The Chandler wobble (CW) and annual wobble (AW) are the two main components of polar motion, which are difficult to separate because of their very close periods. In the light of Fourier dictionary and basis pursuit method, a Fourier basis pursuit (FBP) spectrum is developed, which can reduce spectral smearing and leakage caused by the finite length of the time series. Further, a band-pass filtering method based on FBP spectrum (FBPBPF), which can effectively suppress the edge effect, is proposed in this paper. The simulation test results show that the FBPBPF method can effectively suppress the edge effect caused by spectral smearing and leakage and that its reconstruction accuracy at the boundary is approximately three times higher than the Fourier transform band-pass filtering method, which is based on Hamming windowed FFT spectrum, in extracting quasi-harmonic signals. The FBPBPF method is then applied to Earth’s polar motion data during 1900–2015. Through analyzing the amplitude and period variations of CW and AW, and calculating the eccentricity variation of the AW, we found that: (1) the amplitude of the CW is currently at a historic minimum level, and it is even possible to diminish further until a complete stop; and (2) the eccentricity of the AW has a gradually decreased fluctuation during the last 116 years.

Almost all GPS signal clocks show a periodic fluctuation. Harmonics in GPS satellites are a well-known feature, such as 3-, 4-, 6- and 12-h terms, accurate extraction of these harmonics are helpful to improve the clock modeling. The inaction method (IM) originating from the concept of normal time–frequency transform (NTFT) can precisely extract the periodic signals which significantly present the NTFT spectrum. This method is essentially line-pass filtering, so it can avoid being polluted by noises to the maximum extent and then have the ability to extract the time-varying periodic signals with robustness. The simulation test demonstrates that IM is the best method for extracting the harmonics and time-varying harmonics from a time signal, compared to singular spectrum analysis and zero-phase digital filter. We focus on GPS satellite clock data, after removing 6- and 12-h terms extracted by IM, the oscillation phenomenon in Hadamard deviation virtually disappears; this demonstrates that these periodic signals have been extracted effectively by the IM.

The moving-base gravimeter is one of the key instruments used for Earth gravity survey. The accuracy of the survey data is closely related to the calibration precision of several key parameters, such as the damping delay time, the drift coefficient, the gravity scale factor, and the measurement accuracy. This paper will introduce the development of the CHZ-II gravimeter system in which a cylindrical sampling mass suspended vertically by a zero-length spring acts as a sensitive probe to measure specific force. Meanwhile, a GNSS (Global Navigation Satellite System) positioning system is employed to monitor the carrier motion and to remove the inertia acceleration. In order to achieve high-precision calibrations for the key parameters, a new calibration method performed along forward and reverse overlapping lines is proposed, which is used to calibrate the above parameters and to estimate the measurement accuracy of the instrument used for a normal gravity survey. The calibration principle and the shipboard calibration data processing method are introduced. The calibration was performed for three moving-base gravimeters and the corresponding results are determined, indicating that the method can significantly improve the accuracy of the parameters. For the CHZ-II gravimeter, the measurement accuracy of the survey is 0.471 mGal (1 mGal = 10⁻⁵ m/s²), which improved by 19.5% after applying the calibrated parameters. This method is also practical for use with aviation, marine and even vehicle-carried moving-base gravimeters.

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.