Robust Recursive Least-Squares Fixed-Point Smoother and Filter using Covariance Information in Linear Continuous-Time Stochastic Systems with Uncertainties-Reference-Cited by-同舟云学术

Robust Recursive Least-Squares Fixed-Point Smoother and Filter using Covariance Information in Linear Continuous-Time Stochastic Systems with Uncertainties

Published:2024-05-13 Issue: Volume:20 Page:9-19
ISSN:2224-3488
Container-title:WSEAS TRANSACTIONS ON SIGNAL PROCESSING
language:en
Short-container-title:

Author:

Nakamori Seiichi¹

Affiliation:

1. Professor Emeritus, Faculty of Education, Kagoshima University, 1-20-6, Korimoto, Kagoshima, 890-0065, JAPAN

Abstract

This study develops robust recursive least-squares (RLS) fixed-point smoothing and filtering algorithms for signals in linear continuous-time stochastic systems with uncertainties. The algorithms use covariance information, such as the cross-covariance function of the signal with the observed value and the autocovariance function of the degraded signal. A finite Fourier cosine series expansion approximates these functions. Additive white Gaussian noise is present in the observation of the degraded signal. A numerical simulation compares the estimation accuracy of the proposed robust RLS filter with the robust RLS Wiener filter, showing similar mean square values (MSVs) of the filtering errors. The MSVs of the proposed robust RLS fixed-point smoother are also compared to those of the proposed robust RLS filter.

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Reference30 articles.

1. U. Shaked and C. E. de Souza, Robust minimum variance filtering, IEEE Transactions on Signal Processing, Vol. 43, No. 11, 1995, pp. 2474-2483, DOI: 10.1109/78.482099.

2. C. E. de Souza, U. Shaked, M. Fu, Robust 𝐻∞ filtering for continuous time varying uncertain systems with deterministic input signals, IEEE Transactions on Signal Processing, Vol. 43, No. 3, 1995, pp. 709–719, DOI: 10.1109/78.370625.

3. F. L. Lewis, L. Xie, D. Popa, Optimal and Robust Estimation With an Introduction to Stochastic Control Theory, Second Edition, CRC Press, 2008.

4. S. O. R. Moheimani, A. V. Savkin, I. R. Petersen, Robust filtering, prediction, smoothing and observability of uncertain systems, IEEE Transactions on Circuits and Systems—I: Fundamental Theory and Applications, Vol. 45, No.4, 1998, pp. 446– 457, DOI: 10.1109/81.669068.

5. Z. Quan, S. Han, J. H. Park, W. H. Kwon, Robust FIR Filters for Linear Continuous- Time State-Space Models With Uncertainties, IEEE Signal Processing Letters, Vol. 15, 2008, pp. 621–624, DOI: 10.1109/LSP.2008.2004515.