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Frontiers in Signal Processing
FSP > Volume 3, Number 2, April 2019

Robust RLS Wiener FIR Filter for Signal Estimation in Linear Discrete-Time Stochastic Systems with Uncertain Parameters

Download PDF  (944.7 KB)PP. 19-36,  Pub. Date:May 5, 2019
DOI: 10.22606/fsp.2019.32001

Author(s)
Seiichi Nakamori
Affiliation(s)
Department of Technology, Faculty of Education, Kagoshima University, Kagoshima, Japan
Abstract
This paper proposes the robust recursive least-squares (RLS) finite impulse response (FIR) filtering algorithm using the covariance information and the robust RLS Wiener FIR filtering algorithm in linear discrete-time stochastic systems with the parameter uncertainties. The observation and system matrices contain the uncertain parameters. The uncertain parameters cause the degraded signal. Theorem 2 proposes the robust RLS FIR filter 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 the signal and the degraded signal, and the variance of the white observation noise. Here, it is assumed that the signal and the degraded signal are fitted to the finite-order autoregressive (AR) models. Theorem 3 proposes the robust RLS Wiener FIR filter. The robust RLS Wiener FIR filtering algorithm uses the system and observation matrices for the signal and the degraded signal, the variance of the state vector for the degraded signal, the cross-variance function of the state vector for the signal with the state vector for the degraded signal, and the variance of the white observation noise.
Keywords
Robust RLS Wiener FIR filter; covariance information; Wiener- Hopf equation; uncertain parameters; degraded signal.
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