Abstract
In the last decade, suboptimal Bayesian filtering (BF) techniques, such as Extended Kalman Filtering (EKF) and Particle Filtering (PF), have led to great interest for crop phenology monitoring with Synthetic Aperture Radar (SAR) data. In this study, a novel approach, based on the Grid-Based Filter (GBF), is proposed to estimate crop phenology. Here, phenological scales, which consist of a finite number of discrete stages, represent the one-dimensional state space, and hence GBF provides the optimal phenology estimates. Accordingly, contrarily to literature studies based on EKF and PF, no constraints are imposed on the models and the statistical distributions involved. The prediction model is defined by the transition matrix, while Kernel Density Estimation (KDE) is employed to define the observation model. The approach is applied on dense time series of dual-polarization Sentinel-1 (S1) SAR images, collected in four different years, to estimate the BBCH stages of rice crops. Results show that 0.94 ≤ R2 ≤ 0.98, 5.37 ≤ RMSE ≤ 7.9 and 20 ≤ MAE ≤ 33.
Highlights
Agricultural crops can be regarded as dynamical systems [20]
For a given parcel, at a given acquisition date, the mode of the estimated phenology of all the pixels is considered as the final BBCH estimate for the parcel
The performances of the estimations are discussed and carefully analyzed. These are around the ones obtained by the Particle Filtering (PF) approach applied on S1 VH products in [6], where the authors state that R2 = 0.96 and RMSE = 5.82 are achieved when the transplanting dates are estimated correctly
Summary
Agricultural crops can be regarded as dynamical systems [20]. Within this framework, the crop variables at discrete time tk (which include phenology, crop height, etc.) are referred to as state variables, and collected into a vector, the state vector xk , whose domain is known as state space [25].Since this study is focused on the estimation of only one state variable, phenology, hereinafter a one-dimensional system is considered to describe its evolution with time.We will explore the inter-relations between the state variables, i.e., considering a multidimensional state vector, in future studies.Such a one-dimensional system is shown in (1) [26], where x(tk ), i.e., the phenological stage at time tk , is denoted with xk . f (·) is the prediction model [22], and it is a function, generally non-linear, of the state at time tk−1 , xk−1 , with vk−1 being the system noise.xk = f (xk −1 , vk −1 ) (1)The SAR features measured at time tk are related to the state xk according to (2) [26].y k = h (xk , e k ) (2)Here, yk is the observation vector at time tk , which collects the SAR features relevant to the monitored crop at that time. h(·) is the observation model [22], a vector-valued function, generally non-linear, of xk , with ek being the observation noise. Agricultural crops can be regarded as dynamical systems [20] Within this framework, the crop variables at discrete time tk (which include phenology, crop height, etc.) are referred to as state variables, and collected into a vector, the state vector xk , whose domain is known as state space [25]. We will explore the inter-relations between the state variables, i.e., considering a multidimensional state vector, in future studies. Such a one-dimensional system is shown in (1) [26], where x(tk ), i.e., the phenological stage at time tk , is denoted with xk . F (·) is the prediction model [22], and it is a function, generally non-linear, of the state at time tk−1 , xk−1 , with vk−1 being the system noise. Note that the functions f (·) and h(·) are time-invariant here, since they depend on the state xk , and not on the time index k
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
