Classification of random signals based on their doubly connected Markov models

The article considers the problem of identifying the pre-selected class of an observed signal. This appears to be a relevant issue in the theory of pattern recognition, clustering, statistical decisions, technical diagnostics, and a number of other areas of science and technology. As a signal model, its doubly connected Markov model (complex Markov chain) is used based on three-dimensional probability densities of simulated random processes. The technique for forming class models according to known probabilistic characteristics or according to a classified training sample of samples is regarded. As a part of the Bayesian approach, the posterior probabilities that determine the affiliation of the observed sample of signal samples with each class are defined. An optimal signal classification algorithm is proposed, a decision-making algorithm is developed, decisive statistics are formed that depend on the observed sample of samples and matrices of transition probabilities of the analyzed classes, providing means for decision-making with a given reliability and based on the Wald procedure; their properties are also examined. Statistical simulation of the classification algorithm has been carried out, which confirms its effectiveness. The research results can be used in various systems and devices for detecting objects according to the random signals generated by them, for example, in technical diagnostics equipment.

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