{"title":"Numerical-Analytical Decomposition-Autocompensation Method for Signal Recognition from Incorrect Observations","authors":"Yu. G. Bulychev","doi":"10.1134/s0965542524700180","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A numerical-analytical method is developed for solving the problem of optimal recognition of a set of possible signals observed in the form of an additive mixture involving not only fluctuation measurement errors (with an unknown statistical distribution law), but also a singular disturbance (with parametric uncertainty). The method not only detects signals in the mixture, but also estimates their parameters as based on a given cost functional and accompanying constraints. Based on the idea of generalized invariant unbiased estimation of linear functionals, the method ensures decomposition of the numerical procedure and autocompensation of the singular disturbance without resorting to conventional state space extension. Parametric finite-dimensional representations of the signals and the disturbance are obtained using linear spectral decompositions in given functional bases. The measurement error is described using only its correlation matrix. The random and systematic errors are analyzed, and an illustrative example is given.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Mathematics and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0965542524700180","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
A numerical-analytical method is developed for solving the problem of optimal recognition of a set of possible signals observed in the form of an additive mixture involving not only fluctuation measurement errors (with an unknown statistical distribution law), but also a singular disturbance (with parametric uncertainty). The method not only detects signals in the mixture, but also estimates their parameters as based on a given cost functional and accompanying constraints. Based on the idea of generalized invariant unbiased estimation of linear functionals, the method ensures decomposition of the numerical procedure and autocompensation of the singular disturbance without resorting to conventional state space extension. Parametric finite-dimensional representations of the signals and the disturbance are obtained using linear spectral decompositions in given functional bases. The measurement error is described using only its correlation matrix. The random and systematic errors are analyzed, and an illustrative example is given.
期刊介绍：
Computational Mathematics and Mathematical Physics is a monthly journal published in collaboration with the Russian Academy of Sciences. The journal includes reviews and original papers on computational mathematics, computational methods of mathematical physics, informatics, and other mathematical sciences. The journal welcomes reviews and original articles from all countries in the English or Russian language.
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