Empirical Bayes Estimation of Observation Error Variances in Linear Systems

Abstract

A filter set is developed for estimating the state vector and observation error variances in a discrete-time linear system by use of empirical Bayes techniques. The error variances are assumed to be random and to vary over time. No initial conditions or distributional assumptions are required for the error variances, but all other assumptions for the Kalman filter are assumed to hold. The treatment is analytical, and a Monte Carlo simulation is used to verify the results. Graphs are presented which compare performance with the ideal case of known variances. The filter was found to converge fairly rapidly for the examples considered.