Soil Moisture Estimation for Large-scale Agro-hydrological Systems with Model Mismatch

Developing a precise irrigation control strategy is essential for improving water use efficiency, and this requires accurate soil moisture information. However, certain challenges associated with state estimation must be addressed when dealing with large-scale fields. For instance, a vast farmland may be composed of different types of soil, making it challenging to obtain accurate parameters. Consequently, model mismatch becomes inevitable for agro-hydrological systems. In this study, we focus on addressing the issue of state estimation under such circumstance. A high dimensional nonlinear system is obtained by discretizing a 3D polar Richards equation that characterizes water movement dynamics. The proposed approach represents model mismatch as unknown inputs (UIs) relative to the state equations. To reduce computational complexity, a recursive expectation-maximization (EM) approach is modified from the existing batch EM algorithm to identify the UIs. The extended Kalman filter (EKF) is applied to calculate the posterior expectation of the states. Furthermore, an appropriate set of sensors is chosen to ensure complete observability of the system. The simulation results demonstrate the efficacy of the proposed estimation method.