On the estimation of noise covariances in linear discrete-time systems

Abstract

This paper is concerned with an approach for estimating or tracking the time-varying input and measurement noise covariances in time-varying discrete-time linear systems. The approach is firstly to introduce the estimators for the case where the noise co-variances are unknown constants. (The estimators are defined as the mean squares of the estimators of noises based on all the available measurement data.) They arc then transformed in sequential form, and are subsequently modified by incorporating a fading memory to yield estimates for time-varying noise covariances. The time-varying noise covariance estimates are evaluated as the fading mean squares of the estimates of noises based on all the measurement data up to present time. A numerical example for a simple system indicates acceptable performance of the proposed method.