Recursive least squares fixed-lag Wiener smoothing using autoregressive signal models for linear discrete-time systems

Abstract

This paper newly presents the recursive least-squares (RLS) fixed-lag smoother using the covariance information and then the RLS fixed-lag Wiener smoother in linear discrete-time wide-sense stationary stochastic systems. Here, the additional disturbance in the measurement of the signal is white noise. The signal is uncorrelated with the observation noise. It is assumed that the signal process is fitted to the autoregressive (AR) model of order N. For this AR model of order N, in the proposed fixed-lag smoother, the fixed-lag smoothing estimate for the fixed lag L,1⩽L⩽N-1, can be calculated. The RLS fixed-lag Wiener smoother requires the information of the system matrix, the autovariance function of the state vector, the observation vector, the variance of the observation noise and the coefficients, as a linear combination of K(k+i,s),0⩽i⩽L, for K(k-L,s). In numerical simulation examples, it is shown that the current RLS fixed-lag Wiener smoother shows the stable and feasible estimation characteristics in comparison with the RLS fixed-lag Wiener smoother previously proposed.