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
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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