Don Wiberg SEMINAR: A Simple New Convergent Approximation of the Optimal Recursive Parameter Estimator: Averaged Asymptotic Dynamic Analysis

Tuesday, June 21, 2011
"Moon Room" LANL

A Simple New Convergent Approximation of the Optimal Recursive Parameter Estimator: Averaged Asymptotic Dynamic Analysis

 

Donald M. Wiberg*

 

*University of California Santa Cruz, Santa Cruz, CA 95064
USA (Tel: 831-459-5560; e-mail: wiberg@soe.ucsc.edu).

Abstract: A key feature of a new recursive parameter estimator is its fast convergence.  Here averaging theory supports this claim of fast convergence for system parameters, which heretofore has been supported only by example and also by analogy with optimal nonlinear filtering.  Additionally, averaging theory is used to investigate possible computational shortcuts.  Finally, it is proven that the likelihood function has a unique maximum when only process noise and not system parameters are to be estimated in a stable, observable, single output system when the parameters are identifiable and in the model set.  If the maximum of the likelihood function is unique, then the new parameter estimator must converge to identifiable true parameter values if in the model set.

Keywords: parameter estimation, system identification, recursive estimation, asymptotic analysis, nonlinear filtering, identification algorithms