WSEAS Transactions on Signal Processing
Print ISSN: 1790-5052, E-ISSN: 2224-3488
Volume 20, 2024
Robust Recursive Least-Squares Finite Impulse Response Filter in Linear Continuous-Time Stochastic Systems with Uncertainties
Author:
Abstract: The current research designs an original robust recursive least-squares (RLS) finite impulse
response (FIR) filter for linear continuous-time systems with uncertainties in both the system and observation
matrices. These uncertainties in the state-space model generate the degraded signal and observed value. The
robust RLS FIR filter does not account for the norm-bounded uncertainties in the system and observation
matrices. This study uses an observable companion form to represent the degraded signal state-space model.
The system and observation matrices are estimated based on the author's previous computational methods. The
robust RLS FIR filtering problem aims to minimize the mean-square errors in FIR filtering for the system state.
The robust FIR filtering estimate is formulated as an integral transformation of the degraded observations using
an impulse response function. Section 3 obtains the integral equation satisfied by the optimal impulse response
function. Theorem 1 presents the robust RLS FIR filtering algorithms for the signal and the system state. This
integral equation derives the robust RLS-FIR filtering algorithms. Numerical simulation examples show the
validity of the proposed robust RLS FIR filter.
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Keywords: Robust RLS FIR filter, degraded signal, stochastic systems with uncertainties, observable
companion form, continuous-time stochastic systems, covariance information
Pages: 92-108
DOI: 10.37394/232014.2024.20.11