The periodic noise exists in BeiDou navigation satellite system (BDS) clock offsets. As a commonly used satellite clock prediction model, the spectral analysis model (SAM) typically detects and identifies the periodic terms by the Fast Fourier transform (FFT) according to long-term clock offset series. The FFT makes an aggregate assessment in frequency domain but cannot characterize the periodic noise in a time domain. Due to space environment changes, temperature variations, and various disturbances, the periodic noise is time-varying, and the spectral peaks vary over time, which will affect the prediction accuracy of the SAM. In this paper, we investigate the periodic noise and its variations present in BDS clock offsets, and improve the clock prediction model by considering the periodic variations. The periodic noise and its variations over time are analyzed and quantified by short time Fourier transform (STFT). The results show that both the amplitude and frequency of the main periodic term in BDS clock offsets vary with time. To minimize the impact of periodic variations on clock prediction, a time frequency analysis model (TFAM) based on STFT is constructed, in which the periodic term can be quantified and compensated accurately. The experiment results show that both the fitting and prediction accuracy of TFAM are better than SAM. Compared with SAM, the average improvement of the prediction accuracy using TFAM of the 6 h, 12 h, 18 h and 24 h is in the range of 6.4% to 10% for the GNSS Research Center of Wuhan University (WHU) clock offsets, and 11.1% to 14.4% for the Geo Forschungs Zentrum (GFZ) clock offsets. For the satellites C06, C14, and C32 with marked periodic variations, the prediction accuracy is improved by 26.7%, 16.2%, and 16.3% for WHU clock offsets, and 29.8%, 16.0%, 21.0%, and 9.0% of C06, C14, C28, and C32 for GFZ clock offsets.

Real-time satellite clock offset anomaly monitoring is of great significance for real-time precise point positioning (RT-PPP) applications. Gross errors and phase jumps are the common anomalies in real-time satellite clock offsets. To detect these anomalies quickly and accurately, a real-time anomaly monitoring method based on generalized likelihood ratio test (GLRT) and adaptive Kalman filter (AKF) is proposed. The innovation sequence of AKF is used to reflect the abnormal variation of satellite clock offsets. By adjusting the adaptive factors of AKF, a reliable innovation sequence can be obtained. The GLRT is used as a detector to detect anomalies in satellite clock offsets with the aid of innovation sequence. By comparing the likelihood ratio test statistics with a priori detection threshold, the anomalies can be detected in real time. Based on the different performance of anomalies in the innovation sequence, the gross error and phase jump can be distinguished. Numerical simulations are employed to demonstrate the effectiveness of AKF in resisting the influences of phase jumps. The performance of the proposed anomaly monitoring method is evaluated, and the results show that the monitoring method can provide a quickly detection and identification of satellite clock offset anomalies and has a low probability of false alarm (PFA) and good probability of detection (PD).

Global navigation satellite system (GNSS) ultra-rapid predicted satellite clock offsets are prerequisite for real-time applications. However, noticeable jump at the boundary between adjacent prediction sessions can cause positioning fluctuation. Unlike observation sessions, the accuracy of prediction sessions decreases over time, making boundary jump elimination methods that treat the jump as an overall error unsuitable for prediction sessions. In this paper, the boundary jump components of prediction session are analyzed and a classification elimination method is proposed. Firstly, we analyze the sources of boundary jump and decompose it into four main components, including timescale difference, initial prediction deviation, initial clock bias, and delay error. After that, elimination methods for each component are proposed based on their specific characteristics. Three schemes for processing boundary jumps are designed: the hourly updated ultra-rapid predicted clock offsets are spliced into 24 h continuous arc using no boundary jump processing (S1), the head-tail concatenation method (S2), and the proposed boundary jump classification elimination method (S5). Experimental results demonstrate that the proposed method reduce the magnitude of boundary jumps and improve predicted clock offset accuracy. Compared with S1 and S2, the clock offset standard deviation (STD), root mean square (RMS) and range for multi-GNSS in S5 shows significant improvements of (37.8%, 42.5%), (22.0%, 46.2%), and (28.7%, 28.0%), respectively. PPP experimental results demonstrate that the three-dimensional RMS improvements of S5 compared to S1 and S2 are (41.6%, 17.9%) for BDS-only PPP and (25.1%, 8.3%) for multi-GNSS PPP, respectively.