A comparative study on different machine learning approaches with periodic items for the forecasting of GPS satellites clock bias

Accurately predicting satellite clock deviation is crucial for improving real-time location accuracy in a GPS navigation system. Therefore, to ensure high levels of real-time positioning accuracy, it is essential to address the challenge of enhancing satellite clock deviation prediction when high-precision clock data is unavailable. Given the high frequency, sensitivity, and variability of space-borne GPS satellite atomic clocks, it is important to consider the periodic variations of satellite clock bias (SCB) in addition to the inherent properties of GPS satellite clocks such as frequency deviation, frequency drift, and frequency drift rate to improve SCB prediction accuracy and gain a better understanding of its characteristics. In recent applications, deep learning models have significantly improved handling time-series data. This paper presents four machine learning prediction models that take into consideration periodic variations. Specifically, we utilize precision satellite clock bias data from the International GNSS Service forecast experiments and assess the predictive effects of various models including backpropagation neural network (BPNN), wavelet neural network (WNN), long short-term memory (LSTM), and gated recurrent units (GRUs). The predicted sequences of the four machine learning models are compared with the quadratic polynomial(QP) model. The average prediction accuracy of forecasting has improved by approximately (39.45, 57.57, 27.28, 29.14)% during 1-day forecasting. The results indicate that the machine learning models incorporating periodic variations outperform the standard quadratic polynomial model in terms of predictive accuracy, and the WNN model is better than that of these three machine learning models. This highlights the promising potential of deep learning models in forecasting satellite clock bias.