Modeling the Process of Frequency Estimation and Stabilization in a Radio Engineering System

The article presents a mathematical model and results of numerical modeling of the process of estimating and stabilizing the frequency of simultaneously and independently operating generators in a radio engineering system. The developed model is based on assumptions about the independence of the processes of frequency deviation generated by each signal generator. In this case, in general, the law of distribution of the deviation of the frequency of each generator from the nominal value is unknown. Under these conditions, the approach to estimating and stabilizing the frequency of generators based on finding the maximum of the likelihood function is untenable. To obtain estimates of the frequency deviation of each of the generators, it is proposed to introduce hypotheses about the assumed law of distribution of frequency deviations of each of the generators. Based on these hypotheses, an ordered set of frequency deviation values is formed for each of the generators. Using a quadratic functional calculated as the sum of squared differences between the measured and generated values, the parameters of the frequency deviation distribution law for each of the generators are determined. Based on the obtained data, the current frequency value of each of the generators is estimated and its subsequent stabilization is performed. The results of mathematical modeling are presented, confirming the correctness of the theoretical results obtained and the main regularities noted.