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On‐line almost‐sure parameter estimation for partially observed discrete‐time linear systems with known noise characteristics
Author(s) -
Elliott Robert J.,
Ford Jason J.,
Moore John B.
Publication year - 2002
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.703
Subject(s) - estimator , mathematics , discrete time and continuous time , lemma (botany) , estimation theory , martingale (probability theory) , ordinary differential equation , convergence (economics) , noise (video) , parameter space , matrix (chemical analysis) , differential equation , computer science , algorithm , mathematical analysis , statistics , materials science , poaceae , composite material , artificial intelligence , economic growth , economics , image (mathematics) , biology , ecology
In this paper we discuss parameter estimators for fully and partially observed discrete‐time linear stochastic systems (in state‐space form) with known noise characteristics. We propose finite‐dimensional parameter estimators that are based on estimates of summed functions of the state, rather than of the states themselves. We limit our investigation to estimation of the state transition matrix and the observation matrix. We establish almost‐sure convergence results for our proposed parameter estimators using standard martingale convergence results, the Kronecker lemma and an ordinary differential equation approach. We also provide simulation studies which illustrate the performance of these estimators. Copyright © 2002 John Wiley & Sons, Ltd.