New Results on Optimal Joint Parameter and State Estimation of Linear Stochastic Systems

[+] Author and Article Information
G. Salut

L.A.A.S.-C.N.R.S. 7, 31400 Toulouse, France

J. Aguilar-Martin

Electronic Research Laboratory, University of California, Berkeley, Calif. 94720

S. Lefebvre

Department Génie Electrique, Ecole Polytechnique de Montréal, Québec H3C 3A7

J. Dyn. Sys., Meas., Control 102(1), 28-34 (Mar 01, 1980) (7 pages) doi:10.1115/1.3140618 History: Received February 14, 1980; Online July 21, 2009


In this paper a complete presentation of a new canonical representation of multiinput, multioutput linear stochastic systems is given. Its equivalence with operator form directly linked with ARMA processes as well as with classical state space representation is given, and a transfer matrix interpretation is developed in an example. The importance of the new representation is mainly in the fact that in the joint state and parameters estimation problem, all unknown parameters appear linearly when an input-output record is available. Moreover, if noises are Gaussian and their statistics are known, a conditionally time varying Kalman-Bucy type filter gives the recursive optimal estimation of parameters and state. Historical comments and remarks about the adaptive version of this algorithm are given. Finally an illustrative low order example is described.

Copyright © 1980 by ASME
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