Abstract
In this paper we analyze the bias in a general linear least-squares parameter estimation problem, when it is caused by deterministic variables that have not been included in the model. We propose a method to substantially reduce this bias, under the hypothesis that some a-priori information on the magnitude of the modelled and unmodelled components of the model is known. We call this method Unbiased Least-Squares (ULS) parameter estimation and present here its essential properties and some numerical results on an applied example.
Highlights
The well known least-squares problem [1], very often used to estimate the parameters of a mathematical model, assumes an equivalence between a matrix-vector product Ax on the left, and a vector b on the right hand side: the matrix A is produced by the true model equations, evaluated at some operating conditions, the vector x contains the unknown parameters and the vector b are measurements, corrupted by white, Gaussian noise
The model error is often assumed as an additive stochastic term in the model, e.g., error-in-variables [2,3], with consequent solution methods like Total Least-Squares [4] and Extended Least-Squares [5], to cite a few
In this paper we have analyzed the bias commonly arising in parameter estimation problems where the model is lacking some deterministic part of the system
Summary
The well known least-squares problem [1], very often used to estimate the parameters of a mathematical model, assumes an equivalence between a matrix-vector product Ax on the left, and a vector b on the right hand side: the matrix A is produced by the true model equations, evaluated at some operating conditions, the vector x contains the unknown parameters and the vector b are measurements, corrupted by white, Gaussian noise. To eliminate the bias on the parameter estimates we perturb the right-hand-side without modifying the reduced model, since we assume it describes accurately one part of the true model
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