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
Citations
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Journal ArticleDOI
Projection-Based and Look-Ahead Strategies for Atom Selection
TL;DR: This paper devise two new schemes to select an atom from a set of potential atoms in each iteration of iterative greedy search algorithms, and proposes a look-ahead strategy such that the selection of an atom in the current iteration has an effect on the future iterations.
Sparse Kernel Density Construction Using Orthogonal Forward Regression With Leave-One-Out Test Score and
Sheng Chen,Xia Hong,Chris Harris +2 more
TL;DR: In this article, an orthogonal forward regression (OFR) algorithm is proposed to obtain sparse kernel density estimates based on a regression approach that directly optimizes model generalization capability, and the algorithm incrementally minimizes the leave-one-out test score.
Analysis of Stochastic Gradient Identification of Wiener-Hammerstein Systems for Nonlinearities with Hermite Polynomial Expansions
TL;DR: In this article, the authors investigated the statistical behavior of a sequential adaptive gradient search algorithm for identifying an unknown Wiener-Hammerstein (1958) system with Gaussian inputs.
Journal ArticleDOI
Identification of non-linear parametrically varying models using separable least squares
Fabio Previdi,Marco Lovera +1 more
TL;DR: In this paper, a separable least square (SLS) algorithm is proposed to identify non-linear, possibly parameter varying models in the form of a linear fractional transformation (LFT).
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Computational system identification for Bayesian NARMAX modelling
TL;DR: A computational Bayesian approach to NARMAX model identification that for the first time model uncertainty is characterised as a byproduct of the identification procedure, based on the reversible jump Markov chain Monte Carlo procedure.
References
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Book
Applied Regression Analysis
Norman R. Draper,Harry Smith +1 more
TL;DR: In this article, the Straight Line Case is used to fit a straight line by least squares, and the Durbin-Watson Test is used for checking the straight line fit.
Journal ArticleDOI
Singular value decomposition and least squares solutions
Gene H. Golub,C. Reinsch +1 more
TL;DR: The decomposition of A is called the singular value decomposition (SVD) and the diagonal elements of ∑ are the non-negative square roots of the eigenvalues of A T A; they are called singular values.
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Linear regression analysis
TL;DR: In this paper, the authors take into serious consideration the further development of regression computer programs that are efficient, accurate, and considered an important part of statistical research, and provide up-to-date accounts of computational methods and algorithms currently in use without getting entrenched in minor computing details.
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Input-output parametric models for non-linear systems Part II: stochastic non-linear systems
TL;DR: Recursive input-output models for non-linear multivariate discrete-time systems are derived, and sufficient conditions for their existence are defined.