Maximum likelihood estimates of the central frequency of narrow-band random normal processes from a minimum number of samples

Abstract

The paper presents an analysis of the errors in the maximum likelihood estimates of the central frequency of narrow band random normal processes from a small number of samples. It is shown that these errors are manifested in the form of large outliers of frequency and caused by the presence of several extrema of the likelihood function. By methods of mathematical modeling, the root-mean-square errors of the estimates of the frequency for different signal-to-noise ratios, correlation times, and sampling periods were obtained and studied. The minimum errors were obtained with sampling intervals of 0.1–0.2 of the period of the central frequency. Methods of reducing large outliers are proposed and studied.