Novel robust minimum error entropy wasserstein distribution kalman filter under model uncertainty and non-gaussian noise

Abstract

Recently, the divergence-based minimax approach was proposed and introduced to robust Kalman filtering under model uncertainty and Gaussian noise, and it significantly outperformed the standard Kalman filter. In this study, we consider a new Wasserstein-distribution based Kalman filter in which model uncertainty and non-Gaussian noise exist simultaneously. First, we construct a joint Gaussian distribution of states and observations in state space. Then, we set the equivalent estimator joint Gaussian distribution as a Wasserstein ambiguity set allowable neighborhood centered on the true distribution. Thus, the estimator distribution problem is transformed into a minimax problem, and the model uncertainty is tolerated accordingly. Subsequently, we introduce minimum error entropy to optimize the minimax problem based on Wasserstein ambiguity sets, so as to handle the influence of non-Gaussian noise. The minimax problem constrained by the minimum error entropy is transformed into a semi-positive definite convex optimization problem. By constructing two iterative sub-problems that are mutually conditional, the nonlinear semi-definite program finite convex optimization problem is solved. Finally, the minimum error entropy Wasserstein distribution Kalman filter algorithm is proposed. Additionally, the convergence of the proposed algorithm is clarified, and its effectiveness verified by comparing a series of algorithms in typical simulation scenarios.