Criterion for Minimum of Mean Information Deviation for Distinguishing Random Signals with Similar Characteristics

Abstract

The problem of distinguishing random signals with similar spectral and correlational characteristics is considered. To solve this problem, a criterion for a minimum of the mean divergence of the hypotheses taken with respect to the true distribution in the Kullback–Liebler information metric is proposed. Using this criterion, an optimal algorithm is synthesized, which allows achieving a guaranteed efficiency gain in discriminating random signals of similar structure. An example of its implementation in the problem of automatic speech recognition at the basic, phonetic level of signal processing is considered. Estimates of its effectiveness are obtained. Theoretical estimates of the effectiveness are confirmed by the results of the experiment. The author’s special-purpose information system was used for this. On the basis of the obtained results, recommendations are given for the practical application of the proposed criterion in problems of statistical signal processing, where a problem of verifying close statistical hypotheses arises.