Uncertainty Derivation and Performance Analyses of Clock Prediction Based on Mathematical Model Method

The prediction of the clock offset plays an important role in the generation of a time scale, clock steering, and time offset prediction of the onboard clocks. The mathematical model method based on the stochastic differential equations has been dealt with the clock prediction problem. In this paper, we examine the method from a theoretical point of view. We derive the analytic expressions of the theoretical prediction uncertainties when the clocks are modeled by the sum of a white frequency modulation noise, a random walk frequency modulation noise in both the linear model case and the quadratic polynomial model case. Simulations and an experiment for predicting the time deviations of International Atomic Time-TA(National Time Service Center) are used to validate the theoretical analyses. The simulations and the experiment show that the prediction performances agree with the theoretical evaluations; therefore, we consider that the research is useful in applications. Furthermore, we illustrate that the prediction uncertainty can be minimized only by choosing an optimal observation interval. From simulations, for a typical cesium clock, the method is effective for short-term prediction, whereas for a typical hydrogen maser, for all prediction times the uncertainties of the deterministic part are predominant, and we thus consider that the method in the quadratic polynomial model case deserves further investigation.