Design of FIR Smoother Using Covariance Information for Estimating Signal at Start Time in Linear Continuous Systems

This paper, as a first attempt, examines to design the recursive least-squares (RLS) finite impulse response (FIR) smoother, which estimates the signal at each start time of the finite-time interval in linear continuous-time stochastic systems. It is assumed that the signal is observed with additive white noise and is uncorrelated with the observation noise. It is a characteristic that the FIR smoother uses the covariance information of the signal process in the form of the semi-degenerate kernel and the variance of the observation noise besides the observed value. This paper also presents the recursive algorithm for the estimation error variance function of the RLS-FIR smoother to show the stability condition of the smoother.