WSEAS Transactions on Circuits and Systems
Print ISSN: 1109-2734, E-ISSN: 2224-266X
Volume 24, 2025
Robust Recursive Least-Squares Fixed-Point Smoother and Filter with Polynomial Approximation of Covariance Information for Linear Continuous-Time Stochastic Systems with Uncertainties
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Abstract: The author previously introduced a robust recursive least-squares (RLS) fixed-point (FP) smoothing and filtering algorithm tailored for uncertain linear continuous-time stochastic systems. These estimators rely on covariance information, specifically the cross-covariance between the true signal and the observed data, as well as the auto-covariance of the degraded observations. Although prior research employed finite Fourier series expansions to approximate these covariance functions, the present study instead adopts polynomial representations for both the cross-covariance and auto-covariance functions. Numerical simulation results demonstrate that the mean-square values (MSVs) of the approximation errors are negligible, underscoring the high accuracy of the proposed polynomial-based method. Notably, the estimation accuracies achieved by both the filtering and FP smoothing algorithms remain nearly identical when using either finite Fourier series or polynomial approximations.
Keywords:
Robust RLS fixed-point smoother, robust RLS filter, degraded signal, stochastic systems with uncertainties, continuous-time stochastic systems, polynomial approximation, Fourier series expansion, covariance information
Pages: 373-384
DOI: 10.37394/23201.2025.24.36