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A Direct Computational Method for Estimating the Parameters of a Nonlinear Model

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A Direct Computational Method for Estimating the Parameters of a Nonlinear Model

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dc.contributor.author Eisenfeld, Jerome en
dc.contributor.author Cheng, Stephen W. en
dc.date.accessioned 2010-06-04T14:32:51Z en
dc.date.available 2010-06-04T14:32:51Z en
dc.date.issued 1978 en
dc.identifier.uri http://hdl.handle.net/10106/2366 en
dc.description.abstract We consider the system identification problem which deals with determining information about the unknown constant matrices A, B, and C or the linear dynamical system: [see pdf for notation], where u(t) and y(t) are given discretely on the interval [0,T]. This leads to a nonlinear estimation problem, or a so-called deconvolution problem, which deals with estimating the number of components [see pdf for notation], the decay rates [see pdf for notation], and the corresponding amplitudes [see pdf for notation] in the model: [see pdf for notation] from the given discrete data [see pdf for notation]. Deconvolution problems are important in a number of fields. One of these is the analysis of fluorescence decay experimental data [3]. Many numerical methods are available for approaching this problem. The Isenberg method of moments (or IMOM for short) was found to be the best among these methods in most cases [2]-[7]. A direct computational method which is essentially based on the general moment theory has been developed [7]. This method which was called the direct computational method (or DCM for short) alleviates some long standing difficulties arising from IMOM. Two of these are the cut-off error incurred when integration is required to infinite time and lack of flexibility in weighting the data. In this paper, the theory is presented with the specification of the admissible weighting functions and the estimation of the amplitudes [see pdf for notation]. using the linear least squares method as an option. The filtering scheme, which can be used to filter out one known decay term and increase the accuracy of the estimation, is presented. Numerical examples are provided. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;85 en
dc.subject Deconvolution problems en
dc.subject Isenberg method of moments en
dc.subject Direct computational method en
dc.subject System identification en
dc.subject.lcsh Nonlinear estimation problems en
dc.subject.lcsh Mathematics Research en
dc.title A Direct Computational Method for Estimating the Parameters of a Nonlinear Model en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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