RLS Fixed-Lag Smoother Using Covariance Information Based on Innovation Approach in Linear Continuous Stochastic Systems

This paper newly designs the RLS (recursive least-squares) fixed-lag smoother and filter, based on the innovation theory, in linear continuous-time stochastic systems. It is assumed that the signal is observed with additive white noise and the signal is uncorrelated with the observation noise. It is a characteristic that the estimators use the covariance information of the signal, in the form of the semi-degenerate kernel, and the observation noise. With respect to the RLS fixed-lag smoother, the algorithm for the estimation error variance function is developed to guarantee the stability of the fixed-lag smoother. The proposed estimators have the recursive property in calculating the fixed-lag smoothing and filtering estimates. Also, this paper proposes the Chandrasekhar-type RLS Wiener filter in linear wide-sense stationary stochastic system. Unlike the usual filter including the Riccati-type equations, the Chandrasekhar-type filter does not contain the Riccati-type differential equations and has an advantage of eliminating the possibility of the covariance matrix becoming nonnegative.