Effective noise management and control of periodic fluctuations in spaceborne atomic clocks are essential for the accuracy and reliability of Global Navigation Satellite Systems. Time-varying periodic terms can impact both the performance evaluation and prediction accuracy of satellite clocks, making it crucial to mitigate these influences in the clock bias. We propose methods based on the Fourier dictionary and basis pursuit, namely the Fourier basis pursuit (FBP) spectrum and the Fourier basis pursuit bandpass filter (FBPBPF), to analyze and extract periodic terms in the satellite clock bias. The FBP method minimizes the L1-norm to improve spectral quality, while the FBPBPF reduces boundary effects and noise. Our experimental results show that the FBP spectrum has a more obvious main lobe and reduces spectral leakage compared to traditional windowed Fourier transforms. In simulation experiments, the FBPBPF achieves periodic term extraction with errors reduced by 6.81% to 26.55% compared to traditional signal processing methods, and boundary extraction errors reduced by up to 63.67%. Using the BeiDou Navigation Satellite System’s precise clock bias for verification, the FBP-based prediction method has significantly improved the prediction accuracy compared to the spectral analysis model. For 6, 12, 18, and 24 h predictions, the average root mean square error of the FBP prediction method is reduced by 15.85%, 11.04%, 6.45%, and 4.01%, respectively.

Satellite clock bias exhibits complex, time-varying periodic characteristics due to environmental disturbances. Accurate modeling and prediction of periodic terms play a crucial role in improving the precision and stability of short-term predictions. Traditional models such as spectral analysis model (SAM) estimate the frequency, amplitude, and phase of periodic terms through global fitting, which limits their ability to adapt to abrupt changes at the prediction boundary. To address this limitation, this paper proposes an improved spectral analysis model (IM-SAM) based on the inaction method (IM). The model employs IM to extract the instantaneous frequency, amplitude, and phase parameters of periodic terms precisely at the data endpoint, and utilizes the parameters of periodic terms at the data endpoint for prediction, effectively suppressing periodic fluctuations in prediction errors. Experimental results based on real GPS clock bias data demonstrate that the root mean square (RMS) of IM-SAM prediction errors is reduced by 19.14%, 14.39%, and 10.48% for 3 h, 6 h, and 12 h prediction tasks, respectively, compared with SAM. Furthermore, a kinematic precise point positioning experiment was performed using IM-SAM-predicted clock products and compared with the predicted half of IGS ultra-rapid clock products. The RMS of position error was reduced by 14.3%, 12.6%, and 7.9% in the east, north, and up directions, respectively. These results demonstrate the practical effectiveness and accuracy of IM-SAM in real-time clock prediction and GPS positioning applications.