Robust RLS Wiener Fixed-Interval Smoother in Linear Discrete-Time Stochastic Systems with Uncertain Parameters
This paper proposes the robust RLS Wiener filter and fixed-interval smoothing algorithms based on the innovation approach. As a result, the robust RLS Wiener filtering algorithm is same as the existing robust RLS Wiener filtering algorithm. The estimation accuracy of the fixed-interval smoother is compared with the robust RLS Wiener filter and the following fixed-interval smoothers. In the proposed robust RLS Wiener fixed-interval smoother, the case, where the observed value is replaced with the robust filtering estimate of the signal, is also simulated. (1) The RLS Wiener fixed-interval smoother in which the filtering estimate of the state is replaced with the robust RLS Wiener filtering estimate. (2) The RTS (Rauch-Tung-Striebel) fixed-interval smoother in which the filtering estimate of the state is replaced with the robust RLS Wiener filtering estimate. (3) The RLS Wiener fixed-interval smoother and the RLS Wiener filter. (4) The RLS Wiener fixed-interval smoother in which the filtering estimate of the state is replaced with the robust RLS Wiener filtering estimate and the observed value is replaced with the robust RLS Wiener filtering estimate of the signal. From the simulation results, the most feasible estimation technique for the fixed-interval smoothing estimate is the RLS Wiener fixed-interval smoother. Here, the robust filtering estimate is used and the observed value is replaced with the robust filtering estimate.
F. L. Lewis, L. Xie, and D. Popa, Optimal and Robust Estimation, with an Introduction to Stochastic Control Theory, Second Edition, New York: CRC Press, 2008.
M. S. Mahmoud, Robust Control and Filtering for Time-Delay Systems, New York: Marcel Dekker, 2000.
H. Gao and X. Li, Robust Filtering for Uncertain Systems, A Parameter-Dependent Approach, New York: Springer, 2014.
X. H. Chang, Robust Output Feedback H-inﬁnity Control and Filtering for Uncertain Linear Systems, New York: Springer, 2014.
I. R. Peterson and A. V. Savkin, Robust Kalman Filtering for Signals and Systems with Large Uncertainties, Boston: Birkhauser, 1999.
X. Zhu, Y. C. Soh, and L. Xie, Design and analysis of discrete-time robust Kalman filters, Automatica, vol. 38, pp. 1069–1077, 2002.
F. Yang, Z. Wang and Y. S. Hung, Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises, IEEE Trans. Automat. Control, vol. 47, no.7, pp. 1179–1183, 2002.
Z. Duan, J. Zhang, and C. Zhang, Robust H_2 and H_∞ filtering for uncertain linear systems, Automatica, vol, 42, pp. 1919-1926, 2006.
F. Wang and V. Balakrishnan, Robust adaptive Kalman filters for linear time-varying systems with stochastic parametric uncertainties, in Proc. Amer. Control Conf., San Diego, CA, 1999, pp. 440–444.
S. Nakamori, Robust RLS Wiener signal estimators for discrete-time stochastic systems with uncertain parameters, Frontiers in Signal Processing, vol. 3, no. 1, pp. 1-18, 2019. DOI: 10.22606/fsp.2019.31001
S. Nakamori, Robust RLS Wiener FIR filter for signal estimation in linear discrete-time stochastic systems with uncertain parameters, Frontiers in Signal Processing, vol. 3, no. 2, 2019, pp. 19-36, 2019. DOI: 0.22606/fsp.2019.32001
S. Nakamori, A. Hermoso-Carazo, and J. Linares-Perez, Design of a fixed-interval smoother using covariance information based on the innovations approach in linear discrete-time stochastic systems, Applied Mathematical Modelling, vol. 30, no. 5, pp. 406-417, 2006.
H. E. Rauch, C. T. Striebel and F. Tung, Maximum likelihood estimates of linear dynamic systems”, discrete-time stochastic systems with uncertain parameters, AIAA Journal, vol. 3, no.8, pp.1445-1450, 1965.
D. Simon, Optimal State Estimation, Kalman, H_∞, and Nonlinear Approaches, New Jersey: John Wiley & Sons, 2006.
S. Nakamori, Design of linear discrete-time stochastic estimators using covariance information in Krein Spaces, IEICE Trans. Fundamentals of Electronics, Communication and Computer Sciences, vol. E85-A, no.4, pp.861-871, 2002.
S. Nakamori, H-infinity recursive Wiener fixed-interval smoother based on innovation approach in linear discrete-time stochastic systems, Horizons in Computer Science Research, Vol. 11, pp.145 – 157, New York: Nova Science Publishers, 2015.
A. P. Sage and J. L. Melsa, Estimation Theory with Applications to Communications and Control, New York: McGraw-Hill, 1971.
Copyright (c) 2019 Seiichi Nakamori
This work is licensed under a Creative Commons Attribution 4.0 International License.
The author warrants that the article is original, written by stated author(s), has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author(s).