by a multispectral image (NDVI prod-uct) and the second from a SAR acquisition (HH/VV ratio).Therefore, instead of only one equation, two models are nec-essary in this case to compute the different variables and toprovide the likelihood functions appearing in (4) (update step,3 in Table I).

1) NDVI Observation: The relation between the phenolog-ical state and the particular value of NDVI for each parti-cle is given by (10), which corresponds to a double-logisticcurve. It has been extracted from [21] and included here forcompleteness

y1k+1 = c + d

[1

1 + exp(−r1(xk+1 − f1))

+1

1 + exp(−r2(xk+1 − f2))− 1

]+ e1

k+1 (10)

where c is the minimum NDVI value and c + d the maximumNDVI value. r1 and f1 are parameters of the first logistic curve,r2 and f2 correspond to the second logistic curve, and e1

k+1

represents the observation noise. In Fig. 2, the NDVI measuredin a set of parcels from 2008 to 2013 (excluding 2012 due tolack of ground data) and the fitting made by (10) are presented.More details about this model can be found in [21].

2) SAR Observation: A polarimetric synthetic apertureradar (PolSAR) image provides different products (power ofthe different polarimetric channels, correlations and phase dif-ferences between them, etc.) [32]. This is analogous to themultispectral case, in which different bands capture differentranges of the spectrum.

An analysis of a wide set of polarimetric variables as a func-tion of the phenological evolution of rice fields can be consulted



Fig. 2. Measurements of NDVI (observations) for different parcels from 2008to 2013 (excluding 2012 due to lack of ground data) represented as a functionof phenological state (black circles). The solid line corresponds to the observa-tion equation for the optical system with r1 = 0.84, f1 = 21.07, r2 = −0.10,f2 = 95.40, c = 0.21, d = 0.65. Extracted from [21].

Fig. 3. Measurements of the ratio HH/VV (dB) for a set of parcels between2008 and 2009 represented as a function of phenological state (black circles).The solid line corresponds to the observation equation, i.e., the HH/VV valuefor each phenological state given by (11) with r1 = 0.39, f1 = 21.69, r2 =−0.06, f2 = 63.38, c = −1.01, d = 11.12.

in [33] and [34], for C- and X-band, respectively. From thesestudies, and from previous works which exploited SAR imagesfor rice mapping [35], we have selected the ratio between thetwo backscattering coefficients of the copolar channels (HHand VV) as a measure sensitive to the crop development. Asa key point for our purposes, this ratio exhibits a clear evolutionin the phenological range from state 30 to 70. Consequently,this observation increases the sensitivity provided by the NDVIdata during the phenological range from 30 to 70, i.e., whereNDVI is almost constant (see Fig. 2). However, there is no con-straint in the use of any other radar or polarimetric variable, asfar as it increases the sensitivity to the phenological develop-ment. In our case, the HH/VV ratio is computed from a stack ofTerraSAR-X images acquired with an incidence angle of 30,which is described in [34].

In Fig. 3, the HH/VV ratio measured in a set of parcels in2008 and 2009 is shown. With the same method followed toderive the equation relating phenological states with the NDVI,an equation can be derived for the relation between phenology

and the HH/VV ratio. It is observed in Fig. 3 that the data canbe fitted well also by a double-logistic curve

y2k+1 = c + d

[1

1 + exp(−r1(xk+1 − f1))

+1

1 + exp(−r2(xk+1 − f2))− 1

]+ e2

k+1 (11)

where c is the minimum HH/VV value and c + d the maximum,r1 and f1 are parameters of the first logistic curve, r2 and f2

correspond to the second logistic curve, and e2k+1 represents

the observation noise.

D. Noise Modeling Considerations

To apply the proposed methodology, the noise distributionof each model in (1a) and (1b), i.e., vk and ek, has to be fullycharacterized by its pdf. Providing an analytical expression forthese pdf’s is unfeasible. Consequently, they are computed fromthe fitted model and the individual observations of the model-ing step. In order to accomplish that, it is assumed that everynoise distribution behaves as a nonstationary Gaussian processwhich evolves along the model. The parameters of the distri-butions are computed for each state with significant number ofsamples in the model, and those with no samples are interpo-lated. The mean of the distribution is provided by the previouslyfitted model, and the variance is obtained by analysing the scat-tering of the samples in that state. Therefore, the variabilityof each of the measurements involved (phenological groundtruth and observations) is immersed in the estimation scheme.Simply stated, it allows a representation of the confidence levelon the model value. This procedure is applied over each modelto derive its own particular evolutionary pdf, which is employedafterward in the exploitation of the algorithm for estimationpurposes.

E. Analysis Method

Although there exist alternative methodologies for crop phe-nological estimation, they are based on the estimation of a veryreduced set of stages (4–5) [33], [34], [36], [37] hence the com-parison of the proposed technique with these previous onesis not necessary. The objective of the proposed analysis is toassess that the incorporation of additional sources of informa-tion is useful to reduce the error obtained in the case that onlyconsiders the temporal series of NDVI images.

The described methodology has different applications underthe same context. For instance, the same approach can beemployed to estimate the date of arrival of a particular state, i.e.,prediction of dates. However, this evaluation is not included inthis study and we have focused the analysis on the estimationof the phenological state for a given date. In order to validatethe improvement given by the SAR observations and the incor-poration of temperature on the prediction model, the results aredivided in two groups. The first one corresponds to the effectsof the data fusion with SAR acquisitions (Section IV-A). Inthis case, the prediction model is based just on time evolution.The phenology is inferred in three ways using: 1) exclusively



Fig. 4. Overview and location of the area under analysis. The scene is located in the Southwest of Spain, covering an approximate area of 30 × 30 km. The leftimage corresponds to the visible map from Landsat-7 and the precise location over the Iberian Peninsula. The middle image is the NDVI derived product fromthe same sensor. The right image represents an overlay of the corresponding TerraSAR-X image [HH (dB)] over the visible map. Images were acquired withinconsecutive days, August 3, 2008 and August 4, 2008 for Landsat and TerraSAR-X, respectively. The red star on the visible image indicates the temperatureground station location.

the NDVI time series for each parcel; 2) NDVI in combinationwith SAR data; and 3) based only on SAR data. The analy-sis can be divided in specific ranges to detect whether differentsensitivities are detected or not. Moreover, dealing with remotesensor images is likely to have image drops or gaps betweenacquisitions which can derive in discontinuities on the tem-poral series. An evaluation is also performed in this sense,i.e., with removal of images, to explore the behavior of theapproach under these circumstances. In the second part, thesame three evaluations are carried out by employing the pre-diction model which incorporates the temperature information(Section IV-B).

Regarding the particular aspects of the estimation, the totalnumber of PF employed for the test is N = 5000 and the resam-pling threshold is fixed to Nthrd = 1000 particles. In orderto speed up the convergence of the estimation process, it isassumed that the first observation always is provided in thefirst part of the phenological range. Thus, p(x0) is describedby a uniform distribution of particles between states 0 and40. Alternatively, a uniform distribution along the whole range(0–100) could be used, at the cost of sacrificing convergencetime.

To provide a final value, after each iteration in the estimationapproach the average value of the posterior pdf is selected asestimation. Alternatively, the peak of the distribution could bealso selected, but in our tests both options have yielded sim-ilar results. It is important to clarify that we may encountermultimodal distributions in this algorithm, which are relatedexclusively to the observation model since the early and latestages tend to behave in similar ways (i.e., similar NDVI val-ues). Considering a single observation in one of these rangesderives in a multimodal distribution, almost impossible to relateto one or the other with certainty. Nevertheless, the support of

a dynamical model, i.e., prediction, allows us to remove themultimodal effects on the estimated posterior pdf.

III. DATA SET AND TEST SITE

This methodology has been tested with data acquired overrice fields located in Seville, Southwest of Spain, during 2008and 2009. An overview of the study area is shown in Fig. 4.In this area, rice is cultivated from May to October (during135–150 days), with just one crop per year. The phenologicalinformation, acquired by ground campaign measurements, wasprovided by the local association of rice farmers (Federacionde Arroceros de Sevilla) on a weekly basis more than nineparcels in 2008 and 10 parcels in 2009. In addition, the sowingand harvest dates are known for each parcel. This informa-tion was used in the generation of the model and in thevalidation of the results. The employed parcels in the analy-sis range from 3 to 17 ha, with plant densities from 200 to850 plants/m2.

The number of NDVI images that has been used is12 for 2008 and 8 for 2009. All the NDVI imagesemployed in this work were downloaded from the Servidorde imágenes Landsat y productos derivados de Doñana(http://mercurio.ebd.csic.es/imgs/), a web server maintainedand operated by the Laboratorio de Sistemas de InformaciónGeográfica y Teledetección de la Estación Biológica deDoñana, LAST-EBD, CSIC, Spain. The images were acquiredby Landsat 5 and Landsat 7 with a pixel size of 30 × 30 m.All the images were already geometrically and radiometri-cally corrected [38], [39]. The SAR images were acquired bythe TerraSAR-X with a 11-day revisit period. The number ofemployed acquisitions is 11 for 2008 and 10 for 2009. This dataset is described in depth in [34].



The temperature information is obtained from the meteoro-logical station La Puebla del Río II of the Spanish Sistema deInformación Agroclimática para el Regadío (SIAR) (see loca-tion at Fig. 4). The distance from the meteorological stationto the farthest crop field in this scenario is less than 24 km.According to the information provided by the local authori-ties, we can assume a very low spatial frequency behavior fortemperature (differences between fields are always well below1 C), which means that we consider the same temperaturevalues for all the parcel set.

In order to define a common spatial resolution, the obser-vations from each sensor are computed at parcel level, i.e.,a single observation is generated for each parcel. Evidently,this approach degrades the optimal spatial resolution, but itenables to combine the finer remote sensing resolution with theground truth relative to the phenological state, provided at par-cel level. However, the methodology could be extended withoutany change to a finer spatial grid. On the other hand, if a SARsensor with coarser resolution were used (e.g., Sentinel-1), theapproach working at parcel level would be perfectly applica-ble since the parcel size is large enough to ensure a sufficientnumber of looks in the measurements.

IV. RESULTS AND DISCUSSION

A. Results Considering Only Remote Sensing Data

1) NDVI Time Series: For illustration purposes, the esti-mates obtained for one representative parcel are presented inFig. 5 using in this case just the NDVI time series as observationdata. Each time an image is available, prediction and observa-tion are combined by the PF to provide the current state (solidcircle). When the acquisition is not available, due to the pres-ence of clouds or other system failures, the estimation is limitedto the predicted value (empty circles). For validation purposes,the ground truth data for the parcel under study are shown by adashed line. The estimation series for this parcel consists of atotal of 17 estimations (8 based on NDVI and prediction and 9based exclusively on prediction) with a temporal base of 8 days,producing a root-mean-square error (rmse) of 11.2 states.

It can be observed how after three acquisitions (24 days afterthe first one) a satisfactory convergence to the state of the parcelhas been reached. The prediction model warrants to obtain anacceptable estimation without the incorporation of any image.Nevertheless, one is not able to detect inner parcel changes untilthe assimilation of new acquisitions. This is the case of the lasttwo estimations without images, i.e., based on prediction (lasttwo empty circles). In this case, the parcel behaves in a differentway to the expected by the model and thus the prediction erroris larger in those states. This error is reduced significantly whena new image is available, the last one of the series.

The same procedure was applied to all the available setof parcels and images, providing the results shown in Fig. 6,where the estimated results are compared with the ground truthdata. In the same way, the empty circles represent unavailableobservations (when estimations are based only on the predic-tion model) and the filled circles are estimations consideringboth prediction and observation. A coefficient of determination

Fig. 5. Phenological state estimates and ground truth for one parcel at 2009campaign. Estimates are represented by circles: empty circles for estimationsbased on the prediction and filled ones for estimations combining predictionand NDVI observation. The continuous line represents the linear interpolationbetween estimates and the dashed line the reference or ground truth data for theparcel.

Fig. 6. Phenological state estimates and ground truth for all parcels and avail-able images. The total number of estimates is n = 128, 50 of which are basedon prediction only (empty circles) and 78 on prediction and NDVI observation(filled circles). The dashed line represents the identity, and the continuous lineis a linear regression to the estimation.

R2 = 0.94 is obtained, with a rmse of 6.36 states and a max-imum absolute error (MAE) of 25 states. It is observed thatapproximately after state 40 dispersion increases. This can bedue in part to the fact that the NDVI keeps a constant valuearound 0.8 within the phenological range from states 40 to 80(i.e., it is not sensitive to phenological changes in that range) soit cannot improve the accuracy of the prediction.

2) NDVI-SAR Data Fusion: In order to show the enhance-ment achieved by the fusion approach, the same parcel used inSection IV-A1 is evaluated under the data fusion consideration.



Fig. 7. Phenological state estimation using fusion context (NDVI and SAR)and ground truth for one parcel at 2009 campaign. Estimates are representedby circles, all of them based on prediction and observation. The continuousline represents the linear interpolation between estimates and the dashed linecorresponds to the reference or ground truth data for this parcel.

The results are presented in Fig. 7. The estimation is providedeach time a SAR or NDVI image, or both are available. Thetotal number of images in this case is 19 (8 from the NDVIseries and 11 from SAR data set). The obtained rmse is reducedto 7.1 states.

The improvement provided by the incorporation of the SARacquisitions is noticeable. On the one hand, there is a remark-able increase in the number of observations, from the originalset of 8–19, which doubles the input information. This hasa direct benefit over the estimates, as the accumulated erroris compensated more often and the gap between estimationsis reduced. On the other hand, the convergence time is alsoreduced. Using exclusively NDVI acquisitions it takes around20 days in achieve the convergence, while the NDVI-SARfusion obtains convergent results in just half of the time.

The same estimation procedure is applied to all availableparcels using the fusion method. The results are presented inFig. 8. NDVI and SAR observations are combined to derive anestimation for each parcel, so in this case we show only estima-tions based on simultaneous prediction and observation (solidcircles).

The incorporation of SAR observations improves the resultsusing only optical data, reaching a coefficient of determinationR2 = 0.96 with a rmse of 4.40 states and a MAE of 19 states.The most relevant fact is that the dispersion between states40 and 80 is drastically reduced. Actually, the improvementis even more evident when we focus the analysis in differentranges. In Table II, the specific rmse obtained is disaggregatedfor different BBCH ranges. Each row shows the rmse providedby for the corresponding range and using optical data (secondcolumn), fusion (third column), and the improvement Δ (fourthcolumn). In the first stage (0–40), the improvement providedby the SAR observations is only around 1 state. However, inthe second stage (40–80), the improvement achieved increasesto 3.5 states. The contribution of SAR data is justified in

Fig. 8. Phenological estimation using fusion context (NDVI and SAR) for allavailable parcels and available images. The total number of estimations is n =163, 78 of which are based on NDVI and 85 on SAR observations. The dashedline represents the identity, and the continuous line is a linear regression to theestimation.

TABLE IIRMSE OBTAINED IN SEPARATE BBCH RANGES

this range, since it provides observations with evolution as afunction of phenology, whereas NDVI is mostly constant (notsensitive). In the last stage (80–100), the number of availablesamples is not enough to provide a feasible value. Except forthis range, the statistical significance of the outputs, alongwith the additional results provided in the study, is granted byp-values smaller than 0.0001. This is a direct result of the largenumber of available cases.

The inclusion of SAR images has an impact on some impor-tant aspects. The first one relies directly on the increase of thenumber of observations. Therefore, a greater number of eventscan be observed. The second one is due to the decrease on thetime between observations. The effect of the integration of theprediction model derives in a rise of the accumulated error. Thiserror is bounded each time the observation is combined with thepredicted value, hence a more often update derives in a decreasein the error of the estimates. And the third aspect relies on thecomplementarity of both sensors. The SAR acquisitions con-tribute with higher sensitivity between stages 40 and 80 thanthe optical sensor, improving the accuracy in this range.

The use of a high number of SAR images could derive signif-icantly in an increase in the cost of the operative final service.In this regard, we could think of alternatives for optimize thenumber of required images. From our analysis, the inclusionof a smaller number of SAR images located between stages 40



TABLE IIIRESULTS FOR THE EVALUATION OF RANDOM REMOVAL OF NDVI ACQUISITIONS

TABLE IVRESULTS FOR THE EVALUATION OF RANDOM REMOVAL OF SAR ACQUISITIONS

and 80 improves the estimation process. The results shown inFig. 8 are tested again using just two SAR images per parcel,specifically, one acquired around stage 40 and the other aroundstage 80. In that case, the attained rmse is 4.9, thus between theresults obtained using the whole set of SAR images and usingonly NDVI acquisitions. Therefore, even if that is not the opti-mum result, we have proved that only a small number of SARimages, placed in the proper moment, provide better results thanonly NDVI images.

The geographic area under test is a particular region withlow cloud probability and, therefore, it represents an excellentarea to work with optical sensors. However, this may not bethe case over other territories with higher probability of clouds,deriving in temporal stacks with erratic gaps or in the extremecase a total lack of multitemporal optical data. So as to evaluatehow such scenario affects the proposed approach, the follow-ing analysis carried out by removing images from the stackhas been performed. First, the impact on the optical domainis studied by excluding randomly NDVI acquisitions. The sim-ulation is repeated 30 times, changing randomly the removedimages each time, to be statistically representative. The estima-tion is carried out with an increasing number of omitted images(from 1 to 6), for both the NDVI series and the NDVI-SAR set.Table III summarizes the results for all cases and data domains.Observing the output of the analysis, it is clear that there is

a significant degradation (up to three times) in the rmse whenremoving data from the NDVI data set when it is the only sourceof information. In contrast, dropping these same images fromthe NDVI + SAR data set has a relatively low impact on thermse (an increase around 0.7 with respect to the whole data set).For instance, when we remove five NDVI images, the resultsobtained with only the remaining NDVI data provide rmse =12.9 states, R2 = 0.81, and MAE = 43 states. In contrast, thefusion with SAR data improves the results in this case to rmse= 5 states, R2 = 0.95, and MAE = 19 states.

For completeness, an analog analysis has been engaged fromthe SAR point of view. The summary in this case is shownin Table IV. Similar insights are provided from the analysis,although some differences can be found. The impact over theSAR series in this case is smaller than over the NDVI images,since dropping a total of six SAR acquisitions only doubles thermse from the whole data set. Nonetheless, the fused domainis affected more in this case (an rmse increase of 1.1 for siximages). This indicates a higher relevance of the SAR data overthe fused data results.

B. Results Considering Temperature and Remote Sensing Data

1) NDVI Time Series: In this section, only the estimationresults employing the whole set of parcels is presented. Fig. 9



TABLE VRESULTS FOR THE DIFFERENT COMPLEMENTARY DATA EMPLOYED IN THE ESTIMATION PROCESS

Fig. 9. Phenological state estimates and ground truth for all parcels and avail-able images using the NDVI time-series and CGDd information. The totalnumber of estimations is n = 128, 50 of which are based on prediction (emptycircles), and 78 on temperature-based prediction and NDVI observation (filledcircles). The dashed line represents the identity, and the continuous line is alinear regression to the estimation.

shows the estimation outputs using the NDVI time series asobservation data and taking the temperature into account inthe prediction model. When the observation is unavailable theestimation is obtained only by prediction. The temperatureincorporates information in a daily basis, which is used to leadthe model. This extra information improves the accuracy inthe estimation process. However, the results produced are onlyslightly better than those shown in Fig. 6 because the years ofstudy present similar temperature behavior. The coefficient ofdetermination is R2 = 0.95, with an rmse of 5.83 states and aMAE of 19 states.

2) NDVI-SAR Data Fusion: To complete the analysis, allthe available information (NDVI, SAR, and CGDd) are used inthe estimation. NDVI and SAR images are incorporated in theobservation step and temperature data in the prediction step.The results are illustrated in Fig. 10. The prediction step isdriven by the temperature providing the prior pdf. Then, whenan observation is available (SAR, NDVI, or both), the prioris updated by the likelihood function. In this case, the incor-poration of the three different sources of information yields acoefficient of determination R2 = 0.97 with an rmse of 3.90states and a MAE of 16 states. The high accuracy is dueto the fact that both steps (prediction and observation) areimproved.

Fig. 10. Phenological estimation using fusion context (NDVI and SAR) andCGDd information for all available parcels and available images. The totalnumber of estimations is n = 163, 78 of which are based on NDVI and 85 onSAR observations. The dashed line represents the identity, and the continuousline is a linear regression to the estimation.

As a summary of all results, the rmse obtained for all cased ispresented in Table V. The first row shows the results using thetemporal model, and in the second one the temperature is takeninto account in the prediction step. The first group of columnspresent the accuracy of the results of the estimation consider-ing observations just made by the NDVI time series and thesecond considering also the SAR data information in a fusioncontext. Finally, the third column shows the results consider-ing only SAR observations. A deep evaluation of this case isnot considered in this work but is summarized here to com-plete the global results. More information about the estimationof phenological state using SAR observations can be found in aprevious work [20]. It should be noticed that the rmse with SARobservations improves the obtained with NDVI images. This ismainly due to a regular temporal sampling in SAR (for this case11 days) and the higher sensitivity in the specific range from40 to 60. Predictions are updated every 11 days whereas withNDVI images the time between acquisitions cannot be guar-anteed. The temporal sampling of NDVI data (for this case)is 8 days by default, but the presence of cloud worsens it to32 days in some periods. In any case, the fusion methodologyproduces the best results and the temperature information alsoimproves the estimation, achieving an RSME of 3.90. In termsof the MAE, the lowest value is also obtained with this completeconfiguration.



V. CONCLUSION

In this study, we have developed and evaluated a formula-tion for the incorporation of additional sources of informationto a dynamical methodology for crop phenological estimation.In particular, a methodology based on the PF algorithm, pre-viously defined to exploit time series of NDVI data, has beencomplemented with SAR acquisitions and temperature data.The estimation framework enables providing phenology esti-mates in an online manner, i.e., as a real-time application, withevident benefits for the final users.

Including additional sources to the NDVI, time series hasshown that it is possible to increase in the sensitivity to thephenological evolution. On the one hand, with the incorpora-tion of SAR acquisitions, variations from states 40 to 80 can bedetected better than using only NDVI data. That supports howthis alternative technology represents a valuable complement tothe multispectral product. Moreover, the total number of obser-vations is increased, reducing the temporal acquisition period,and subsequently improving the tracking of the crop dynam-ical development. The improvement provided by data fusionis especially noticeable when the number of NDVI images islow. On the other hand, the use of temperature has shown aslight improvement in the estimation process. In this case, thesmall temperature variations considered during the generationof the prediction model limit importantly the contribution ofthis variable. It can be also interpreted as if the effects of thetemperature were already incorporated in the temporal model.From our analysis, we can conclude that the reliance on dif-ferent sources of information allows us to derive more solidoutcomes than strategies based on a single data source.

Ongoing works are addressed to increase the value of theestimation results and to provide a reliable operational product.From the methodological point of view, some considerationscan be addressed to define a multidimensional observationspace (considering all bands from multispectral sensors and/orall polarimetric channels from a SAR), which could increasethe sensitivity to all the phenological range. In order to fullyvalidate the potential of the contribution of the temperature, anextended analysis employing a representative data set has alsoto be considered.

From the application point of view future evaluations shouldinclude alternative study areas and derive the capability todetect cultivation problems, such us plagues or nutrient deficits.For this purpose, the impact of the resolution on the algorithmperformance should be studied. It would be interesting to ana-lyze in a future work how to extract the optimal resolution (orthe integration) of different resolution remote sensing products.Finally, the evaluation of the methodology over other type ofcrops, such as cereals, should be carried out to prove the wholepotential of the proposed framework.

ACKNOWLEDGMENT

The authors would like to thank the support of the Federaciónde Arroceros de Sevilla for providing the ground mea-surement data and for their helpful comments. All NDVIimages employed in this work were derived from images

acquired by satellites Landsat 5 and Landsat 7. Imageswere freely downloaded from the Servidor de imágenesLandsat y productos derivados de Doñana, a web server(http://mercurio.ebd.csic.es/imgs/) maintained and operated bythe Laboratorio de Sistemas de Información Geográfica yTeledetección de la Estación Biológica de Doñana, LAST-EBD, CSIC, Spain. All SAR images have been provided byDLR in the framework of projects LAN0021 and LAN0234of the prelaunch AO of TerraSAR-X. Temperature informationobtained from the Sistema de Información Agroclimática parael Regadío (SIAR), Spanish Ministry of Agriculture, Food andEnvironment.

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Caleb De Bernardis was born in Mar del Plata,Buenos Aires, Argentina, in 1989. He receivedthe Ingeniero Tecnico (B.S.) degree (summa cumlaude) in sound and image engineering from theUniversity of Alicante, Alicante, Spain, in 2010,and the Ingeniero (M.S.) degree in telecommunica-tion engineering from the Technical University ofValencia (UPV), Valencia, Spain, in 2014. He iscurrently pursuing the Ph.D. degree in computer sci-ence at Signals, Systems, and TelecommunicationsGroup, University of Alicante. He collaborated with

the Nanophotonics Technology Centre (NTC), Valencia, Spain, in 2013.

Fernando Vicente-Guijalba was born in Elche,Alicante, Spain, in 1981. He received the Tech. Eng.(B.S.) and M.S. degrees in telecommunications engi-neering from the University of Alicante, Alicante,Spain, in 2006 and 2014, respectively.

He has been a Predoctoral Fellow with theSignals, Systems, and Telecommunications Groups,University of Alicante, since 2012. His research inter-ests include dynamical systems analysis with appli-cations in the polarimetric and interferometric SARmethods.

Tomas Martinez-Marin received the Tech. Eng.(B.S.) degree in in telecommunication engineeringfrom the University of Alcalá (UAH), Alcalá deHenares, Spain, in 1990, and the M.S. and the Ph.D.degrees in telecommunications engineering from theTechnical University of Madrid (UPM), Madrid,Spain, in 1995 and 1999, respectively.

He joined the University of Alcalá as an AssistantProfessor in 1990. In 1997, he joined EuropeanUniversity of Madrid (UEM), Madrid, Spain, as anAssistant Professor. Since 2000, he has been with the

Department of Physics, System Engineering and Signal Theory, University ofAlicante (UA), Alicante, Spain, where he is currently an Associate Professor.His research interests include reinforcement learning, optimal control, intelli-gent vehicles, and SAR filtering algorithms.

Juan M. Lopez-Sanchez (S’94–M’00–SM’05) wasborn in Alicante, Spain, in 1972. He receivedthe Ingeniero (M.S.) and Doctor Ingeniero (Ph.D.)degrees in telecommunication engineering from theTechnical University of Valencia (UPV), Valencia,Spain, in 1996 and 2000, respectively.

From 1998 to 1999, he was a PredoctoralGrantholder of the Space Applications Institute, JointResearch Centre of the European Commission, Ispra,Italy. Since 2000, he has been leading the Signals,Systems, and Telecommunication Group, University

of Alicante, Alicante, Spain, where he has been a Full Professor sinceNovember 2011. He has coauthored more than 55 papers published in refereedjournals and more than 100 papers and presentations published in internationalconferences and symposia. His research interests include microwave remotesensing for inversion of biophysical parameters, polarimetric and interfero-metric techniques, SAR imaging algorithms, and applications of radar remotesensing in agriculture and geophysics.

Dr. Lopez-Sanchez was the Chair of Spanish Chapter of the IEEE Geoscienceand Remote Sensing Society, from 2006 to 2012. He was the recipient of theIndra Award for the Best Ph.D. Thesis About Radar in Spain, in 2001.


Capıtulo 3

Trabajo no publicado

En este capıtulo se exponen los trabajos no publicados hasta la fecha. En primer

lugar, se presenta el diseno e implantacion del espacio de estados y la etapa de

filtrado para utilizar las imagenes RADAR, captadas por los satelites Sentinel-1A

y Sentinel-1B, en la estimacion del estado fenologico del arroz, ver seccion 3.1. En

segundo lugar, se detalla la labor realizada para el modelado de los sensores que iran

embarcados en los UAV, ası como las pruebas de campo realizadas y los resultados

obtenidos, ver seccion 3.2.

75

Capıtulo 3. Trabajo no publicado 76

3.1. Modelos de estimacion fenologica basados en

observaciones RADAR Sentinel-1 y datos de

temperatura

3.1.1. Introduccion

Recientemente, la ESA ha puesto a disposicion de los usuarios las imagenes del

segundo satelite RADAR de la constelacion Copernico. El disponer de dos satelites

ha permitido reducir el tiempo entre visitas de 12 a 6 dıas en Europa. Esto supone

un gran avance en el marco de la teledeteccion y datos de acceso libre dada su

alta frecuencia de revisita. Se tratan de datos dual-pol VV y VH en banda C.

Si bien el uso de estos sensores es diverso Joshi et al., uno de los campos en los

que mas relevancia y utilidad aplicada tiene es en la agricultura. En este sentido,

la teledeteccion ha tenido gran importancia sirviendo como herramienta para la

monitorizacion de cultivos dando soporte a agricultores, productores, etc. Su uso

permite cubrir grandes extensiones en un mismo instante de tiempo. Ademas, el

uso de tecnologıa RADAR supone una ventaja frente a los sensores opticos, mas

extendidos en aplicaciones de agricultura. En presencia de nubes los sensores RADAR

pueden seguir trabajando, cosa que no es posible con la tecnologıa optica.

En trabajos previos se ha demostrado la eficacia del uso de datos RADAR

en agricultura Steele-Dunne et al.. Si bien en ciertos trabajos se demostro que la

polarizacion HH, y en concreto el ratio HH/VV es la que mejor detecta los cambios en

el desarrollo de los cultivos Lopez-Sanchez et al., se han conseguido buenos resultados

usando el Sentinel-1 en temas de clasificacion y deteccion de tipos de cultivos Kontgis


et al., estimacion de humedad de suelo Bousbih et al.. En este sentido, el tener

imagenes de forma semanal abre un nuevo panorama en el desarrollo de herramientas

que permiten explotar las ventajas de series temporales. Uno de los metodos que

permite trabajar y aprovechar al maximo el uso de series temporales es el enfoque

dinamico.

El uso de un enfoque dinamico en la estimacion de parametros biofısicos, como

la fenologıa, ha sido objeto de estudio en los ultimos anos y ha mostrado ser una

herramienta potente para obtener resultados precisos empleando la teledeteccion

como fuente de observacion. En este contexto permite reducir la incertidumbre

presente en los propios sensores. Esta metodologıa ha sido probada con anterioridad

como medio para monitorizar la evolucion y el desarrollo de cosechas de arroz

empleando elementos de teledeteccion. En concreto se probo utilizando imagenes

RADAR del TerraSAR-X De Bernardis et al. y opticas De Bernardis et al.. Incluso se

demostro su utilidad en el contexto de fusion de datos RADAR y opticos De Bernardis

et al..

En el siguiente trabajo se estudia la posibilidad de emplear un enfoque dinamico

en el uso de series temporales Sentinel-1 para la estimacion de la fenologıa en

cultivos de arroz. Para esto se han disenado modelos de prediccion y observacion para

poder minimizar la incertidumbre de las observaciones haciendo uso del conocimiento

adquirido del comportamiento de las variables polarimetricas a lo largo del desarrollo

de los cultivos. Para combinar ambos datos se emplea un filtro basado en el uso

de partıculas conocido como Filtro de Partıculas. Este filtro permite combinar las

distribuciones estadısticas empleando muestras de las mismas (partıculas) sin necesidad

de disponer de funciones conocidas.


En este trabajo, se elabora un modelo basado en un espacio de estados de 3

dimensiones que complementa los datos polarimetricos del sensor con los datos de

temperatura acumulada. Esta fusion y el enfoque utilizado nos permiten compensar

la ausencia de las polarizaciones HH y HV, que a priori son mas sensible a la deteccion

de cambios en los cultivos, con el bajo tiempo de revisita del sensor.

3.1.2. Metodologıa desarrollada

Enfoque Dinamico

Las observaciones RADAR pueden verse alteradas por el estado fenologico del

cultivo o por otros fenomenos que no guarden relacion con el propio desarrollo del

arroz. Es por esto, que inferir la fenologıa utilizando observaciones aisladas no es

una opcion aconsejable. Ademas, al tener un comportamiento cıclico, los cultivos

suelen presentar valores similares en la observacion ante estados diferentes, haciendo

imposible determinar en que etapa se encuentra el cultivo. Dados estos limitantes, el

enfoque dinamico se presenta como la mejor solucion para inferir el estado fenologico

a partir de series temporales, tal como se demostro en trabajos previos De Bernardis

et al.. El analisis del comportamiento de las senales, con el transcurso del tiempo, es

idoneo para realizarlo empleando la metodologıa basada en espacio de estados. Un

espacio de estado queda definido por los siguientes conceptos: el estado, las variables

de estado, el espacio de estados, las observaciones del sistema y las ecuaciones de

estados. El estado describe las condiciones del sistema, mientras que, las variables

de estados son el conjunto mınimo necesario de variables que describen el estado

del sistema. El espacio de estados es aquel en el que los ejes que lo describen queda

conformado por las variables de estado. Los cambios de estado a lo largo del tiempo


a medida que evoluciona el sistema, dejaran una firma en el espacio. Esta firma es

la que se conoce como modelo de prediccion dado que describe su comportamiento.

Las observaciones del sistema son aquellas variables que pueden ser medidas. Su

representacion matematica se basa en las siguientes expresiones:

Xk = f(Xk−1, uk−1, Vk−1) (3.1)

Zk = h(Xk, wk) (3.2)

donde Xk es el estado del sistema, un vector conformado por las variables de

estado. El ındice k marca un determinado instante de tiempo. Zk es el vector de

observacion conformado por cada una de las observaciones. f() es la funcion que

representan el cambio de estado entre dos instantes de tiempo, conocido el estado

anterior y h() es la funcion que relaciona las observaciones con el vector de estado del

sistema. Por otro lado, vk−1 y wk son distribuciones de ruido conocidas que afectan

al modelo de prediccion y observacion.

En nuestro caso se confecciona un espacio de estados utilizando las observaciones

SAR. Estas observaciones iran cambiando a medida que el cultivo va variando su

etapa fenologica, conformando una firma polarimetrica. Esta firma sera nuestro

modelo de prediccion, 3.1. Una de las ventajas de trabajar en espacio de estados

es que podemos hacer uso de la prediccion para combinarla con la observacion y

reducir el ruido de esta 3.2. La prediccion y la observacion se combinan en una etapa

de filtrado, alguno de los mas extendidos son los filtros basados en la inferencia

bayesiana Bergman.


3.1.3. Filtro de Partıculas

Los filtros basados en inferencias bayesianas tratan de determinar el estado del

sistema Xk, en el instante k, haciendo uso del conjunto de observaciones hasta dicho

instante. En definitiva, se trata de determinar la funcion densidad de probabilidad

p(xk|y1:k), que se puede aproximar siguiendo la regla de Bayes 3.3.

p(xk|y1:k) ∝ p(xk|xk−1)p(yk|xk) (3.3)

Para resolverlo se divide el proceso en dos etapas, prediccion y actualizacion. La

etapa de prediccion se usa para generar la funcion distribucion de probabilidad (pdf)

conocida como pdf a prior, p(xk|xk−1). Una vez que la observacion este disponible

se puede obtener p(yk|xk) para proceder a la etapa de actualizacion. El filtro de

partıculas realiza una aproximacion de la pdf de forma secuencial empleando un

total de N muestras, ver 3.4. Estas muestras se denominan partıculas. Cada partıcula

representa un estado posible dentro de nuestro espacio de estados, con una probabilidad

de ser el estado correcto denominada peso, w. El conjunto de las N muestras conforman

la distribucion de probabilidad dentro de dicho espacio y su peso marca si dicho

estado es mas o menos probable. Cada partıcula pasara por las etapas de prediccion

y actualizacion de forma iterativa. A medida que k transcurre y se incorporan nuevas

observaciones, aquellas partıculas que mas proximas estan al verdadero estado del

sistema se veran reforzadas adquiriendo un mayor peso, mientras que las partıculas

mas alejadas perderan peso hasta poder incluso desaparecer.

p(xk|y1:k) ≈N∑

i=1

wikδ(xk − xik) (3.4)


Para evitar la reduccion del numero de partıculas con peso representativo y por

lo tanto tener una pdf con pocas muestras, el filtro incorpora una etapa denominada

remuestreo. En esta etapa, las partıculas con peso despreciable son sustituidas por

nuevas partıculas colocadas en el entorno de las partıculas mas probables. Tras esta

etapa el peso de las partıculas se reinicia dando lugar a un nuevo comienzo en el

proceso de actualizacion pero esta vez con las partıculas distribuidas en aquellos

estados mas probables. Para decidir si se aplica o no el remuestreo se calcula el

numero de partıculas con un peso representativo en la pdf mediante la ecuacion 3.5.

Si este numero es inferior a un umbral fijado por el usuario, entonces se procede

a aplicar la etapa de redistribucion de partıculas. En este trabajo hemos fijado el

umbral de resampling al 30 % de N.

Neff =1

∑Ni=1(wi

k)2(3.5)

Construccion del Espacio de Estados

Para confeccionar nuestro espacio de estados se ha propuesto el uso de las senales

de backscatter disponibles en el satelite Sentinel-1. Se puede disenar un espacio de

estados de una unica dimension utilizando uno de los canales polarimetricos, VV,

VH o utilizar una relacion entre ambos como el ratio VH/VV. El trabajar en una

unica dimension puede limitar la deteccion de ciertos cambios en las senales. En el

caso de usar las adquisiciones del Sentinel-1, se comprobo que por su configuracion

(resolucion polarimetrica y espacial) no son sensibles a la deteccion de cambios

utilizando un espacio de estados de una sola dimension. En este caso se ve limitada la

informacion que se puede inferir al estudiar el comportamiento de ambas senales de


forma simultanea. Por este motivo, se opto por trabajar con un espacio de estados de

2 dimensiones, conformado por la senales polarimetricas VV y VH, donde cada eje

queda descrito por cada una de las variables. Este enfoque nos permite ampliar los

posibles cambios no detectados en una unica dimension. De esta forma podemos ver

la evolucion y los cambios que sufren ambas variables a medida que la fenologıa se

desarrolla a lo largo de la campana. Cada posicion en el espacio queda definida por un

unico valor de VV y un unico valor de VH. En la figura 3.1 se ilustra la evolucion de

los canales polarimetricos a medida que los cultivos se desarrollan y van cambiando

de etapa fenologica. Para esta representacion se analizaron los cambios de cada uno

de los pıxeles (10x10m) de un total 6 parcelas. Las 10 etapas se corresponden con las

etapas marcadas en la escala BBCH Meier. En esta figura solo se representa el valor

promedio de las distribuciones VV y VH para cada etapa y con el fin de facilitar su

representacion. Del analisis de los datos se puede apreciar que existe un cruce entre

las transiciones de estado, entre los rangos 0-9 a 10-19 y de 30-39 a 40-49. Ademas,

remarcar que existe una elevada dispersion haciendo que distintas etapas fenologicas

compartan un mismo estado en el espacio 2D. Este tipo de circunstancias dificultan

la deteccion del estado de los cultivos. Ademas, impide adoptar un enfoque dinamico,

ya que se incumple la condicion necesaria de unicidad en la solucion. Es decir, dos

trayectorias no pueden cortarse.

Por las razones comentadas, se busco anadir una dimension mas que permita

diferenciar con mayor claridad las distintas etapas. Dado que uno de los fenomenos

que mas influencia tiene en el desarrollo del arroz es la temperatura acumulada

J. W. Enz y Fanning, se decidio anadirla a nuestro modelo conformando un espacio de

estado de tres dimensiones. En concreto, se utilizo la temperatura acumulada descrita


−26 −25 −24 −23 −22 −21 −20 −19−22

−20

−18

−16

−14

−12

−10

VH (dB)

VV

(d

B)

0-9

10-19

20-29

30-39

40-49

50-59

60-69

70-79

80-89

90-99

Phenological stage

Figura 3.1: Evolucion multitemporal promedio de las variables VH, VV a lo largo delas distintas etapas fenologicas en cultivos de arroz.

en Boschetti et al.. Estas tres variables conforman un sistema de tres dimensiones

donde cada eje representa una de las observables, tal como se muestra en la figura

3.2. Nuevamente, la posicion en dicho espacio hace referencia al estado del sistema,

mientras que los cambios entre estados describen la dinamica o firma del objeto

bajo estudio. En este caso hemos logrado evitar la existencia de cruces en la firma y

aquellas etapas en las que se producıa un mayor solape de los datos radar queda

separada al incorporar una nueva variable. De esta forma el espacio de estados

queda definido empleando los siguientes margenes e incrementos para cada una de las

observables: los valores mınimos para las variables polarimetricas se restringen a -35

dB y los maximos a 10 dB, siendo la resolucion mınima 0.5 dB. Los valores mınimos

y maximos para la temperatura acumulada son de 0 o y 1320 o y la resolucion mınima

es de 30 o.


−26−24

−22−20

−18

−25

−20

−15

−100

200

400

600

800

1000

1200

0-9

10-19

20-29

30-39

40-49

50-59

60-69

70-79

80-89

90-99

Phenological stage

VV (dB)

VH(dB)

CG

Dd (

ºC)

Figura 3.2: Evolucion multitemporal promedio de las variables VH, VV y CGDd alo largo de las distintas etapas fenologicas en cultivos de arroz.


Modelo de prediccion

Los modelos de prediccion nos permiten tener una idea de cual va a ser la nueva

observacion conocido el estado anterior y el tiempo transcurrido entre observaciones.

Si bien hay distintas formas de obtener un modelo, hemos decidido obtener la matriz

de transicion entre todos los estados posibles.

Para esto, se analizan las transiciones de cada pıxel en un intervalo de tiempo fijo.

Este tiempo viene marcado por el periodo de observacion, que sera de 6 dıas en el

caso de que ambos satelites esten disponibles, o de 12 dıas si solo uno esta operativo.

Cada pıxel representa una determinada celda de nuestro espacio de estados. Esta

celda viene definida por su valor de VH, VV y CGDd. Lo primero que hacemos es

determinar que celdas o estados quedan ocupados para un mismo instante de tiempo

k. Esto da como resultado un vector de m elementos, donde m es igual al numero

de pıxeles. En el siguiente instante de tiempo se confecciona un nuevo vector, donde

guardamos la nueva celda a la que ha transitado cada estado. Una vez realizado el

analisis sobre todos los pıxeles de todas las parcelas y durante toda la campana,

tendremos como resultado una matriz de tamano m x J . A partir de esta matriz

se obtiene la denominada matriz de transicion. Esta matriz esta conformada por

la probabilidad de transicion entre estados. Es decir, representa la probabilidad de

transitar a un determinado estado desde otro estado transcurrido un tiempo t.

A continuacion se ilustra mediante un ejemplo concreto la matriz de transicion

resultante tras la etapa de entrenamiento. Para el caso del estadoX = 13,5dB,−19,5,

1020 se representan hacia que nuevos estados es mas probable transitar. En la

imagen se indica la posicion del estado origen, y en color las celadas a las que

se ha transitado. Los distintos colores representan la probabilidad de transicion.


Los nuevos estados mas probables se indican en tonos rojizos, mientras que los

tonos azules indican celdas menos probables. Las celdas en blanco son estados no

posibles, dado que no han sido explorados partiendo desde el estado origen en la

etapa de entrenamiento. En este caso, se puede ver un efecto de multimodalidad en

la transicion que justifica el uso de la metodologıa presentada en este trabajo. Tras

la etapa de prediccion tendrıamos partıculas concentradas en torno a dos nucleos

principales. En el caso de las dimensiones que contemplan las variables temperatura

frente a polarimetrıa, 3.5, se puede ver que hay una mayor concentracion en el eje

CGDd debido a que la temperatura sufre cambios mas lentos y de menor dispersion

que los que se pueden observar en las senales de backscattering.

-35

-30

-25

-20

-15

-10

-5

0

-30 -25 -20 -15 -10 -5 0-35

VH

(dB

)

VV(dB)

Máxima

Mínima

Probabilidad

Estado origne

Figura 3.3: Probabilidad de transicion VV y VH cuando el estado origen es X =−13,5dB,−19,5, 1020.


-35

-30

-25

-20

-15

-10

-5

0

VV

(dB

)

420120 270 570 720 870 1020 1170 13200

CGDd(º)

Máxima

Mínima

Probabilidad

Figura 3.4: Proyeccion VV contra CGDd de la probabilidad de transicion cuando elestado origen es X = −13,5dB,−19,5, 1020.

-35

-30

-25

-20

-15

-10

-5

0

VH

(dB

)

420120 270 570 720 870 1020 1170 13200

CGDd(º)

Máxima

Mínima

Probabilidad

Figura 3.5: Proyeccion VH contra CGDd de la probabilidad de transicion cuando elestado origen es X = −13,5dB,−19,5, 1020.


Observacion

En el proceso de observacion se actualiza el estado del sistema combinando el

estado de prediccion con el de observacion. Para esto se hace uso de las distribuciones

generadas por las variables observadas tanto de los canales polarimetricos VV, VH,

como de la temperatura. Para la parcela bajo analisis en un determinado instante

tendremos una distribucion de valores polarimetricos definida por el conjunto de

pıxeles de la parcela. En el caso de la temperatura, se asume un error de mas menos

5 grados en la medida dada por la estacion base. Estas distribuciones se combinan

para obtener la distribucion de observacion tal como se muestra en la ecuacion 3.6.

p(Zk|Xk) =p(z1|x1) + p(z2|x2) + p(z3|x3)

3(3.6)

donde Xk = x1, x2, x3 representa el estado en el instante k, siendo x1 VH,

x2 VV y x3 CGDd. p(z1|x1) se corresponde con la probabilidad de observar VH

conocida la distribuicion p(z1), p(z2|x2) y p(z3|x3) representan lo mismo pero para

las observables VV y CGDd respectivamente. La ecuacion3.6 se aplica para cada

una de las partıculas y nos da como resultado la probabilidad de que la partıcula sea

observada. Para actualizar el peso de la partıcula y ası combinar la observacion y la

prediccion, basta con multiplicar P (Z|X) por el peso que tuviera la partıcula en el

instante anterior.

Wk = Wk−1 ∗ P (Z|X) (3.7)

donde Wk representa el nuevo peso de las partıculas, Wk−1 es el peso que tenıan

previamente y p(Zk|Xk) el resultado de aplicar 3.6. Si la prediccion (Xk)y la observacion

(Zk) estan proximas, el nuevo peso de la partıcula Wk se vera reforzado, mientras


que, en caso contrario, se vera reducido.

Determinacion de la fenologıa

Como resultado final del filtro nuestro objetivo es determinar el estado fenologico

de la parcela. Para esto debemos caracterizar nuestro espacio de estado identificando

que valor fenologico representa cada posicion. Para ello, se hace uso de las medidas

de campo facilitadas por la asociacion de arroceros de Sevilla. Para cada dato de

observaciones en un determinado instante se obtiene la posicion de cada uno de

los pıxeles de la parcela. A estas posiciones se les asignan los valores fenologicos

determinados por las medidas de campo. De esta forma, el estado del sistema queda

definido por la posicion dentro del espacio de estados. Esta posicion define a su vez

la etapa fenologica actual. Si bien en la teorıa no debe darse la posibilidad de que

una posicion comparta mas de un estado fenologico, hemos encontrado casos en los

que esto se sucede, debido principalmente al hecho de que las medidas de campo

quedan definidas por un valor mınimo y un valor maximo para toda la parcela.

Para solventar este inconveniente hemos incorporado este suceso en la estadıstica

del sistema para determinar el estado final. De esta forma cada posicion del espacio

de estado no tendra asociado un unico valor fenologico sino una distribucion de

probabilidad de posibles valores fenologicos. Al incluir esta informacion en el filtrado

podemos solventar esta etapa de incertidumbre.

3.1.4. Filtrado

Una vez implementados los modelos de prediccion y observacion se procede a

estimar la fenologıa sobre los cultivos de testeo. El primer paso consiste en distribuir


las N partıculas iniciales, definiendo cuantas y donde se colocan. En nuestro caso

hemos utilizado un N igual al 10 % del total de celdas exploradas en la etapa de

entrenamiento (estados visitados), que se situa en torno a los 10100 estados. Para

determinar la posicion inicial de cada partıcula, se hace uso de las distribuciones

resultantes de la primera observacion. Es decir, que la primera observacion no se

utiliza para filtrar sino para la distribucion inicial. Las variables VV y VH quedan

definidas por la pdf polarimetrica mientras que para la variable CDGd se asume una

distribucion Gaussiana con desviacion estandar de 5 grados. El peso de todas las

partıculas se almacena en un vector W0 de longitud N donde todas las muestras son

equiprobables. Las siguientes etapas son iterativas y tienen lugar cada vez que una

nueva observacion esta disponible.

En primera instancia se ejecuta la etapa de prediccion. En este punto se utiliza

el modelo descrito en 3.1.3 para desplazar las partıculas a sus nuevas posiciones.

Para poder emplear el modelo basta con conocer el estado actual y cuanto tiempo

ha transcurrido entre observaciones. Por ejemplo, si fue generado con observaciones

cada 12 dıas, la prediccion nos da el nuevo estado a 12 dıas. Nuestro modelo guarda

para cada estado explorado a que estado se ha transitado y con que frecuencia. Esta

informacion es consultada por cada partıcula para obtener a que nuevas posiciones

puede desplazarse. De todos los estados posibles se escoge uno de forma aleatoria.

Aquellos estados que fueron alcanzaron mas veces en la etapa de entrenamiento, son

mas probables de ser seleccionados. Si una partıcula se encuentra en un estado que

no fue explorado previamente, nuestro modelo no sabra donde debe transitar. En

este caso, se realiza una busqueda en el modelo de la celda mas proxima con datos

de transicion. Una vez localizada, se calcula la nueva posicion con los datos de la


celda vecina.

La siguiente etapa consiste en actualizar el peso de las partıculas. Para esto, se

hara uso de la expresion expuesta en el apartado 3.1.3. El peso de cada partıcula

se vera reforzado o debilitado segun sea la distribucion de la observacion. Si la

distribucion es muy acentuada, es decir, hay poca dispersion, solo las partıculas

proximas a estos valores se veran reforzadas, mientras que las que estan mas alejadas

perderan peso. En este caso, al tratarse de una observacion con poca incertidumbre,

se le esta dando mas peso a la observacion que a la prediccion. Pero si por el contrario,

se trata de una observacion con mucha incertidumbre (distribucion con alto grado

de dispersion), el peso de las partıculas casi no se vera afectado, dando ası mas

importancia a la prediccion. Dado que la variable CGDd presenta una distribucion

constante en todas las observaciones, la dispersion de la observacion vendra marcada

por las variables polarimetricas.

Una vez actualizado el peso, se extrae su valor fenologico de cada partıcula. Para

esto se hace uso del modelo presentado en el apartado3.1.3. De todos los estados

fenologicos posibles para la celda actual se escoge uno de forma aleatoria. Aquellos

estados mas representativos en la celda seran mas probables de ser elegidos. De

esta forma transformamos cada partıcula a estado fenologico y el peso de cada una

representa la probabilidad de cada estado fenologico. Al igual que en la etapa de

prediccion, si la celda no contiene informacion del estado fenologico por falta de

medidas de campo, se toma como referencia la celda mas proxima.

Para finalizar el bucle se computa el numero de partıculas efectivas. Si es inferior

a 0,3 ∗N entonces se debe implementar la etapa de resampling. Esta etapa hace una

redistribucion de las partıculas en aquellas posiciones mas probables y el peso de


las partıculas se reinicia. El proceso se reanuda cuando una nueva observacion esta

disponible.

3.1.5. Conjunto de datos

Esta metodologıa ha sido desarrollada y testeada sobre parcelas de arroz localizadas

en Sevilla, al sureste de Espana durante las campanas 2016 y 2017. El periodo

del cultivo en este area cubre los meses que van desde mayo a octubre, con solo

un cultivo por ano. La informacion fenologica fue adquirida mediante medidas de

campo de forma semanal realizadas por la Federacion de Arroceros de Sevilla. Se

inspeccionaron un total de 6 parcelas en la campana de 2016 y 2017 con una superficie

de entre 4 y 13 ha. Ademas de la fenolgogıa, se proporciono informacion de las fechas

de siembra, cosecha, y la produccion total. Esta informacion se utilizo para asociar

los estados del sistema a los estados fenologicos del cultivo, tal y como se explico

en la seccion 3.1.3. Las imagenes fueron procesadas empleando el software SNAP

version 6.0. Para reducir el ruido speckel se aplico un filtro IDAN con ventanas de

busqueda de 15x15 y multilook de 3x3.

3.1.6. Resultados

A continuacion se presentan los resultados obtenidos para las campanas 2016 y

2017 respectivamente. Se estimo la fenologıa para cada una de las parcelas utilizando

las observaciones Sentinel-1, la temperatura acumulada y la metodologıa propuesta.

Los resultados se compararon con las medidas de campo facilitada por la Federacion

de Arroceros de Sevilla (GT).

Se analizaran los valores obtenidos para cada campana por separado dado que en


el ano 2016 el satelite Sentinel-1B aun no estaba en funcionamiento, lo que supone

un periodo de observacion de 12 dıas, mientras que en 2017 este tiempo se reduce a

6 dıas.

Para la evaluacion de los resultados se empleo la tecnica conocida como metodo

de validacion cruzada, con el fin de aislar la parcela bajo testeo de las usadas en la

etapa de generacion de los modelos. Consiste en usar todas las parcelas menos una

para la generacion de los modelos y la que se deja fuera del entrenamiento usarla

posteriormente para la obtencion de los resultados. Esta etapa se repite cada vez que

evaluamos una nueva parcela.

Campana 2016

En la Figura 3.6 se presentan las estimaciones junto con las medidas de campo

para la campana 2016. Un total de 6 parcelas fueron evaluadas. En cırculos negros

se muestra la estimacion fenologica para cada observacion RADAR donde el eje de

abscisas indica el dıa del ano (DOY) y el eje de ordenadas la fenologıa. La estimacion

queda definida por el valor medio de la PDF a la salida del Filtro de Partıculas

mientras que las medidas de campo indican el estado fenologico mınimo y maximo

para cada fecha en dicha parcela.

De los resultados se puede apreciar como la tendencia general (cambios en las

velocidades de desarrollo) se pueden seguir muy bien con el filtro, sin embargo, en

un elevado numero de estimaciones, no se logra quedar dentro de los margenes. Por

otro lado, destacar que las parcelas A y B tienen perdida de una imagen lo que hace

dar una prediccion a 24 dıas empeorando los resultados. En la parcela A la imagen

que se pierde es entre la 6 y 7 haciendo que el filtro pierda la buena tendencia que


tenıa. Y en el caso de la parcela B es entre la 1 y la 2 ,lo cual dificulta su enganche

inicial.

Para cuantificar la precision en las estimaciones se presenta en el cuadro 3.1 un

analisis del error cometido en el total de las estimaciones. En la primera fila, marcada

como estimaciones sin error, se muestra el total de inferencias que quedan dentro de

los margenes maximos y mınimos dados por las medidas de campo. Los elementos de

esta fila son considerados como acierto por parte de la metodologıa. En total se logra

un acierto del 23 %. En la segunda fila se presentan aquellas estimaciones que no caen

dentro de los margenes dados por las medidas de campo pero que en cualquier caso

el error que se comete es inferior a 5 estados fenologicos. En este caso el porcentaje

aumenta hasta el 46 %. En la tercera fila se muestran las estimaciones con un error

mayor a 5 estados e inferior a 10, con un total del 13 % de las estimaciones. En la

cuarta fila tenemos otro 13 % con un error mayor a 10 y menor a 15. En la quita fila

el error es de entre 15 y 20 estados, con un total del 3 % y finalmente con un error

superior a los 20 estados tenemos unico caso.

Cuadro 3.1: Error cometido en las estimaciones para la campana 2016Error Numero de estimaciones

Sin error 14 (23,0 %)error <= ±5 estados 28 (46,0 %)

±5 < error <= ±10 estados 8 (13,1 %)±10 < error <= ±15 estados 8 (13,1 %)±15 < error <= ±20 estados 2 (3,2 %)±20 < error <= ±25 estados 1 (1,6 %)

Por ultimo, el cuadro 3.2 presenta la matriz de confusion que permite cuantificar

la precision de la metodologıa a la hora de clasificar entre distintos estados fenologicos.

En este caso se agrupan los 100 estados en las 9 etapas mas caracterısticas (sin contar

germinacion). Esta matriz muestra el grado de coincidencia entre la prediccion (filas)


160 180 200 220 240 260 280 300 3200

10

40

60

80

100

Fen

olo

gía

BB

CH

Estimaciones

Esados máximos medidos

Esados mínimos medidos

DOY

160 180 200 220 240 260 280 3000

10

30

50

70

90

DOY

150 200 250 3000

20

40

60

80

100

DOY150 200 250 3000

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Figura 3.6: Estimacion fenologica medida en BBCH y medidas de campo para loscultivos estudiados en 2016. Las medidas de campo se dan en valores maximos (lıneacontinua) y mınimos (lınea discontinua). Las estimaciones se marcan con un cırculonegro.


y las medidas de campo (columnas). La diagonal principal de la matriz muestra la

cantidad de predicciones correctas para dicho rango, con lo cual, cuanto mayor sea

este valor mas preciso es el metodo empleado. Al igual que antes, si la estimacion

queda entre los valores maximos y mınimos, se da por buena. El factor K para este

caso es de K = 0,61. Este factor indica la mejora respecto a la probabilidad de

acertar en la clasificacion de forma aleatoria. La precision total en la prediccion es

del 65 %.

Esta baja precision se debe principalmente a la poca precision en los estados 50

al 59. En esta etapa es donde hay mayor dispersion de los datos y la parcela suele ser

mas heterogenea. De un total de 9 casos, solo 5 son aciertos mientras que tenemos

2 en la etapa anterior (40-49), uno en una etapa posterior 60-69 e incluso un caso

que se clasifica en 2 etapas anteriores 30-39. Hay un segundo caso de baja precision,

que se da en la etapa 70-79. Sin embargo, en este caso tenemos baja representacion

estadıstica, dado que solo hay dos muestras. Otra etapa con baja presicion es la que

se da en la etapa 80-89 donde solo el 44 % se clasifica de forma correcta. En este

caso los errores elevados en la clasificacion vienen derivados principalmente de las

parcelas A y B que tuvieron perdida de una imagen.


Cuadro 3.2: Matriz de confusion para la estimacion fenologica en la campana 2016

10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99 Totals Precision de Usuario

10-19 - %

20-29 2 10 1 13 77 %

30-39 3 7 10 70 %

40-49 1 3 4 75 %

50-59 1 2 5 1 9 55 %

60-69 1 3 4 75 %

70-79 1 1 2 50 %

80-89 2 3 4 9 44 %

90-99 1 3 4 75 %

Total 2 13 10 5 6 6 4 6 3 55

Precision Productor 0 % 77 % 70 % 60 % 83 % 50 % 25 % 66 % 100 % Total: 65 %

25 68 Kappa: 0.616

Campana 2017

A continuacion se presentan los resultados obtenidos para la campana 2017. En

este caso el periodo entre imagenes se reduce a la mitad respecto al ano anterior,

siendo de 6 dıas. El numero total de estimaciones que tenemos es de 134.

En la Figura 3.7, al igual que antes, se presentan las estimaciones y medidas

de campo para las mismas 6 parcelas. En cırculos negros se muestra la estimacion

fenologica para cada observacion RADAR donde el eje de abscisas indica el dıa del

ano (DOY) y el eje de ordenadas la fenologıa. La estimacion queda definida por el

valor medio de la PDF a la salida del Filtro de Partıculas mientras que las medidas

de campo indican el estado fenologico mınimo y maximo para cada fecha en dicha

parcela. Para analizar la precision de las estimaciones se presentan los resultados

del error cometido en las estimaciones en el cuadro 3.3 columna 2. La primera fila,


marcada como estimaciones sin error, son todas aquellas estimaciones que quedan

dentro de los margenes maximos y mınimos dados por las medidas de campo. En

este caso, se puede apreciar que un total de 85 estimaciones (el 63 %) quedan dentro

y se pueden considerar como estimaciones buenas. En la segunda fila se presentan

aquellas estimaciones que no caen dentro de los margenes dados por las medidas de

campo pero que en ningun caso distan mas de 5 estados fenologicos. Para este caso

se obtienen un total de 40 estimaciones, es decir, un 30 % aproximadamente. En el

caso de que este error este entre los 6 y 10 dıas encontramos 7 estimaciones(5 %) y

entre 11 y 15 estados tenemos solo 2 estimaciones.

Cuadro 3.3: Error cometido en las estimaciones para la campana 2017Numero de estimaciones

Error Observacion cada 6 dıas Observacion cada 12 dıas

Sin error 85 (63,5 %) 28 (41 %)error <= ±5 estados 40 (29,8 %) 25 (37 %)

±5 < error <= ±10 estados 7 (5,2 %) 10 (15 %)±10 < error <= ±15 estados 2 (1,5 %) 3 (4 %)±15 < error <= ±20 estados 2 (3 %)

Por ultimo el cuadro 3.4 presenta la matriz de confusion con una precision total

del 90 % y el factor K = 0,89. Se puede observar una mejora sustancial en la etapa

80-89, donde se pasa del 44 % en 2016 al 100 % de acierto en 2017. En la etapa 70-79 se

aumenta el numero de casos haciendo que la precision obtenida tenga mayor sentido

estadıstico. Al igual que en 2016, la etapa 50-59 presenta valores bajos de precision,

en este caso un 62 %.

Para poder evaluar el el efecto de la reduccion del tiempo de revisita sobre esta

metodologıa, se analiza la campana 2017 utilizando solo observaciones cada 12 dıas.

Para esto, se extrae una de cada dos observaciones generando un periodo entre

imagenes equivalente al que se tiene en 2016. Una vez realizado el diezmado, se


140 160 180 200 220 240 260 280 3000

20

40

60

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DOY

Parcel A Parcel B

Parcel D

Parcel E Parcel F

100

120 140 160 180 200 220 240 260 2800

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Parcel C

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Estimaciones



Estimaciones



Estimaciones



Estimaciones



Estimaciones



Estimaciones



Figura 3.7: Estimacion fenologica medida en BBCH y medidas de campo para loscultivos estudiados en 2017. Las medidas de campo se dan en valores maximos (lıneacontinua) y mınimos (lınea discontinua). Las estimaciones se marcan con un cırculonegro.


Cuadro 3.4: Matriz de confusion para la estimacion fenologica en la campana 201710-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99 Totals User’s Accuracy

10-19 17 17 100 %

20-29 1 22 2 25 88 %

30-39 1 23 24 95 %

40-49 1 8 9 88 %

50-59 4 8 1 13 62 %

60-69 4 1 5 80 %

70-79 9 1 10 90 %

80-89 14 14 100 %

90-99 11 11 100 %

Total 18 23 26 12 8 4 11 15 11 128

Producer’s Accuaracy 94 % 95 % 88 % 66 % 100 % 100 % 81 % 93 % 100 % Total: 90 %

25 68 Kappa: 0.895

procede a aplicar el mismo proceso que se empleo para ambas campanas. Utilizando

nuevamente el metodo de validacion cruzada se entrenan los modelos con las parcelas

que no se usaran para evaluar la estimacion, es decir, 5 para entrenar y 1 para evaluar.

Una vez entrenado se estima la fenologıa cada 12 dıas. En el cuadro 3.3 columna 3

se presentan los resultados. El numero de estimaciones que se consideran sin error,

dado que se encuentran entre los valores maximos y mınimos medidos en campo, es

de 28, un 41 % del total. A una distancia inferior o igual a 5 estados tenemos un

total de 25 observaciones, lo que representa el 37 %. Un total de 10 estimaciones se

encuentran con un error de entre 5 y 10 estados, 3 con un error de entre 10 y 15, y

encontramos 2 estimaciones con un error entre 15 y 20 estados.

3.1.7. Discusion

El hecho de aumentar el numero de observaciones reduciendo el tiempo entre

adquisiciones muestra una mejora clara de la estimacion cuando se emplea una

metodologıa basada en enfoque dinamico. Se puede observar una gran diferencia

entre los valores obtenidos para la campana de 2016 (observaciones cada 12 dıas)


y los valores obtenidos para la campana de 2017 (6 dıas). Analizando la matriz de

confusion resultante para cada campana, ver cuadros 3.2 y 3.4, se observa que el

factor K aumenta en un 25 % y que la mejora, en terminos de precision total, es

de aproximadamente un 20 %. Si bien el efoque y la solucion adoptada es la misma

en ambas campanas y la interpretacion a partir de los datos es la misma, el hecho

de aumentar la frecuencia de observacion nos produce un aumento considerable a la

hora de clasificar la etapa fenologica de los cultivos. Ademas de comparar entre las

dos campanas se procedio a evaluar la campana 2017 utilizando observaciones cada

12 dıas, eliminando una de cada dos observaciones. En este caso los resultados son

similares a los que se obtuvieron en la campana 2016.

En 2016 el 68 % de las estimaciones cometıan un error igual o inferior a 5 estados,

de los cuales solo el 23 % estaba dentro de los valores dados por los agricultores. Algo

similar ocurre cuando se estima sobre la campana de 2017 a 12 dıas. En este caso

solo el 78 % de las estimaciones contienen un error igual o inferior a 5 estados, de

los cuales, el 41 % se considera sin error. Cuando trabajamos con observaciones a 6

dıas en la campana de 2017, se logra alcanzar un 93 % de estimaciones con un error

inferior a 5 estados y de las cuales el 63 % estan dentro de los valores maximos y

mınimos marcados por las medidas de campo. Esto se debe principalmente al hecho

de que al reducir el tiempo entre actualizacion, el error acumulado en la etapa de

prediccion es menor, dando lugar a una estimacion mas precisa. Otra de las mejoras

se puede observar en el error cometido total en cada una de las campanas.

Analizando los datos de la campana de 2017 que mejores estimaciones dan, se

puede observar un aumento de la incertidumbre a partir del estado 50 dado que

la observacion empieza a ser menos sensible a la deteccion de cambios. Se puede


apreciar como la precision baja al 62 % entre las etapas 50-59 cuando en la etapa

anterior, 40-49, era del 88 %. La informacion proporcionada por la prediccion nos

permite compensar esa perdida de sensibilidad y mantener unos niveles aceptables

para seguir la tendencia del desarrollo. Si la informacion aportada por la observacion

seguirıa sin ser concluyente durante muchas etapas seguidas, la precision total serıa

peor dado que el error acumulado en la etapa de prediccion seguirıa aumentando. Sin

embargo, la observacion vuelve a aumentar su sensibilidad a partir de la etapa 60,

haciendo que la precision vuelva a aumentar alcanzando un 80 % en la etapa 60-69.

Del analisis individual de cada parcela, ver figuras 3.6 y 3.7, se puede apreciar

el seguimiento o motorizacion del desarrollo del arroz. Algunos casos, como Mınima

en 2016 o Ermita en 2017, presenta unos resultados notoriamente peores al resto.

En este caso ambas parcelas presentan un desarrollo que se aleja demasiado de lo

esperado por el modelo de prediccion. Esta falta de encaje hace que la prediccion y

la observacion no converjan en un buen resultado.

3.1.8. Conclusiones y futuras lıneas de trabajo

En el presente trabajo se desarrollo una metodologıa novedosa que permite la

fusion de observaciones SAR del Sentinel-1 con la informacion de temperatura acumulada.

Se describen los pasos para confeccionar un espacio de estados de 3 dimensiones y

la implementacion de la etapa de filtrado para poder facilitar las estimaciones del

estado del cultivo.

Se realizo la estimacion del estado fenologico en cultivos de arroz a lo largo de dos

campanas, 2016 y 2017. Se evaluo el efecto de trabajar con observaciones a 12 y 6

dıas. Se demostro la eficacia de reducir el tiempo entre observaciones aumentando el


numero de las mismas. Si bien es un sensor dual-pol (menor resolucion polarimetrica

que la que se puede obtener con otros sensores como puede ser el TerraSAR-X),

su fortaleza radica en poder tener series temporales de alta frecuencia de revisita.

Con la metodologıa presentada se puede sacar el maximo partido a este beneficio.

Ademas, se pueden complementar los datos con otro tipo de informacion como lo es

la temperatura, un factor determinante en el desarrollo del arroz. Se han conseguido

mejoras sustanciales al reducir el tiempo de adquisicion de 12 a 6 dıas. Se consigue

que el 93 % de las estimaciones tengan un error inferior a 5 estados, mientras que

a 12 dıas en el mejor de los casos se alcanzo el 78 %. Ademas, se obtuvo la matriz

de confusion donde se clasificaba en las 9 etapas mas representativas del desarrollo

del cultivo segun la escala BBCH. El factor kappa paso de K = 0,616 a K = 0,895

al disminuir el tiempo entre observaciones a la mitad. Ademas, la precision total

aumento del 65 % al 90 %.

Si bien en este trabajo se facilita la estimacion del estado fenologico, se puede

seguir el mismo trabajo para inferir otro tipo de parametros biofısicos que guarden

relacion con las observaciones SAR. Ademas, es posible fusionar otras fuentes de

informacion simplemente anadiendo una nueva dimension al espacio de estados. Se

plantea como futuro trabajo incorporar una nueva dimension que facilite informacion

del sensor optico Sentinel-2. Por otro lado, debido a que el numero de datos de

campo es limitado, en ciertas etapas del filtrado nos encontramos en celdas donde

los modelos no disponen de informacion. En este trabajo, este efecto se resolvio

recurriendo a los datos de la celda mas proxima. Sin embargo, este efecto se vera

minimizado a medida que incorporemos nuevos datos de campo. La metodologıa

presentada permite incorporar los nuevos datos a los modelos ya entrenados. Ademas,


una posible lınea de trabajo serıa utilizar algun metodo basado en redes neuronales

artificiales (Deep Learning) para resolver la problematica de no disponer de datos

utilizando la informacion de las celdas vecinas.

3.2. Estudio de medidas utilizando sensores embarcados

en UAV

3.2.1. Introduccion

A lo largo de esta tesis se ha presentado el desarrollado de una serie de herramientas

que permiten inferir el estado de los cultivos empleando series temporales. Estas series

temporales han sido proporcionadas por un conjunto de satelites que nos permitieron

cubrir grandes extensiones en un mismo instante de tiempo. Sin embargo, surge el

interes de poder complementar estos datos con imagenes adquiridas por otro tipo de

medio, en concreto, los vehıculos aereos no tripulados (UAV). Estos elementos estan

en auge hoy en dıa, siendo utilizado para distintos fines: transporte, militar, ocio,

inspeccion, etc. Uno de los usos que mas acogida esta teniendo es en la agricultura.

Este encaje se debe principalmente a que permite tener mayor control en el momento

en el que se desea (no dependes del momento en el que pasa el satelite) y tener una

mayor definicion de imagen (los pıxeles pueden ser de centımetros). Ademas, como se

demostro en la seccion 3.1, reducir el tiempo entre observaciones aumenta la precision

de la estimacion. En este sentido, el drone nos da libertad total para fijar el tiempo

entre revisitas, pudiendo disponer de un muestreo diario de alta resolucion.

Las camaras multiespectrales son los sensores embarcados en UAV que mas se han

utilizado en agricultura. Como se explico en De Bernardis et al., estos sensores son


sensibles a los cambios biofısicos de los cultivos y podemos incluir su informacion

en nuestros modelos para detectar cambios internos en las plantas. Generan una

observacion similar a la de los satelites opticos aunque suelen presentar peor resolucion

espectral y disponer de un menor numero de bandas. Sin embargo, cuentan con la

ventaja de tener una mayor resolucion espacial y total libertad en la captura.

Ademas de los cambios internos, para poder detectar el estado del cultivo es

necesario conocer los cambios estructurales. El RADAR ha demostrado ser sensible

a dichos cambios. Sin embargo, embarcar un sistema RADAR en un UAV supone

una serie de desafıos en su configuracion, montaje y procesado de datos que produce

un costo importante comparado con el de los sensores opticos. Una solucion podrıa

ser sustituir el RADAR por un sensor Laser 3D. Hoy en dıa, existen en el mercado

sensores como el Puck LITE de la empresa Velodyne LiDAR capaces de trabajar a

100m y de 500g de peso. La desventaja respecto a trabajar con un RADAR es la no

sensibilidad a la humedad del terreno, algo que sı puede ser inferido por medio de

este. Sin embargo, si solo queremos detectar los cambios estructurales, como es este

caso, son una buena opcion.

3.2.2. Objetivo

El objetivo de este trabajo es la adaptacion de la metodologıa para el uso de

sensores embarcados en UAV o sensores terrestres colocados en estaciones base.

Para esto, se procedera al estudio del comportamiento de los sensores que iran

embarcados en el UAV para poder independizar los efectos en las observaciones

debido al desarrollo del cultivo respecto a las alteraciones sufridas por el propio

montaje y vuelo del drone. Sobre el drone se embarcaran dos sensores, una camara


multiespectral y un escaner laser. El objetivo es utilizar el sensor optico como medio

complementario a las observaciones satelitaes opticas y el escaner laser como sensor

complementario a las observaciones RADAR. Ademas, se incluira un sensor terrestre

de temperatura con lo que mejorarıamos las medidas dadas por estaciones base mas

alejadas. En definitiva, se trata de utilizar la metodologıa desarrollada en esta tesis

para fusionar los datos terrestres y satelitales con el fin de inferir el estado de los

cultivos.

3.2.3. Pruebas y medidas

La primera prueba se realizo en el municipio de Ripollet, Barcelona, donde se

tomaron medidas empleando un sensor optico. En la figura 3.8 se puede apreciar una

imagen captada desde el UAV sobre la zona de pruebas. La camara multiespectral

utilizada es la Parrot Sequoia. Esta camara dispone de un sensor pancromatico y

de 4 canales adicionales centrados en las bandas; Verde, Rojo, Infrarrojo cercano e

Infrarrojo lejano. A partir de los datos captados por las bandas Rojo e Infrarrojo

cercano se procede a calcular el NDVI, 3.8. Este ındice sirve como un indicativo del

estado o salud del cultivo. Alcanza su valor maximo, igual a 1, cuando la vegetacion

se encuentra en buen estado de salud y valores mas bajos en caso contrario. En

ausencia de vegetacion los valores son proximos a 0.

NDV I =INFRARROJO −ROJOINFRARROJO −ROJO (3.8)

Dado que los sensores de cada uno de los canales no se encuentran en la misma

posicion, es necesario calcular el desplazamiento que existe entre cada uno de ellos

para poder aplicar la ecuacion 3.8 o de lo contrario estarıamos computando pıxeles


Figura 3.8: Imagen pancromatica del recinto donde se realizaron las primeras pruebasde los sensores de medida embarcados en el UAV.


con informacion geografica diferente. Es decir, se realiza una corregistracion de los

datos de infrarrojo y rojo antes de aplicar la ecuacion 3.8. Este ajuste se realizo

de forma experimental en el laboratorio empleando imagenes de un entorno con

referencias. El resultado del calculo de NDVI sobre la imagen 3.8 se muestra en la

figura 3.9. La escala de color muestra en tonos mas verdes los valores de NDVI que

son mas altos, mientras que a medida que nos aproximamos a la tonalidad roja los

valores de NDVI son mas bajos.

Figura 3.9: Imagen pancromatica del recinto donde se realizaron las primeras pruebasde los sensores de medida embarcados en el UAV.

Esta primera prueba sirvio para el ajuste de los datos captados por la camara y


como toma de contacto con el manejo de los instrumentos.

3.2.4. Elaboracion de un sistema de medidas de campo sobre

cultivos de arroz empleando los sensores que se utilizaran

en el UAV

La segunda prueba tuvo lugar en el municipio de Agramon, provincia de Albacete,

donde se realizaron pruebas sobre cultivos de arroz. El objetivo de este apartado

consiste en la elaboracion de un sistema de medidas que nos permita capturar la

dinamica intrınseca de los sensores que iran embarcados en los UAV. Se mide la

evolucion y el desarrollo de los cultivos a lo largo de la campana. Estos datos nos

permitiran elaborar los modelos de prediccion y observacion aislando los efectos

derivados del propio vuelo del drone. Ası, podremos tener una prediccion fiable del

comportamiento de las senales en cada etapa fenologica. Debido a la localizacion del

sistema de medida (en medio de un arrozal), se debıa disenar de forma que pudiera

trabajar en condiciones externas, sin posibilidad de alimentacion por medido de la

red electrica y sin comunicacion con el laboratorio por falta de cobertura.

Descripcion de la estacion base

El sistema debe ser capaz de tomar datos de ambos sensores (camara y laser)

de forma diaria y almacenarlos para su posterior analisis. Para la alimentacion se

recurrio al uso de un panel solar de 100W con una capacidad maxima a la salida de

5A. Este panel alimenta a un conjunto de baterıas que da una autonomıa maxima

de 22Ah. A las baterıas se conecta un regulador para estabilizar la tension de salida

y alimentar el resto de componentes.


En la figura 3.10 se pueden observar los elementos que componen el sistema y

su interconexion. El regulador consta de dos salidas USB a 5V y dos salidas mas

de 12 V. Los puertos USB se utilizan para alimentar una Raspberry pi 2 y para

alimentar la camara multiespectral Parrot Sequoia, respectivamente. La salida de 12

V se utiliza para alimentar un Arduino y un servomotor. Por ultimo, el sensor laser

se alimenta a traves de la propia Raspeberry Pi mediante USB. Con la carga total el

conjunto de baterıas permite funcionar al sistema durante un total de 18 horas sin

recibir carga alguna.

Para poder controlar y sincronizar ambos sensores, ası como almacenar los datos,

se implemento el software y los protocolos de comunicacion necesarios empleando la

Raspberry Pi 2. Se programo la captura de datos opticos a las 12 del mediodıa, una

captura diaria, mientras que en el caso de los datos laser se procedıa a realizar

una captura cada hora. Este incremento en el numero de datos diarios se debe

principalmente a dos motivos. Por un lado, aumentar el numero de muestras nos

permite obtener una mayor fiabilidad estadıstica a la hora de promediar la altura

del cultivo y, por otro lado, reducir el efecto de perdida de datos (en caso de posibles

fallos del sensor laser) sobre el total de medidas. El laser es un sensor 2-D, es decir,

que captura datos de distancia en 2 dimensiones realizando un giro de 270o. Para

obtener la tercera dimension y emular ası el sensor LiDAR 3D, se procedio a montar

el laser sobre un servomotor. De esta forma, podemos realizar n medidas obteniendo

un total d n cortes de plano. El control del motor se programo sobre un controlador

Arduino. El proceso para la captura de datos laser es el siguiente: La Raspeberry

se comunica con el controlador para indicarle que posicion del motor debe adoptar.

Una vez el motor alcanza la posicion indicada, la Raspberry le comunica al Laser que


RA

SP

BE

RR

Y

REGULADOR

+ + +- - -

+

+

+

-

-

-

12v 7Ah

12v 7Ah

12v 6Ah POWER

US

BD

ATA

POWER

RED CONECTOR

USB

SEQUOIA

US

BD

ATA

& P

OW

ER

ARDUINO

PANEL SOLAR

12 V

POWER

0.4 A

0.3 A

0.3 A

0.1 A

0.3 A

Figura 3.10: Esquema de interconexion de los elementos de captura de datos


comience la captura de datos. Una vez almacenados los datos, la Raspberry vuelve

a indicarle al motor una nueva posicion. Cuando el motor alcanza la nueva posicion

el proceso de captura se repite hasta realizar un total de 20 medidas por hora.

En la figura 3.11 y 3.12 se puede ver el montaje de cada uno de los componentes

del sistema de medidas. Finalmente, se coloco sobre un arrozal para poder captar

medidas durante el crecimiento y desarrollo del cultivo, ver figura 3.13.

Figura 3.11: Vista interna de los elementos de captura de datos


Figura 3.12: Sensor optico y laser utilizados.


Figura 3.13: Sistema de medidas instalado en arrozal.


3.2.5. Analisis de los datos

La siembra se realizo a finales del mes de mayo del 2017, sin embargo, debido

a complicaciones hardware la estacion base no pudo instalarse hasta el dıa 17 de

julio de 2017. Esto supone una perdida considerable de datos referente a las etapas

iniciales del desarrollo del cultivo. La toma de datos funciono de forma continua

hasta el dıa 23 de agosto de 2017, cuando el nivel de baterıas se redujo provocando

un corte de alimentacion. Este corte se debio a a varios dıas de tormenta seguidos,

que imposibilitaron la carga de las baterıas. Ademas, el sistema laser sufrio una

averıa que imposibilito la captura de datos.

A continuacion se muestran en la figura 3.14 algunas de las imagenes captadas

por la Sequoia en distintas etapas del desarrollo (incluidos el primer y ultimo dıa de

toma de datos). En la figura 3.15 se puede ver el resultado al aplicar el calculo del

NDVI.

A partir de todas las imagenes NDVI se extrajo el valor promedio y su desviacion

estandar para cada fecha, ver figura 3.16. En el promedio solo se contemplan los

pıxeles que contienen vegetacion, excluyendo los valores que proceden del suelo. Del

analisis se puede observar que existe poca variacion en terminos generales en los

valores de NDVI para las fechas de estudio, mostrando un desarrollo constante.

A modo comparativo, se analizaron las imagenes captadas por el satelite optico

Sentinel-2 con el fin de estudiar los valores de NDVI a lo largo de la campana. En la

figura 3.17 se muestran de forma simultaneas las evoluciones de los datos captados

por la Parrot Sequoia y los captados por el satelite Sentinel-2. Se puede observar

que existe una buena correlacion entre ambos datos. Ademas, la etapa en que se

encuentran nuestras medidas coincide con la etapa de menor variacion en terminos


19-07 30-07

23-08

11-08 18-08

Figura 3.14: Imagenes captadas con camara Parrot Sequoia para distintas fechas.


19-07 30-07

23-08

11-08 18-08

Figura 3.15: Imagenes NDVI captadas con camara Parrot Sequoia para distintasfechas


200 205 210 215 220 225 230 2350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

NDVI

doy

Figura 3.16: Evolucion temporal promedio y desviacion del NDVI para los datoscaptados con la camara Parrot Sequoia (en rojo)


de NDVI, debido a que el cultivo se encuentra en etapas de desarrollo donde este

ındice se encuentra en estado de saturacion, ver figura 3.18.

160 180 200 220 240 260 280 3000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

NDVI

DOY

Sentinel-2

Sequoia

Figura 3.17: Evolucion temporal promedio y desviacion del NDVI para los datoscaptados con la camara Parrot Sequoia (en rojo) y con el Sentinel-2 (en azul)


200 205 210 215 220 225 230 2350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

NDVI

DOY

Sentinel-2

Sequoia

Figura 3.18: Evolucion temporal promedio y desviacion del NDVI para los datoscaptados con la camara Parrot Sequoia (en rojo) y con el Sentinel-2 (en azul)


3.2.6. Conclusion

De este estudio hemos comprobado la buena correlacion entre los datos opticos

que iran embarcados en el UAV y los datos complementarios que podemos obtener

a traves de los satelites. Debido a problemas hardware con el sensor laser no se ha

podido disponer de estos datos para su analisis. Este trabajo ha servido para elaborar

un primer prototipo de un sistema de medidas que permita generar los modelos de

prediccion para cada sensor. Este sistema puede ser instalado en cualquier lugar para

caracterizar el comportamiento de cultivos de arroz u otro tipo de cultivos. Aunque

en este capıtulo no se ha podido disponer de un gran numero de datos, actualmente se

han corregido los errores y problemas hardware, sustituyendo el sensor laser por uno

de mayores prestaciones. La estacion base se volvio a instalar el dıa 5 de junio de 2018

y se espera tener el sistema funcionando hasta finalizar la campana el mes de octubre

de 2018. Ademas, se instalo un sensor de temperatura que mide la temperatura cada

hora. Con estos nuevos datos y los adquiridos en la campana anterior se podran

elaborar y entrenar los modelos para proceder a su montaje sobre el UAV.


Capıtulo 4

Conclusiones

Actualmente, y cada vez mas, el numero de sistemas de monitorizacion remota

crece dotandonos de una mayor cantidad de datos de observacion. El como extraer

de ellos la mayor cantidad de informacion es crucial para elaborar herramientas de

estimacion precisas. Dado que en otros campos el uso de un enfoque dinamico se

ha mostrado como la mejor solucion, en esta tesis se ha elaborado y presentado una

metodologıa basada en un enfoque dinamico para explotar el uso de series temporales

de teledeteccion.

Se plantea el uso de espacio de estados como un medio eficaz para determinar el

estado de un objeto bajo observacion remota. Esta metodologıa nos permite reforzar

las propias observaciones con estimaciones procedentes de un modelo de prediccion.

Para combinar la observacion y la prediccion se ha propuesto el uso del Filtro de

partıculas. Se trata de distribuir un determinado numero de elementos (partıculas) en

nuestro espacio de estados, quedando definidas por dos valores: la posicion (estado)

y su peso (probabilidad de ser el estado correcto). La evolucion y la actualizacion de

las muestras con el paso del tiempo da lugar a una funcion densidad de probabilidad

123

Capıtulo 4. Conclusiones 124

que representa la probabilidad del estado del sistema.

Este enfoque nos ha permitido abordar la estimacion fenologica del arroz empleando

distintas fuentes de observacion. En concreto, se han utilizado imagenes satelitales

opticas y RADAR tanto en banda X como en banda C. Tambien datos de sensores

que iran embarcados en UAV, como camaras multiespectrales o sensores laser y

datos de temperatura adquiridos por estaciones bases. Ademas de la posibilidad de

detectar el estado actual del cultivo, en la seccion 2.1 se muestra el potencial del

uso de los modelos para predecir en que momento se va a alcanzar o se alcanzo una

determinada etapa.

Uno de los puntos fuertes de esta metodologıa se ha demostrado en la seccion 2.2.

A diferencia de otro tipo de tecnicas, gracias a trabajar con un filtro iterativo

podemos disponer de un sistema de estimaciones en tiempo real. Es decir, que no

es necesario disponer de toda la serie de datos para poder determinar el estado

actual, sino que cada vez que una observacion esta disponible procedemos a realizar

la estimacion.

Por otro lado, esta estrategia da solucion a como fusionar datos de distinta

naturaleza en un marco de trabajo comun. Por ejemplo, en la seccion 2.3 se han

combinado series de datos opticos, RADAR y temperatura para estimar el estado

fenologico del arroz. Se demostro que la posibilidad de usar diversos canales de datos

mejora el resultado de las estimaciones finales. Al reducir el tiempo de revisita, las

predicciones son menos imprecisas y logramos reducir el error total. El disponer de

sensores complementarios nos permite ser sensibles a un mayor abanico de fenomenos

del que podemos detectar trabajando con un unico tipo de sensor. El aumento en la

sensibilidad se traduce en mejores estimaciones. Si bien en este trabajo se utilizaron


tres fuentes de observacion concretas, la metodologıa nos permite anadir nuevas o

sustituirlas por otras diferentes. Con lo cual, tenemos una herramienta solida para

fusionar series de datos de teledeteccion.

Los trabajos realizados sirven de guıa para los usuarios que quieran emplear el

enfoque dinamico en el marco de la teledeteccion. En la seccion 3.1 se detalla un

ejemplo de como confeccionar los modelos de prediccion y observacion utilizando un

espacio de estados en 3 dimensiones. En este caso se utilizan observaciones del satelite

Sentinel-1 para definir 2 de las dimensiones y se anade la temperatura para conformar

la tercera. Se demuestra como el anadir datos de distinta naturaleza nos ayuda a

detectar determinados eventos. Ademas de los modelos, se explica como realizar la

etapa de filtrado. Esta etapa nos permite combinar las inferencias realizadas por

cada uno de los modelos, dando mas peso a las observaciones menos ruidosas que a

la prediccion y en caso contrario mas peso a la prediccion. En este caso, el sensor

utilizado solo dispone de datos en dos polarizaciones VV y VH, dado que el Sentinel-1

carece de la polarizacion HH que a priori es la mas sensible a los cambios en los

cultivos. Sin embargo, cuenta con un tiempo de revisita muy bajo, en torno a 3-6 dıas

en Europa. Esta metodologıa permite compensar la menor resolucion polarimetrica

aprovechar el elevado numero de datos que es capaz de generar.

En definitiva, se plantearon y desarrollaron una serie de herramientas que permiten

abordar problemas en el ambito de la teledeteccion y que permiten sacar el maximo

provecho al uso de series temporales, algo que cada vez esta siendo mas frecuente

hoy en dıa. Actualmente, hay algunas empresas que estan dando cobertura global y

de alta resolucion de forma diaria. Es entonces cuando este tipo de tecnicas pueden

sacar el maximo provecho de todos esos datos.


Apendice A

Publicaciones en congresos

1. C. De Bernardis, F. Vicente-Guijalba, T. Martinez-Marin y J. M. Lopez-Sanchez,

“ Particle filter approach for crop phenological stage estimation using time series of

NDVI images” en 2015 IEEE International Geoscience and Remote Sensing Symposium

(IGARSS), pp.3385-3388, Milan (Italia), Julio 2015.

2. C. De Bernardis, F. Vicente-Guijalba, T. Martinez-Marin y J. M. Lopez-Sanchez,

“Monitorizacion de la fenologıa en cultivos de arroz en tiempo real empleando imagenes

de NDVI y filtrado de partıculas,” en Actas XVI Congreso de la Asociacion Espanola

de Teledeteccion, pp.52-55, Sevilla (Espana), Ocutbre 2015.

3. J. M. Lopez-Sanchez, F. Vicente-Guijalba, C. De Bernardis y T. Martinez-Marin,

“Monitorizacion de una campana completa de cultivo de arroz mediante imagenes

radar polarimetricas en banda C: resultados y aplicaciones,” en Actas XVI Congreso

de la Asociacion Espanola de Teledeteccion, pp.52-55, Sevilla (Espana), Ocutbre

2015.

127

Apendice A. Publicaciones en congresos 128

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