New design of fixed-interval smoother using covariance information in linear stochastic continuous-time systems

RLS Wiener FIR Predictor and Filter Based on Innovation Approach in Linear Discrete-Time Stochastic Systems

“…Starting with (9) and (10) for the optimal impulse response functions, we derive the RLS Wiener FIR prediction and filtering algorithms for the signal based on the invariant imbedding method [15], [16]. Theorem 1 presents the RLS Wiener FIR prediction and filtering algorithms.…”

“…In [15], the typos in the RLS Wiener FIR filtering algorithm [13] are corrected. In [16], the RLS-FIR smoother is presented in estimating the signal at each start time of the finite interval in linear continuous-time stochastic systems. Here, the auto-covariance function of the signal process is expressed in the semi-degenerate kernel form.…”

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

“…The fixed-interval smoothing and filtering algorithms are presented in Theorem 1. The corrected point in the expression of the impulse response function from that in the fixed-interval in [10] is clarified. The details are discussed after the proof of Theorem 1.…”

“…In [9], the optimal fixed-lag smoother and its error variance matrix are derived for the continuous linear systems with the white measurement noise. In [10], the RLS fixed-interval smoother, using the covariance information, is designed based on the innovation approach in linear continuous-time stochastic systems. Here, it is assumed that the observation noise is white.…”

“…Also, in [13], based on the innovation theory, the RLS Wiener fixed-interval smoothing algorithm is presented for the measurement with colored observation noise. This paper, by correcting the expression of the impulse response function in [10], newly proposes the 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.…”