Design of fixed-lag smoother using covariance information based on innovations approach in linear discrete-time stochastic systems

This paper newly designs the recursive least-squares (RLS) Wiener fixed-lag smoother and filter using the covariance information in linear discrete-time stochastic systems. The estimators require the information of the observation matrix, the system matrix for the state variable, related with the signal, the variance of the state variable, the cross-variance function of the state variable with the observed value and the variance of the white observation noise. It is assumed that the signal is observed with additive white noise. The current fixed-lag smoothing algorithm has a characteristic, as shown in Theorem 1, that the fixed-lag smoothing estimate of the state vector is calculated in the reverse direction of time.