Robust RLS Wiener Signal Estimators for Discrete-Time Stochastic Systems with Uncertain Parameters

Abstract

This paper proposes the robust recursive least-squares (RLS) Wiener fixed-point smoother and filter in linear discrete-time stochastic systems with parameter uncertainties. The uncertain parameters exist in the observation matrix and the system matrix. The uncertain parameters cause to generate the degraded signal. In this paper, the degraded signal process is fitted to the finite order autoregressive (AR) model. The robust RLS Wiener estimators use the system matrices and the observation matrices for both the signal and the degraded signal, the variance of the state vector for the degraded signal, the cross-variance of the state vector for the signal with the state vector for the degraded signal, and the variance of the white observation noise. Also, this paper proposes the robust recursive fixed-point smoother and filter, by using the covariance information of the state vector for the degraded signal, the cross-covariance information of the state vector for the signal with the state vector for the degraded signal, the observation matrices for both the degraded signal and the signal besides the variance of the white observation noise. In estimating the signal process expressed by the second order AR model, the proposed robust RLS Wiener filter is superior in estimation accuracy to the robust Kalman filter and the RLS Wiener filter.

Robust Recursive Least-Squares Finite Impulse Response Predictor in Linear Discrete-Time Stochastic Systems with Uncertain Parameters

“…Also, from the auto-covariance functi on ̆ ̆ of the degraded signal ̆ , the auto-variance function , of the state is expressed as , and into the robust RLS Wiener FIR prediction algorithm of Theorem 3, the prediction estimates are calculated recursively. In evaluating Φ in (7), , in (66) and , in (67), the 2,000 number of signal an d degraded signal data are used. Fig.1 3, for the white Gaus sian observation noises 0,0.…”

“…The recursive least-squares (RLS) Wiener estimators use the complete information of the state-space model but the information of the input matrix and the input n oise variance [6]. For the discrete-time stochastic sy stems with the uncertain parameters, in the estim ation of the signal, the robust RLS Wiener estimators [7] and the robust RLS Wiener finite im pulse response filter [ 6] are proposed. The estimation accuracy of the robust RLS Wiener esti mators [7] are superior to the robust Kalman filter [9] and the RLS Wiener filter [6].…”

“…For the discrete-time stochastic sy stems with the uncertain parameters, in the estim ation of the signal, the robust RLS Wiener estimators [7] and the robust RLS Wiener finite im pulse response filter [ 6] are proposed. The estimation accuracy of the robust RLS Wiener esti mators [7] are superior to the robust Kalman filter [9] and the RLS Wiener filter [6]. The FIR Kal man filter [10]- [14] is l ess sensitive to the uncertainties in the state-space model.…”

“…The FIR Kal man filter [10]- [14] is l ess sensitive to the uncertainties in the state-space model. In Nakam ori [8] it is shown that, as the finite interval increases, the mean square-value (MSV) of the estimation errors by the robust RLS Wiener FIR filter [ 8] becomes gradually small and approaches that by the r obust RLS Wiener filter [7]. Nakamori [15] proposes the RLS Wie ner FIR prediction and filtering algorithms based on the innovation approach in linear discrete-time stochastic systems.…”