Affinely parametrized state-space models

Ways to maximize the Likelihood Function

Journal article (2018)

Authors

Adrian Wills The University of Newcastle, Australia
C. Yu Beijing Institute of Technology
Lennart Ljung Linköping University
M.H.G. Verhaegen Team Raf Van de Plas - Mechanical, Maritime and Materials Engineering
Research Group
Team Raf Van de Plas (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2018 Adrian Wills, C. Yu, Lennart Ljung, M.H.G. Verhaegen
DOI: https://doi.org/10.1016/j.ifacol.2018.09.170
Difference-of-convex optimization Expectation-maximization algorithm Maximum-likelihood estimation Parameterized state-space model
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Published Date

2018

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Raf Van de Plas

Abstract

Using Maximum Likelihood (or Prediction Error) methods to identify linear state space model is a prime technique. The likelihood function is a nonconvex function and care must be exercised in the numerical maximization. Here the focus will be on affine parameterizations which allow some special techniques and algorithms. Three approaches to formulate and perform the maximization are described in this contribution: (1) The standard and well known Gauss-Newton iterative search, (2) a scheme based on the EM (expectation-maximization) technique, which becomes especially simple in the affine parameterization case, and (3) a new approach based on lifting the problem to a higher dimension in the parameter space and introducing rank constraints.