System identification of nonlinear state-space models

Authors:
Thomas B. Schön;Adrian Wills;Brett Ninness
Affiliations:
Division of Automatic Control, Linköping University, SE-581 83 Linköping, Sweden;School of Electrical Engineering and Computer Science, University of Newcastle, Callaghan, NSW 2308, Australia;School of Electrical Engineering and Computer Science, University of Newcastle, Callaghan, NSW 2308, Australia
Venue:
Automatica (Journal of IFAC)
Year:
2011

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Abstract

This paper is concerned with the parameter estimation of a general class of nonlinear dynamic systems in state-space form. More specifically, a Maximum Likelihood (ML) framework is employed and an Expectation Maximisation (EM) algorithm is derived to compute these ML estimates. The Expectation (E) step involves solving a nonlinear state estimation problem, where the smoothed estimates of the states are required. This problem lends itself perfectly to the particle smoother, which provides arbitrarily good estimates. The maximisation (M) step is solved using standard techniques from numerical optimisation theory. Simulation examples demonstrate the efficacy of our proposed solution.