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State estimation of stochastic systems with switching measurements: A polynomial approach
Author(s) -
Germani A.,
Manes C.,
Palumbo P.
Publication year - 2009
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1441
Subject(s) - control theory (sociology) , filter (signal processing) , computer science , polynomial , gaussian , algorithm , filtering problem , markov chain , mathematical optimization , mathematics , filter design , mathematical analysis , physics , control (management) , quantum mechanics , artificial intelligence , computer vision , machine learning
Abstract The state estimation problem is here investigated for a class of stochastic linear switching‐output systems, in which the output matrix switches in a finite set of possible values according to a not directly measured discrete Markov sequence. This note presents a real‐time algorithm, based on the optimal polynomial filtering approach, which achieves the simultaneous estimation of both the continuous system state and the switching parameter. The state and observation noises do not need to be Gaussian. It is shown that the optimal filter of degree one (best affine filter) does not solve the parameter estimation problem, due to a structural first‐order unobservability property, and therefore the use of higher‐order filters becomes necessary. As an application of the proposed filter, the problem of the online simultaneous estimation of the transmitted signal and of the impulse response samples of a multipath fast‐fading digital communication channel is considered in this paper. Differently from other approaches, the polynomial filter solves the problem without the use of training sequences (preambles) in the transmitted data, so that the information flow through the channel is not interrupted. Copyright © 2009 John Wiley & Sons, Ltd.