The prediction of Satellites’ Clock Bias (SCB) plays an important role in optimizing the clock bias parameters in navigation messages, meeting the requirements of real-time dynamic precise point positioning and providing the prior information required for satellite autonomous navigation. Satellite-borne atomic clocks are often affected by many factors in space, which makes it difficult to describe the clocks’ bias and behavior with fixed model to achieve reliable high-precision prediction. The composition and characteristics of clock bias for satellite-borne atomic clock are described and analyzed, a clock bias prediction algorithm based on Nonlinear autoregressive model with exogenous input (NARX) recurrent neural network is proposed, the advantages of this model in SCB and other time series prediction are introduced in detail. The SCB data from four different clock types are selected for calculation and analysis. The comparative results show that, for both 6h and 24h forecasts, the accuracy and stability of NARX model are significantly better than three commonly used models, especially in the prediction of satellite cesium atomic clock.

The time scale of the global navigation satellite system (GNSS) is the core element for its position, navigation and timing services. A highly stable atomic clock is essential to ensure the reliability of the GNSS time scale. This study proposed a novel hybrid denoising model combining variational mode decomposition (VMD), K–L divergence, permutation entropy (PE), and Savitzky–Golay (SG) filter for satellite atomic clocks. Firstly, the key parameter of VMD is solved efficiently by taking the minimum sum of K–L divergence of decomposed modes as the constraint condition, and the optimised parameters are applied to the decomposition process. On this basis, the PE algorithm is used to determine the modes decomposed by VMD into signal-dominant and noise-dominant components by searching for the mutation of PE value at two adjacent points. Finally, the noise-dominant components are denoised by the SG filter and then reconstructed with the signal-dominant components to form the denoised signal. The analysis of the simulated signal shows that the method can effectively remove noise from the simulated signal, and the resulting denoised signal is similar to the pure signal. Compared with commonly used ensemble empirical mode decomposition and wavelet denoising methods, the signal-noise ratio of the proposed method is improved by 21.2% and 28.9%, and the root mean square error is improved by 24.1% and 29.8%, respectively. The results of experimental data testify that the K–L VMD-PE-SG-based denoising method can significantly reduce the dominant noise within one day, thus effectively improving the short to medium-term frequency stability. Compared with the original signal, the stability of the smoothing time within 76 800 s is generally improved, and the degree of improvement depends on the type of atomic clock and the smoothing time.

Satellite atomic clocks are the key elements for position, navigation, and timing services of the Global navigation satellite system (GNSS); it is necessary to research the characteristics of BDS-3 on-orbit satellite atomic clocks for their further optimization. In this study, clock offset data with a duration of 620 days since BDS-3 was officially commissioned were applied to long-term characteristic analysis. To begin with, the precision clock offset data of Deutsches geoforschungs zentrum (GFZ) processed by a MAD-based method were used as reliable test data. Herein, the working principle and main characteristics of satellite atomic clocks are analyzed and discussed, and thus, a comprehensive long-term characteristic analysis scheme is designed. On this basis, the performance indicators—mainly including physical parameters, periodic characteristics, frequency drift rate, frequency accuracy, frequency stability—were calculated and analyzed respectively, revealing the long-term characteristics of the BDS in orbit satellite atomic clocks during the test period. The results of experimental data testify that the performance of BDS-3 satellite atomic clocks is significantly superior to that of BDS-2, especially in terms of drift rate and frequency stability, and the performance of passive hydrogen maser (PHM) is generally superior to that of rubidium atomic frequency standards (RAFS). Within about half a year since BDS-3 was officially commissioned, the frequency stability of BDS-3 satellite atomic clock gradually improved and then reached the order of 10⁻¹⁵, reflecting the effectiveness of system maintenance and inter-satellite link. Furthermore, some novel conclusions are drawn, such as the long-term period term of the fitting residual and drift rate, which may be caused by the earth’s revolution.

The variation law of satellite clock bias (SCB) can be regarded as a grey system because the spaceborne atomic clock is very sensitive and vulnerable to many factors. GM (1,1) model is the core and foundation of the grey system, which has been highly valued and successfully applied in SCB prediction since its production. However, there are still some problems to be further studied such as the lack of stability of its prediction effect in practical application. In view of this, an improved GM (1,1) model by optimizing the initial condition has been proposed in this paper so as to increase the prediction performance. The new initial condition is obtained by the weighted combination of the latest and oldest components of the original clock bias sequence. And the weight values of these two components are acquired from a method of minimizing the sum of squares of fitting errors. We adopt GPS rapid precision SCB data provided by the International GNSS Service (IGS) for 15 mins, 30 mins, 1 h, 3 h, 6 h, 12 h, and 24 h prediction experiments. The results show that the improved GM (1,1) model is effective and feasible, and its prediction accuracy and stability are significantly better than those of the traditional GM (1,1) model, ARIMA model, and QP model, even for the SCB signal with obvious fluctuation.

The nonlinear and nonstationary characteristics of satellite clock bias (SCB) have a harmful effect on the accuracy and stability of SCB forecast. To eliminate the influence of nonlinearity and non-stationarity, a hybrid forecast model was constructed that combines complementary ensemble empirical mode decomposition (CEEMD) and quadratic polynomial (QP), called CEEMD-QP. First, the SCB sequence is decomposed into several intrinsic mode function (IMF) components and one residual term by CEEMD. Second, permutation entropy (PE) and the correlation coefficient are used to quantitatively determine the IMF component with more noise and weak correlation with the original SCB signal. Finally, the SCB is reconstructed with the IMFs and residual components, and QP model is used to fit and forecast the clock bias. We adapt the observation part of ultra-rapid precise SCB data of GPS provided by IGS to forecast experiments. The results show that the CEEMD-QP method has obvious advantages of forecast accuracy and stability in short-term forecast.

High-precision time frequency lays a foundation for the normal operation and accurate service of the global navigation satellite system (GNSS). The satellite clock, a payload vital to GNSS operation, has become a hot topic in GNSS technology research. This paper gives a systematic introduction to the operation features and principles of satellite clock, and an overview of its research status and current development. On this basis, several techniques that deserve attention of the satellite clocks are categorized in terms of precise orbit determination and clock estimation, performance assessment and characteristic analysis, and clock offset prediction. On this basis, a comprehensive description and analysis is given separately. In the end, this paper gives some prospects over the development trend of techniques of the satellite clock based on the current research achievements and development of the GNSS.