Optimal Nonlinear Estimation of Linear Stochastic Systems

[+] Author and Article Information
M. A. Hopkins

Department of Electrical Engineering, Gleason Building, Rochester Institute of Technology, 1 Lomb Memorial Drive, Rochester, NY 14623

H. F. VanLandingham

Bradley Department of Electrical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061

J. Dyn. Sys., Meas., Control 116(3), 529-536 (Sep 01, 1994) (8 pages) doi:10.1115/1.2899248 History: Received July 22, 1993; Online March 17, 2008


This paper presents a new nonlinear method of simultaneous parameter and state estimation called pseudo-linear identification (PLID), for stochastic linear time-invariant discrete-time systems. No assumptions are required about pole or zero locations; nor about relative degree, except that the system transfer function must be strictly proper. Under standard gaussian assumptions, for completely controllable and observable systems, it is proved that PLID is the minimum mean-square-error estimator of the states and model parameters, conditioned on the input and output measurements. It is also proved, given persistent excitation, that the parameter estimates converge a.e. to the true parameter values. All results have been extended to the multiple-input, multiple-output case, but the single-input, single-output case is presented here to simplify notation.

Copyright © 1994 by The American Society of Mechanical Engineers
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