UDC 621.396
CALCULATION OF PROBABILITY DISTRIBUTION DENSITY OF POLYNOMIAL COEFFICIENT ESTIMATES IN THE LEAST SQUARE METHOD
V. A. Belokurov, Dr. Sc. (Tech.), professor, department of radioengineering systems, RSREU, Ryazan; orcid.org/0000-0002-8893-550X, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
Q. T. Nguyen, post-graduate student, department of radioengineering systems, RSREU, Ryazan; orcid.org/0009-0004-7370-6482, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
The issues of calculating probability distribution density of polynomial coefficients which are obtained using the least squares method, are considered. The aim of the work is to derive the distribution laws of polynomial coefficients estimates calculated using the least squares method. The analytical form of probability distribution densities of these coefficients is necessary to calculate a detection threshold when detecting signals against the background of non-stationary noise. The paper provides analytical expressions for corresponding probability distribution densities. In order to determine the reliability of the results obtained, simulation modeling was carried out, within which the corresponding histograms were obtained being used in Chi-square goodness-of-fit test. Test statistics corresponding to the significance level of 0.05 is 5.42 and 6.92, respectively.
Key words: : probability distribution density, least squares method, polynomial coefficients.