Objectives The nonlinear characteristics of satellite clock offset sequences are complex. To effectively separate the correction error of the periodic term while accounting for non-functionalized factors and improving the accuracy of clock bias prediction, this study extends the clock error periodic term model to a semi-parametric clock error model.

Methods By employing the kernel estimation method, both the window width parameter and parameter solution of the kernel function are comprehensively considered, resulting in the establishment of a semi-parametric varying coefficient model. First, the kernel estimation method is introduced, and the parameter components are modified by Taylor expansion. By synthesizing the kernel function and window width parameters, the parameters and periodic term correction estimates of the semi-parametric varying coefficient model are obtained via a three-step estimation method. Then, score test statistics are constructed to detect outliers, and an outlier identification method is proposed for the semi-parametric varying coefficient clock difference prediction model with periodic correction. Finally, to avoid over-fitting or under-fitting of the observed values, a support vector machine is used to further fit the pre-processed clock residual data, thereby improving the model's fitting and prediction accuracy. The reliability of the proposed model is verified by comparing BDS-3 satellite clock difference data with conventional methods.

Results Experimental results show that the proposed model can accurately and efficiently determine the constant value of the BeiDou-3 global navigation satellite system (BDS-3) clock difference, identify and separate periodic term corrections, and significantly improve the quality and efficiency of BeiDou navigation satellite system clock difference data preprocessing. The prediction accuracy of the proposed combined forecast model surpasses that of the traditional quadratic polynomial model, periodic term model, and semi-parametric model. For 1 h, 6 h, and 12 h forecasts, the average prediction accuracy for BDS-3 satellite clock difference data is better than 0.164 ns.

Conclusions The proposed model provides a high level of precision and efficiency in preprocessing and predicting BDS-3 satellite clock difference data. It demonstrates superior performance compared to traditional models and offers significant potential for broader applications in satellite clock offset prediction tasks.