A Gaussian approximation filter for nonlinear systems with compound noises

In practical applications, measurements may contain many different noise components due to complex environments and other factors. The Gaussian approximation filter, constrained by its requirement for Gaussian characteristics in measurement noises, faces challenges in obtaining a satisfactory filtering performance under compound noise environments. In this article, an improved Gaussian approximation filter is designed for nonlinear systems with compound measurement noises. Hypothesis tests on the prior and posterior residuals are designed to identify the types of noise present in the system. Subsequently, a posterior residual-based adaptive compensation is proposed to mitigate the adverse effects of compound noise on the Gaussian approximation filter. Moreover, it is demonstrated that when the measurement acceptance rate exceeds a certain critical threshold, the estimation error remains bounded. Finally, the effectiveness of the proposed algorithm and analysis is validated through simulations in the context of target tracking.