Solving Rician Data Analysis Problems: Theory and Numerical Modeling Using Computer Algebra Methods in Wolfram Mathematica

• Published in: Programming and computer software Vol. 50; no. 2; pp. 208 - 213
• Main Author: Yakovleva, T. V.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.04.2024; Springer Nature B.V
• Subjects: Algebra; Algorithms; Artificial Intelligence; Complex systems; Complex variables; Computer algebra; Computer Science; Computing costs; Cost analysis; Data analysis; Information systems; Mathematical analysis; Maximum likelihood method; Nonlinear equations; Numerical methods; Numerical models; Operating Systems; Optimization; Parameter estimation; Probability distribution; Random variables; Real time operation; Signal processing; Software Engineering; Software Engineering/Programming and Operating Systems; Standard deviation; Statistical methods; Statistical models; System effectiveness
• ISSN: 0361-7688; 1608-3261
• DOI: 10.1134/S0361768824020154

This paper considers theoretical foundations and mathematical methods of data analysis under the conditions of the Rice statistical distribution. The problem involves joint estimation of the signal and noise parameters. It is shown that this estimation requires the solution of a complex system of essentially nonlinear equations with two unknown variables, which implies significant computational costs. This study is aimed at mathematical optimization of computer algebra methods for numerical solution of the problem of Rician data analysis. As a result of the optimization, the solution of the system of two nonlinear equations is reduced to the solution of one equation with one unknown variable, which significantly simplifies algorithms for the numerical solution of the problem, reduces the amount of necessary computational resources, and enables the use of advanced methods for parameter estimation in information systems with priority of real-time operation. Results of numerical experiments carried out using Wolfram Mathematica confirm the effectiveness of the developed methods for two-parameter analysis of Rician data. The data analysis methods considered in this paper are useful for solving many scientific and applied problems that involve analysis of data described by the Rice statistical model.