Consensus‐based approach for parameter and state estimation of agro‐hydrological systems

Abstract

The development of advanced closed-loop irrigation systems requires accurate soil moisture information. In this work, we address the problem of soil moisture estimation for the agro-hydrological systems in a robust and reliable manner. A nonlinear state-space model is established based on the discretization of the Richards equation to describe the dynamics of agro-hydrological systems. We consider that model parameters are unknown and need to be estimated together with the states simultaneously. We propose a consensus-based estimation mechanism, which comprises two main parts: 1) a distributed extended Kalman filtering algorithm used to estimate several model parameters; and 2) a distributed moving horizon estimation algorithm used to estimate the state variables and one remaining model parameter. Extensive simulations are conducted, and comparisons with existing methods are made to demonstrate the effectiveness and superiority of the proposed approach. In particular, the proposed approach can provide accurate soil moisture estimate even when poor initial guesses of the parameters and the states are used, which can be challenging to be handled using existing algorithms.

State estimation for one‐dimensional agro‐hydrological processes with model mismatch

“…After substituting Equation ( 16) into the above Equation (15), we can obtain the recursive form for the likelihood of complete data, as shown below:…”

“…On the other hand, precise estimation of soil parameters is also crucial. [15] Parameter estimation holds significant importance in the domain of chemical engineering, as it plays a pivotal role in refining and optimizing process models. [16] In recent times, significant attention has been given to the challenge of parameter estimation for nonlinear functions and auxiliary models.…”

Data‐driven parallel Koopman subsystem modeling and distributed moving horizon state estimation for large‐scale nonlinear processes

“…This ensures the generated data can represent an accurate numerical approximation of the Richards equation in (25). Following the discretization procedure and the boundary conditions adopted in Yin et al 19 and Bo et al, 54 a two-point forward difference can be conducted to approximate the time derivatives, and a two-point central difference can be conducted to approximate the spatial derivatives. With discretization in both time and space, the dynamic model in (25) can be simulated to generate soil moisture samples for different locations of the soil profile.…”

“…To provide optimal estimates in the presence of constraints, distributed moving horizon estimation approaches were proposed. 19,20 More relevant results on distributed state estimation can be found in References 21-23. It is worth mentioning that the aforementioned methods assume high-fidelity (first-principles) system/process models are available, and good estimation performance is premised on the high accuracy of the existing dynamic model. However, from an application perspective, it can be challenging to establish a first-principles model with accurate model parameters due to the availability of very limited first-principles knowledge-this is especially critical when dealing with large-scale complex nonlinear processes.…”

“…The weighting matrices are set as follows: P i,0 ¼ 0:1  I 36 , 19 and Bo at al. 54 Specifically, the estimates of the soil moisture are required to stay within ½À1:0, À 1:0  10 À6 as has been employed in Yin et al 19 It is noted that these constraints are imposed on the first state to the 12th state of each local estimator that represents the soil moisture in the 12 compartments of the same subsystem. No constraints need to be imposed on the 24 lifted state variables of the subsystems.…”