Robust RLS Wiener Fixed-Lag Smoother for Discrete-Time Stochastic Systems with Uncertain Parameters
Keywords:Robust RLS Wiener estimator; fixed-lag smoother; discrete-time stochastic systems; uncertain parameters; auto-regressive model
This paper, by combining the robust recursive least-squares (RLS) Wiener filter and the RLS Wiener fixed-lag smoothing algorithm, proposes the robust RLS Wiener fixed-lag smoothing algorithm. In the robust estimation problem, it is assumed that the system and observation matrices include some uncertain parameters. With the observations generated by the state-space model including the uncertain parameters, the robust RLS Wiener fixed-lag smoother estimates the signal recursively as the time advances. Both the signal and the degraded signal processes are fitted to the finite order auto-regressive (AR) models. The robust RLS Wiener fixed-lag smoother uses the following information. (1) The covariance function of the state for the degraded signal. (2) The cross-covariance function of the state for the signal with the state for the degraded signal. (3) The observation matrices for the signal and the degraded signal. (4) The system matrices for the signal and the degraded signal. (5) The variance of the white observation noise. A numerical simulation example shows that the robust RLS Wiener fixed-lag smoother, proposed in this paper, is superior in estimation accuracy to the H-infinity RLS Wiener fixed-point smoother and the RLS Wiener fixed-lag smoother. In the appendix, by using MAXIMA and MATLAB, the derivation method of the coefficients, used in the robust RLS Wiener fixed-lag smoothing algorithm, is shown.
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