RLS Filter Using Covariance Information and RLS Wiener Type Filter based on Innovation Theory for Linear Discrete-Time Stochastic Descriptor Systems

  • Seiichi Nakamori Kagoshima University
Keywords: Discrete-time stochastic systems, RLS Wiener type filter, Covariance information, Descriptor systems; Innovation theory

Abstract

It is known that the stochastic descriptor systems are transformed into the conventional state equation, the observation equation and the other equation, by using the singular value decomposition. Based on the preliminary problem formulation for the linear discrete-time stochastic descriptor systems in section 2, this paper, in Theorem 1, based on the innovation theory, proposes the recursive least-squares (RLS) filter using the covariance information of the state vector in the state equation and the covariance information of the observation noise in the observation equation. The state equation and the observation equation are transformed from the descriptor systems. Secondly, in Theorem 2, based on the innovation theory, this paper proposes the RLS Wiener type filter for the descriptor systems. It might be advantageous that these filtering algorithms in this paper are derived based on the innovation theory in a unified manner.

A numerical simulation example is demonstrated to show the estimation characteristics of the proposed RLS Wiener type filtering algorithm for the descriptor systems.

References

J. Feng, T. Wang and J. Guo, Recursive estimation for descriptor systems with multiple packet dropouts and correlated noises, Aerospace Science and Technology, 32(2014) 200-211.

M. H. Terra, J. Y. Ishihara and A. C. Padoan Jr., Information filtering and array algorithms for descriptor systems subject to parameter uncertainties, IEEE Trans. Signal Processing, 55(2002) 1-9.

J. Y. Ishihara, M. H. Terra and J. C. T. Campos, Robust Kalman filter for descriptor systems, IEEE Trans. Automatic Control, 31(2006) 1354-1358.

J. Y. Ishihara, M. H. Terra and J. C. T. Campos, Optimal recursive estimation for discrete-time descriptor systems, International Journal of Systems Science, 36(2005) 605-615.

J. Y. Ishihara and M. H. Terra, Robust state prediction for descriptor systems, Automatica, 44(2008) 2185-2190.

J. Sjöberg, Descriptor Systems and Control Theory, Division of Automatic Control Department of Electrical Engineering Linköpings universitet, SE-581 83 Linköping, Sweden WWW: http://www.control.isy.liu.se, 26th April 2005.

A. P. Sage and J. L. Melsa, Estimation Theory with Applications to Communications and Control, New York: McGraw-Hill, 1971.

S. Nakamori, Recursive estimation technique of signal from output measurement data in linear discrete-time systems, IEICE Trans. Fundamentals of Electronics, Communication and Computer Sciences, E78-A (5) (1995) 600–607.

Published
2018-08-29
Section
Research Articles