Noise covariance matrix estimation with subspace model identification for Kalman filtering

Abstract

SummaryA problem frequently encountered in Kalman filtering is the tuning of the noise covariance matrices. Indeed, misspecifying their values can drastically reduce the performance of the Kalman filter. Unfortunately, in most practical cases, noise statistics are not known a priori. This paper focuses on a method relying on subspace model identification theory to determine them accurately. This solution is developed for linear time invariant systems with stationary random disturbances having constant covariance matrices. Practically, these noise covariance matrices are determined from the comparison between an estimated state space representation and the discrete time state space representation involved in the Kalman filter equations. The method developed in this paper departs from most of the solutions available in the literature by the fact that it does not need any tuning parameter to be chosen by the user. After discussing theoretical results, several numerical examples are given to demonstrate the efficiency of the approach.