Fractal behavior of GNSS time offsets and fractal interpolation forecasting method for multi-GNSS time synchronization

Synchronization between system times of Global Navigation Satellite Systems (GNSSs), or GNSS time interoperability, is one of the prerequisites of GNSS interoperability. We explored the fractal behavior of time offsets between Coordinated Universal Time (UTC) and GNSS time scales (GNSST). A fractal-based prediction method for forecasting UTC-GNSST time offsets is developed. Through data analysis, the self-similarity behavior in UTC-GNSST time offsets is revealed, which is proven by calculating the Hurst exponent. The values of the fractal dimension and correlation metric indicated that the time series of UTC-GNSST time offsets have long memory, of which the memory span is 1247 days and could be obtained from V-statistics. Subsequently, the fractal interpolation-based mathematic model was built, and the prediction accuracy was tested through numerical experiments. Compared with the polynomial and gray prediction models, the fractal interpolation forecast model was found to have higher prediction accuracy. The prediction accuracies of UTC-GPST and UTC-GLOT using fractal interpolation forecast model in short term are less than 1.3 and 5.5 ns, and in long term are less than 2.3 and 8.3 ns, with an improvement by at least 50 and 30% compared to polynomial and gray model.