Method for estimating the frequency-time parameters of signals in the system of simultaneously and independently functioning generators.
Authors:   Rostov-on-Don Research Institute of Radio Communication, Nansen str., 130, Rostov-on-Don 344038, Russia, Gabriel'yan D.D. , Lazarenko S.I. ,   Don State Technical University, Gagarin sq., 1, Rostov-on-Don 344002, Russia, Kulbikayan B.Kh. ,   Rostov State Transport University, Rostovskogo Strelkovogo Polka Narodnogo opolcheniya sq., 2, Rostov-on-Don 344038, Russia, Safaryan O.A. ,   Don State Technical University, Gagarin sq., 1, Rostov-on-Don 344002, Russia, Sakharov I.A. ,   Rostov branch of the Russian Customs Academy, Budenovsky prosp., 20, Rostov-on-Don 344002, Russia
Published: December 2020

The issues of assessing the current frequency of each of the total of simultaneously and independently functioning generators within the electronic system are considered. The most common case is considered, in which the deviation of the true values of the nominal parameters of generators from the estimated values of these parameters has an unknown distribution law, and random deviations of frequency from the true nominal value are subject to the normal distribution law with the corresponding variance. The proposed method of obtaining parameters estimates of both independently functioning generators (true nominal frequency values and long-term instability, accidental deviation of frequency caused by short-term instability of the generator) is based on the measurement of the signals phases of each of the generators during several measuring intervals. The first step in obtaining estimates is to line the relationship between deviations of generator parameters from nominal values and the random deviation of the generator frequency by deviation of the measured phase value from the intended nominal value. This allows the formation of a system of linear algebraic equations relative to unknown values of frequency par deviations and relative instability, random deviation of frequency. Minimally necessary number of measuring intervals estimated in the materials of the article. The method proposed in the article is a further generalization of the previously proposed method of statistical frequency stabilization of the system of simultaneously and independently functioning generators, in which, based on finding the extremum of the multidimensional likelihood function, formed under the assumption of a normal distribution law for each of the arguments, the current duration of the measurement time interval, the nominal frequency and the relative instability of each of the generators. The suggested generalization is as follows: formation of an overdetermined system of equations, the unknowns in which are the deviation of the duration of the measurement time interval from the nominal value, the deviation of the values​​of the nominal frequencies of each of the generators from the corresponding assumed values, the deviation of the values ​​of the relative instabilities of each of the generators from the corresponding assumed values; formation of a system of normal equations, based on the results of the solution of which, a joint assessment 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 ​​is carried out; measurements of the signal phases of each of the generators at each time interval of the measurement. The proposed generalization allows us to abandon the following assumptions: exactly known values ​​of the nominal frequency and relative instability of each of the generators; about the known distribution law of the deviation of the values​​of the specified parameters from the assumed values. At the same time, the use of the proposed method leads to the need to measure the phases of the signals of each of the generators not in one, but in several measurement intervals. On the basis of numerical modeling, an increase in the accuracy of estimating the duration of time intervals of measurements and, accordingly, the frequency of generators is analyzed. It is shown that the refinement of the values ​​of the relative frequency instability of each of the generators does not lead to a practically significant increase in the accuracy of estimates of the current values ​​of the generator frequency. A transition to a simplified likelihood function is proposed, in which only the duration of the measurement time interval and the nominal frequency of each of the generators are estimated.