Improving the Conditioning of Maximum Likelihood Sine Wave Fitting

Balázs Renczes, Vilmos Pálfi

Abstract

In this paper, a scaling method is proposed and studied for the maximum likelihood sine fitting algorithm. It is shown that similarly to the case of least squares fitting, this method can significantly improve the conditioning of the investigatedalgorithm. The maximum error in the solution of a linear system of equations strongly depends on the condition number of the coefficient matrix. Namely, the condition number of the coefficient matrix upper bounds the relative error of the solution.It is shown that the condition number of the maximum likelihood fitting is connected to the Hessian matrix. Thus, this matrix is analyzed to find general properties increasing the condition number. It is pointed out that the scaling factor applied for the least squares fitting also decreases the conditioning of the Hessian matrix significantly. By this means, the numerical stability of the maximum likelihood fitting is improved. Theoretical results are verified through simulations.

Keywords

signal processing, maximum likelihood estimation, sine fitting, condition number, numerical accuracy

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DOI

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IMEKO TC

TC4 - Measurement of Electrical Quantities

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