Moving Horizon Estimator with Pre-Estimation for Crop Start Date Estimation in Tropical Area

Accurate crop start date estimation is crucial for crop yield forecasting which is important not only for a government but also for agriculture-based or trading companies. The estimation can be done using the Normalized Difference Vegetation Index (NDVI) computed from radiant energy from the crops of interest. The NDVI collected from the Moderate Resolution Imaging Spectroradiometer (MODIS) aboard the Terra satellite is chosen in this study thanks to its free availability which is suitable for a developing country. In a tropical country as Thailand, the NDVI data is very noisy due to high density of clouds. An appropriate estimation technique must therefore be implemented. In this paper, the NDVI is modelled by a triply modulated cosine function with the mean, the amplitude and the initial phase as state variables. The state and the NDVI of single rice crop in the northeast Thailand are estimated using the Extended Kalman Filter (EKF), the Unscented Kalman Filter (UKF), the Moving Horizon Estimator (MHE) and the Moving Horizon Estimator with Pre-Estimation (MHE-PE). The MHE-PE, recently proposed in the literature, is an optimization-based estimator using an auxiliary estimator to describe the dynamics of the state over the horizon which has been shown to overcome the classical MHE strategy in terms of accuracy and computation time. The EKF and the MHE-PE provide the smallest start date estimation error compared to the others, which is 0 day in mean and 18 days in standard deviation. However, the EKF fail to detect the NDVI of pre-plant crops and parasite weeds while the MHE-PE does not.