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

Phil Howlett, Anatoli Torokhti () and Pablo Soto-Quiros ()
Additional contact information
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

Mathematics, 2025, vol. 13, issue 12, 1-20

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.

Keywords: large covariance matrices; least squares linear estimate; singular value decomposition; error minimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/12/1945/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/12/1945/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:12:p:1945-:d:1676995

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().