Design of RLS Wiener fixed-lag smoother using covariance information in linear discrete stochastic systems

In this paper, we propose a new design for the recursive least-squares (RLS) Wiener fixed-lag smoother and filter in linear discrete-time wide-sense stationary stochastic systems. It is assumed that the signal is observed with additive white observation noise. The signal is uncorrelated with the observation noise. The estimators require knowledge of the system matrix, the observation matrix and the variance of the state vector. These quantities can be obtained from the auto-covariance function of the signal. In the estimation algorithms, moreover, the variance of the observation noise is assumed to be known, as a priori information.