Generalized method for statistical estimation of frequency of simultaneously and independently functioning generators
The questions of estimating the current frequency of each of the generators when they function simultaneously and independently as parts of a radio-electronic or information-telecommunication system are considered. Frequency estimates are obtained based on measurements of the signal phases of each of the generators at each measurement time interval, determining the deviations of the measured phase values from the assumed nominal values, and obtaining estimates from the maximum condition of the generated likelihood function. The proposed approach is a generalization of the previously proposed method of statistical frequency stabilization of the system of simultaneously and independently operating generators, which is based on finding the extremum of the one-dimensional likelihood function was determined for the current time interval measurement and, accordingly, the current value of the oscillator frequency. The proposed generalization is as follows: - formation of a three-dimensional likelihood function, the arguments of which are the deviation of the duration of the time interval of measurements from the nominal value, the deviation of the nominal frequency values of each of the generators from the corresponding assumed values, the deviation of the relative instability values of each of the generators from the corresponding assumed values; - joint estimation of the duration of each of the measurement time intervals, frequency deviations and relative instabilities of each of the generators from the corresponding assumed values; - measurement of the signal phases of each generator at each measurement time interval. The proposed generalization allows us to reject assumptions about exactly known values of the nominal frequency and relative instability of each of the generators. At the same time, the use of the proposed likelihood function leads to the need to measure the signal phases of each of the generators not at one, but several measurement intervals. On the basis of numerical modeling, we analyzed the increase in the accuracy of estimating the duration of time intervals of measurements and, accordingly, the frequency of generators. It is shown that refining the values of relative frequency instability of each generator does not lead to a practically significant increase in the accuracy of estimates of the current frequency values of generators. A transition to a simplified likelihood function is proposed, in which only the duration of the time interval of measurements and the nominal frequency of each of the generators are evaluated.