Prospects for ultrasonic signal resolution

Purpose of the work: To assess the potential possibilities of processing ultrasonic signals taking into account the singularity of the correlation matrix based on the transformed likelihood function. Methods: The problem of resolving ultrasonic signals is solved by the method of maximum likelihood with Helstrom substitution. Relative variance of estimates of signal amplitudes on bases of which working area of solutions is determined is introduced. The singularity of the correlation matrix is taken into account. Results: The problem of resolution of ultrasonic signals by the method of maximum likelihood in the region prohibited by the Rayleigh criterion is considered. To eliminate ambiguity, the solution is converted, due to Helstrom substitution. Hardware-based resolution and statistical approach to signal resolution are discussed. The relative variance of amplitude estimates is introduced, on the basis of which the working region of resolution of two signals is determined, determined by changing the correlation coefficient from 0 to the value 0.9. The influence of the singularity of the correlation matrix on the possibility of signal resolution is analyzed. Noise singular maxima are considered, limiting the solution of the detection problem, and therefore the resolution of two or more signals. A method of estimating the resolution of two limited signals is proposed, which allows solving the problem of detecting signals and their resolution in the presence of singular noise maxima.

Authors: R. V. Simonov, V. A. Pakhotin, I. V. Lieberman

Direction: Physics

Keywords: theory of optimal reception, maximum likelihood method, Helstrom substitution, high-resolution region of signals, singularity of correlation matrix

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