STEPWISE CHANGE OF THE MATHEMATICAL EXPECTATION OF THE RAPIDLY FLUCTUATING GAUSSIAN PROCESS WITH UNKNOWN INTENSITY
Abstract
A technically simple method for determining the stepwise change in the mathematical expectation of the band Gaussian process with unknown intensity is proposed. For this purpose, new approximations of solving statistics under various hypotheses were developed, and their maximization in unknown parameters was carried out. Structural diagrams of the appropriate detection and measurement devices in the form of simple single-channel units are developed. To determine the performance quality of the synthesized algorithms, the asymptotically exact expressions for their characteristics, such as type I and type II error probabilities (in revealing a change point) and conditional biases and variances of estimates (in measuring the parameters of the analyzed random process) were found using the local Markov approximation method. A new technique for analytically calculating the characteristics of the discontinuous parameter estimate (the abrupt change point) taking into account abnormal errors is presented. An experimental check of the specified algorithms is performed using statistical modeling methods. It is established that the presented detector and measurer are operable, and the theoretical formulas for the type I and type II error probabilities and conditional biases and variances of the obtained estimates are in satisfactory agreement with the corresponding experimental data in a wide range of parameter values of the analyzed process. The obtained results can be used in synthesizing and analyzing new technically simple algorithms for processing rapidly fluctuating random processes with abruptly changing characteristics under the conditions of various parametric a priori uncertainty.
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