Adaptive EKF Filtering Based on Model Feature Constraints

In the realm of state estimation for the majority of practical engineering applications, nonlinear systems have been prevalent. Traditional Kalman filtering, rooted in model feature constraint theory, exhibited limitations by being restricted to linear systems and proved inadequate for addressing nonlinear systems. In response to this challenge, this paper introduces a novel Nonlinear Adaptive Kalman Filtering approach that extends the application of model feature constraint theory to nonlinear systems. Firstly, the paper leverages the EKF filtering framework as a foundation and derives the optimal estimation theory for Gaussian noise statistical feature constraints (model parameter ratios) in nonlinear systems. A series of theoretical proofs are presented to verify the existence of Gaussian model parameter ratio features in nonlinear systems. Secondly, the paper combines model parameter ratios with covariance matching and introduces corresponding parameter estimation criteria for nonlinear systems. This approach transforms the adaptive filtering problem into an optimization problem with constraints. To obtain the optimal solution for estimating the system model, the Wild Horse Optimizer is employed to solve this optimization problem. Ultimately, by revealing and validating the existence of model parameter ratios in optimal nonlinear Kalman filtering, the feasibility of the proposed method is demonstrated. Experimental results further affirm the applicability of model feature constraint theory in nonlinear systems.