Robust Filtering of Discrete-Time Linear Systems With Correlated Process and Measurement Noises

Abstract

The Gaussian noise assumption is only an approximation to reality and practical engineering systems are often subject to non-Gaussian disturbances, instrument failures and human errors, which all induce outliers. This paper deals with the problem of robust filter design for discrete-time linear systems with correlated process and measurement noises. In the presence of correlated noises, the impact of outliers may spread through correlations and even cause the breakdown of a robust estimator. To address this issue, the robust estimation problem is formulated as a regularized linear regression problem in which the outliers are explicitly modeled and regularized with $\ell _{1}$ -norm to promote sparse solutions. Because of the explicit modeling of outliers, their negative influences propagated through correlations can be estimated and reduced. Hence more accurate estimation results can be expected. By selecting an appropriate regularization parameter, the proposed filter reduces to the well-known Kalman filter and hence is capable of providing a good balance between robustness and optimality. Besides, the extra flexibility of assigning different weights to state and measurement outliers makes it possible to put more focus on outliers from a specific source. Examples using both simulated and experimental data demonstrate the effectiveness of the proposed robust filtering approach.