Extraction of Periodic Terms in Satellite Clock Bias Based on Fourier Basis Pursuit Bandpass Filter

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.