Solving the Problem of Detecting Ultrasonic Signals in the Area of their High Correlation

Purpose of the work: To study the possibilities of solving the problem of detecting a set of signals in the area of their high correlation, taking noise singular maxima into account. Methods: The problem of separate signal detection is solved on the basis of the maximum likelihood method with Helstrom substitution and taking noise singular maxima into account. The fundamentals of the theory are outlined, and the results of model calculations are presented. Results: The main factor limiting the possibility of solving the problem is considered. It is related to the singularity of the correlation matrix obtained by solving the likelihood equations. The statistics of estimates of signal amplitudes and values of noise singular maxima depending on the signal-to-noise ratio are presented. Expressions defining the dispersion of signal amplitudes and the dispersion of the values of noise singular maxima are given. The structure of noise singular maxima in the solution domain is shown depending on the difference in reception time and noise level. A method for limiting the search area of the maximum functional of likelihood ratios is proposed, which significantly improves the signal detection capabilities. The results of model calculations illustrating the effectiveness of the proposed method are presented.