Orthogonal least squares methods and their application to non-linear system identification
TLDR
Identification algorithms based on the well-known linear least squares methods of gaussian elimination, Cholesky decomposition, classical Gram-Schmidt, modified Gram- Schmidt, Householder transformation, Givens method, and singular value decomposition are reviewed.Abstract:
Identification algorithms based on the well-known linear least squares methods of gaussian elimination, Cholesky decomposition, classical Gram-Schmidt, modified Gram-Schmidt, Householder transformation, Givens method, and singular value decomposition are reviewed. The classical Gram-Schmidt, modified Gram-Schmidt, and Householder transformation algorithms are then extended to combine structure determination, or which terms to include in the model, and parameter estimation in a very simple and efficient manner for a class of multivariate discrete-time non-linear stochastic systems which are linear in the parameters.read more
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References
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Journal ArticleDOI
Orthogonal parameter estimation algorithm for non-linear stochastic systems
TL;DR: In this article, an orthogonal parameter estimation algorithm is proposed which allows each parameter in a linear-in-the-parameters nonlinear difference equation model to be estimated sequentially and quite independently of the other parameters in the model.
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Identification of non-linear output-affine systems using an orthogonal least-squares algorithm
TL;DR: In this article, an orthogonal least-squares algorithm is derived that can determine the term to regress upon, detect significant terms in the model expansion, and provide the final parameter estimates.
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A prediction-error and stepwise-regression estimation algorithm for non-linear systems
TL;DR: The identification of non-linear systems based on a NARMAX (Non-linear AutoRegressive Moving-Average model with exogenous inputs) model representation is considered, and a combined stepwise-regression/prediction-error estimation algorithm is derived.