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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Using zero-norm constraint for sparse probability density function estimation
Xia Hong,Sheng Chen,Chris Harris +2 more
TL;DR: It is shown that under certain condition, the kernel weights of the proposed pdf estimator based on the zero-norm approximation can be updated using the multiplicative nonnegative quadratic programming algorithm.
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A comparative study on global wavelet and polynomial models for non-linear regime-switching systems
TL;DR: It is shown from numerical results that wavelet models are superior to polynomial models, in respect of generalisation properties, for describing severely non-linear RS systems.
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Joint k-step analysis of Orthogonal Matching Pursuit and Orthogonal Least Squares
TL;DR: In this article, the exact recovery analysis of Orthogonal least squares (OLS) was extended to OMP using the Exact Recovery Condition (ERC) and it was shown that OMP is guaranteed to exactly recover the unknown support in at most k iterations.
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Projection support vector regression algorithms for data regression
Xinjun Peng,Dong Xu +1 more
TL;DR: A novel projection SVR (PSVR) algorithm and its least squares version, i.e., least squares PSVR (LS-PSVR), where the projection axis not only minimizes the variance of the projected points, but also maximizes the empirical correlation coefficient between the targets and the projected inputs.
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Computational system identification of continuous-time nonlinear systems using approximate Bayesian computation
TL;DR: This paper derives a system identification framework for continuous-time nonlinear systems, for the first time using a simulation-focused computational Bayesian approach that performs well in noisy scenarios, especially in comparison to competing techniques that rely on signal derivative estimation.
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.
Journal ArticleDOI
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.