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Decrease in Computational Load and Increase in Accuracy for Filtering of Random Signals

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  • Phil Howlett

    (STEM Discipline, University of South Australia, Mawson Lakes, Adelaide, SA 5001, Australia)

  • Anatoli Torokhti

    (STEM Discipline, University of South Australia, Mawson Lakes, Adelaide, SA 5001, Australia)

  • Pablo Soto-Quiros

    (Escuela de Matemática, Instituto Tecnológico de Costa Rica, Cartago 30101, Costa Rica)

Abstract

This paper describes methods for optimal filtering of random signals that involve large matrices. We developed a procedure that allows us to significantly decrease the computational load associated with numerically implementing the associated filter and increase its accuracy. The procedure is based on the reduction of a large covariance matrix to a collection of smaller matrices. This is done in such a way that the filter equation with large matrices is equivalently represented by a set of equations with smaller matrices. The filter we developed is represented by x = ∑ j = 1 p M j y j and minimizes the associated error over all matrices M 1 , … , M p . As a result, the proposed optimal filter has two degrees of freedom that increase its accuracy. They are associated, first, with the optimal determination of matrices M 1 , … , M p and second, with an increase in the number p of components in the filter. The error analysis and results of numerical simulations are provided.

Suggested Citation

  • Phil Howlett & Anatoli Torokhti & Pablo Soto-Quiros, 2025. "Decrease in Computational Load and Increase in Accuracy for Filtering of Random Signals," Mathematics, MDPI, vol. 13(12), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:1945-:d:1676995
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    References listed on IDEAS

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    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
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