Estimation of optimal Kalman filter gain from nonoptimal filter residuals

摘要

Abstract: This paper presents a novel method of estimating the optimal steady state Kalman filter gain of a linear discrete time-invariant system from a non-optimal Kalman filter residual sequence. The relation between the optimal residual sequence and a signal derived from the non-optimal residual sequence is described by a moving average (MA) model whose coefficients are expressed in terms of the state space parameters and the optimal steady state Kalman filter gain. In order to identify the MA model, a whitening filter of the derived signal, which corresponds to an autoregressive (AR) model of the signal, is first identified using the least- squares method. Then the inverse filter of the whitening filter, which corresponds to the MA model, is calculated. From the coefficients of the identified MA model, the optimal steady state Kalman filter gain can be obtained. Numerical example is provided to illustrate the feasibility of this approach. !11