Prediction of Navigation Satellite Clock Bias by Gaussian Process Regression

Many studies have been carried out in the past for forecasting satellite clock bias utilizing models such as the grey model, linear model, quadratic polynomial model, etc., but the accuracy of these models has not met the requirements for real-time applications. One reason for the fact is that onboard atomic clocks can be easily affected by various factors such as environment and temperature and this leads to complex aspects like periodic and stochastic variations, which are not sufficiently described by conventional models. A hybrid prediction model is thus developed in this work in order to be used particularly in describing the stochastic variation behavior satisfactorily. The proposed hybrid prediction model for satellite clock bias combines the quadratic model plus harmonic model to overcome the linear and periodic effects, and Gaussian process regression (GPR), whose input is reconstructed by the delay coordinate embedding to access linear or nonlinear coupling characteristics. The simulation results have demonstrated that the prediction accuracy of the proposed model is better that of the IGS ultra-predicted (IGU-P) solutions at least on a daily basis.