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On new parametrization methods for the estimation of linear state–space models
Author(s) -
Ribarits T.,
Deistler M.,
Hanzon B.
Publication year - 2004
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.833
Subject(s) - parametrization (atmospheric modeling) , separable space , mathematics , likelihood function , least squares function approximation , function (biology) , state space , ordinary least squares , mathematical optimization , estimation theory , algorithm , canonical form , computer science , statistics , mathematical analysis , physics , quantum mechanics , estimator , evolutionary biology , pure mathematics , biology , radiative transfer
In this paper we introduce two variants of a new parametrization for state–space systems which we will both call separable least squares data driven local co‐ordinates (slsDDLC). SlsDDLC is obtained by modifying the parametrization by data driven local co‐ordinates (DDLC). These modifications lead to analogous parametrizations, and we show how they can be used for a suitably concentrated likelihood criterion function. The concentration step can be done by an ordinary or generalized least squares step. An obvious consequence is the reduced number of parameters in the iterative search algorithm. The application of the parametrizations to maximum likelihood identification is exemplified. Simulations indicate that the usage of slsDDLC for concentrated likelihood functions has numerical advantages as compared to the usage of the more commonly used echelon canonical form or conventional DDLC for the likelihood function. Copyright © 2004 John Wiley & Sons, Ltd.