Recursive Least-Squares Fixed-Interval Smoother Using Covariance Information based on Innovation Approach in Linear Continuous Stochastic Systems

Abstract

This paper newly proposes the recursive least-squares (RLS) fixed-interval 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 process is uncorrelated with the observation noise. It is a characteristic that the estimators use the covariance function of the signal, in the form of the semi-degenerate kernel, and the variance of the observation noise. Also, the algorithm for the estimation error variance function of the RLS fixed-interval smoother is developed to validate the stability of the proposed fixed-interval smoother. The numerical simulation example shows that the estimation accuracy of the proposed fixed-interval smoother is superior to that of the existing fixed-interval smoother using the covariance information.