Improving Clock Prediction Algorithm for BDS-2/3 Satellites Based on LS-SVM Method

The satellite clock prediction is crucial to support real-time global satellite precise positioning services. Currently, the clock prediction for the Chinese BeiDou navigation satellite system (BDS) is still challenging to satisfy the precise positioning applications. Based on the exploration of existing prediction models, an improved model combing the spectrum analysis model (SAM) and the least-squares support-vector machine (LS-SVM) is proposed especially for BDS-2/3 satellites. Considering satellite-specific characteristics, the parameters of the LS-SVM method are optimized satellite by satellite, including input length, regularization and kernel parameters. The improved model is evaluated by comparing the predicted clocks of existing methods and the improved model. The bias of the predicted clock offsets are within +/- 1.0 ns for most medium Earth orbits (MEOs) over three hours employing the improved model, which is better than that of the existing methods and can be applied for several real-time precise positioning applications. The predicted clock offsets are further evaluated by applying clock corrections to precise point positioning (PPP) in both static and kinematic modes for 10 international GNSS service (IGS) Multi-GNSS Experiment (MGEX) stations, including five stations in the Asia-Pacific region. According to the practical engineering experience, 2 dm and 5 dm are defined for static and kinematic PPP, respectively, as a convergence threshold. Then, in the static PPP, the improved model is demonstrated to be effective, and positioning accuracies of some stations obtain more than 15% improvements on average for each direction, which enables them to get sub-decimeter positioning, especially in the Asia-Pacific region. In the kinematic PPP, the improved model performs much better than the others in terms of both the convergence time and the positioning accuracy. The convergence time can be shortened from 1.0 h to below 0.5 h, while the positioning accuracies are enhanced by 16.3%, 10.8%, and 18.9% on average in east, north, and up direction, respectively.