Quadratic covariance‐constrained filtering for linear and non‐linear systems with non‐Gaussian noises

Abstract

This study considers a robust quadratic covariance‐constrained filtering problem for discrete time‐varying linear and non‐linear dynamic systems with non‐Gaussian noises. Non‐Gaussian noises are presumed to be unknown, bounded, and limited in a specified ellipsoidal set. In this approach, first, a general standard linear form of the filter is introduced for state estimation in linear dynamic systems. The filter gain is obtained by minimizing the upper bound of the estimation error's covariance matrix. The Lyapunov theory demonstrates the stability of this filter. Second, we extend the proposed filtering approach to non‐linear dynamic systems that are considered as a combination of linear and non‐linear terms. The Lipschitz‐like condition is assumed for the non‐linear part. A new filter structure is proposed in this case and the filter gain is obtained by the same idea to minimize the upper bound of the error's covariance matrix. Finally, four numerical examples are presented to signify the effectiveness and performance of the proposed filters for linear and non‐linear systems.