The simulation of atomic clock error stability

Clock error plays an indispensable role in timekeeping services and navigation systems, with its frequency stability being a crucial metric for evaluating corresponding time-frequency equipment. In this paper, the constant component of clock error is modeled as the sum of phase offset, frequency offset, frequency drift and periodic terms, and the stochastic component is modeled as the sum of power law noises. A simulation method based on the Monte Carlo method is presented. The formulae of power law noises simulation and of periodic terms identification and separation applicable to overlapping Hadamard variance are derived. The simulation results of ground-station and satellite clock errors show that the mean squared relative error between the simulation stability and the corresponding real-clock stability is less than 0.01, demonstrating the excellent performance of the proposed method. Furthermore, the method is extended to derive formulae applicable to overlapping Allan variance and modified Allan variance.