Isaac Scientific Publishing

Frontiers in Signal Processing

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

Download PDF (427.4 KB) PP. 1 - 18 Pub. Date: January 10, 2019

DOI: 10.22606/fsp.2019.31001

Author(s)

  • Seiichi Nakamori
    Department of Technology, Faculty of Education, Kagoshima University, Kagoshima, Japan

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.

Keywords

Discrete-time stochastic systems; robust RLS Wiener filter; robust RLS Wiener fixedpoint smoother; robust estimation technique; uncertain parameters.

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