Optimal Grid-Based Filtering for Crop Phenology Estimation with Sentinel-1 SAR Data

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.