SELECTION OF A STATISTICALLY OPTIMAL CRITERION FOR THE AGREEMENT OF A UNIFORM DISTRIBUTION FOR RANK SIGNAL PROCESSING UNDER CONDITIONS OF A PRIORI UNCERTAINTY
Abstract
The aim of the work is to choose a statistically optimal algorithm for making a decision about the presence or absence of a signal for rank signal processing when solving the detection problem under conditions of a priori uncertainty. Research objectives: 1) analysis of the decisionmaking algorithm given in open sources for ranking procedures; search for its shortcomings; 2) selection and justification of the optimal (in the statistical sense) decision-making algorithm for use in rank signal processing; 3) conducting an experiment to obtain the characteristics of the selected decision-making algorithm; 4) analysis of the results obtained. A model of signal processing against the background of interference in conditions of a priori uncertainty is proposed. The model consists of a rank detector and a solver that compares the empirical distribution of ranks with the theoretical one. The rank detector allows you to reduce the problem of detecting asignal against the background of interference with an unknown distribution to the problem of testing a simple hypothesis about the distribution of ranks. The decision device is based on the use of a nonparametric Watson Consensus criterion, which has a high power (the probability of not making a second – kind error-skipping a signal). The use of the proposed approach to solving the detection problem under conditions of a priori uncertainty provides the following characteristics of the system: 1) the use of rank procedures ensures that the parameters of the detection system are insensitive to changing parameters of signals and interference; 2) the chosen decision-making algorithm provides acceptable characteristics of the system under conditions of significant a priori uncertainty. The proposed approach to solving the detection problem can find a place in many scientific fields where there is a priori uncertainty. For example, in radar, sonar, communications, medicine and other fields of science and technology.
