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

This paper newly designs the recursive least-squares fixed-lag smoother using the covariance information in linear discrete-time stochastic systems. It is assumed that the signal is observed with additive white observation noise and the signal is uncorrelated with the observation noise. The fixed-lag smoother uses the covariance function of the signal in the semi-degenerate kernel form and the variance of the observation noise. The proposed fixed-lag smoother is suitable for the estimations of stationary or non-stationary stochastic signals generally.