On the Least-Squares Fitting of Data by Sinusoids

Yaroslav D. Sergeyev (), Dmitri E. Kvasov () and Marat S. Mukhametzhanov ()
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Yaroslav D. Sergeyev: Università della Calabria
Dmitri E. Kvasov: Università della Calabria
Marat S. Mukhametzhanov: Università della Calabria

A chapter in Advances in Stochastic and Deterministic Global Optimization, 2016, pp 209-226 from Springer

Abstract: Abstract The sinusoidal parameter estimation problem is considered to fit a sum of damped sinusoids to a series of noisy observations. It is formulated as a nonlinear least-squares global optimization problem. A one-parametric case study is examined to determine an unknown frequency of a signal. Univariate Lipschitz-based deterministic methods are used for solving such problems within a limited computational budget. It is shown that the usage of local information in these methods (such as local tuning on the objective function behavior and/or evaluating the function first derivatives) can significantly accelerate the search for the problem solution with a required guarantee. Results of a numerical comparison with metaheuristic techniques frequently used in engineering design are also reported and commented on.

Keywords: Nonlinear regression; Least-squares fitting; Lipschitz-based deterministic methods; Metaheuristics; Numerical comparison (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-29975-4_11

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