Perspective algorithm for prediction of time information in GLONASS synchronization systems

In order to increase the accuracy of predicting time information in synchronization systems (this accuracy, in turn, depends on the mathematical model describing the departure of the time scale and on the accuracy of estimates of its parameters), it is proposed to process time information using a two-step algorithm. In the first step, in order to find the trend in the class of linearly or parabolically varying functions, the maximum likelihood method is used, which can be implemented taking into account the posterior probability. In the second step, after highlighting the trend of the time scale departure, it is proposed to predict the observation noise using the least squares method (which can be supplemented with L2 regularization), where it is proposed to use trigonometric functions as basic ones. The optimal choice of the period of the first harmonic and the multiplicity of the considered harmonics in the decomposition of the observation noise is carried out using its approximate canonical decomposition by trigonometric functions with random coefficients. These parameters, as well as the variances of random decomposition coefficients, are in accordance with the spectral density of the power of the observation noise estimated at the observation interval and with a given accuracy of reproducing its variance. The advantage of the approximate canonical decomposition of observation noise in comparison with the strict orthogonal Karhunen-Loev decomposition is shown. The paper substantiates the optimal choice of observation and forecasting intervals