Recently, the performance of the new-generation BeiDou Navigation Satellite System (BDS) satellite clocks has attracted considerable attention. There are two types of BDS clocks developed in China—namely, the new rubidium (Rb-II) and passive hydrogen maser (PHM)—and these can affect positioning, navigation and timing (PNT) services. In this paper, to comprehensively evaluate and analyze the performance of BDS satellite atomic clocks, the physical characteristics are exhibited, including phase, frequency, frequency drift and noise. The physical characteristics are applied to detect the switching of satellite clocks. The frequency stability of atomic clocks is assessed by overlapping Allan deviation (ADEV) and overlapping Hadamard deviation (HDEV). The periodic characteristics of satellite clock bias data are studied through spectrum analysis. Based on 550 day precision satellite clock bias data provided by Wuhan University, China, experiments were performed, focusing on the performance of the Rb-II and PHM clocks installed on BDS-3. Some valuable conclusions are obtained: (a) the BDS-3 satellite clocks perform better than BDS-2. The root mean square value of the frequency drift of BDS-3 satellite clocks is enhanced by 41% compared to BDS-2. The noise of BDS-3 is 0.216 ns, which is 55% better than BDS-2. (b) The frequency stability of BDS-2 satellite clocks is worse than that of BDS-3. The mean daily stability of BDS-2 and BDS-3 satellite clocks by ADEV is 5.29 × 10 ⁻¹⁴ and 5.36 × 10 ⁻¹⁴ , respectively, while that with HDEV is 2.35 × 10 ⁻¹⁴ and 0.70 × 10 ⁻¹⁴ . For PHM clocks, the stability at 10 000 s with ADEV and HDEV is 2.29 × 10 ⁻¹⁴ and 2.25 × 10 ⁻¹⁴ , respectively, while the daily stability is 0.77 × 10 ⁻¹⁴ and 0.67 × 10 ⁻¹⁴ , respectively. (c) BDS geostationary orbit (GEO) and inclined GEO satellite atomic clocks have multiple significant periodic terms while the medium earth orbit satellite clocks only own one or two, which are related to the corresponding satellite orbital periods.

Multi-constellation will greatly improve the accuracy, completeness, effectiveness and continuity of the Beidou Navigation Satellite System (BDS)/Global Positioning System (GPS) bridge health monitoring. Firstly, the reliability of the monitoring results was ensured by using the dual-base station mode. For the dynamic post-processing mode, the empirical mode decomposition–wavelet transform coupled model was used to reduce the noise of original coordinate sequences. Finally, the self-programmed software was adopted to solve the observation data of 48 consecutive hours and thus analyse the daily deformation characteristics of the bridge. The experiment results show that under the good conditions of the satellite number and their geometric distribution, the monitoring results of the BDS/GPS combination system were in good agreement with the results of the GPS single system and BDS single system. However, in the complex environment of the bridge, especially when the signals were severely affected, the advantages of using the BDS/GPS combination system for deformation monitoring were more obvious.

Global navigation satellite system (GNSS) has been widely used in many deformation monitoring fields in recent years and can achieve centimeter-level or even sub-centimeter-level real-time monitoring accuracy through the carrier phase double-differenced technique. However, this technique cannot eliminate or weaken multipath errors, which become the main error source for GNSS deformation monitoring. Therefore, extracting deformation information from coordinate series mixed with multipath errors has become a key issue for further improving the accuracy of GNSS deformation monitoring. In this paper, we propose an approach to overcome this issue called empirical wavelet transform-independent component analysis with reference (EWT-ICA-R). The specific process is as follows. First, EWT is employed to model the multipath errors from a priori GNSS coordinate series, and the model is input to ICA-R as a reference signal. Then, the GNSS deformation monitoring series mixed with multipath errors and deformation information is decomposed into sub-series of different scales using EWT, and these sub-series are input to ICA-R as multi-channel signals. Finally, ICA-R is used to calculate the input signals together to obtain the multipath errors in the GNSS deformation monitoring series and then subtract the multipath errors from the GNSS deformation monitoring series to obtain accurate deformation information. Experiments show the following: (1) For the vibration deformation experiments, the correlation coefficients between the deformation information extracted by the proposed method and the real values reached 0.981, 0.981, and 0.885 in the E, N, and U directions, respectively, and the corresponding root mean square errors decrease to 0.694 mm, 0.694 mm, 1.852 mm, respectively. (2) For the slow-deformation experiment, the correlation coefficients in the three directions were all higher than 0.98, and the corresponding root mean square errors decrease to 1.345 mm, 1.546 mm, and 3.866 mm, respectively. The experiments verified the feasibility of the proposed method to accurately extract deformation information, which makes it possible to obtain sub-millimeter GNSS deformation information and provide effective technical support for deformation monitoring in related fields.

Currently, the four major Global Navigation Satellite Systems (GNSS) are capable of supporting multi-frequency signals, and Real-time (RT) State Space Representation (SSR) correction products have been enriched and improved. Multi-GNSS, multi-frequency observations and multiple satellite RT SSR correction products present new opportunities to implement precise RT time transfer. This study extends the traditional post-processing dual-frequency undifferenced (UD) Precise Point Positioning (PPP) time transfer to RT multi-frequency scenarios, establishes models for dual-frequency, triple-frequency, quad-frequency and penta-frequency multi-GNSS PPP time transfer, and evaluates the product availability, orbit accuracy and clock offset accuracy of RT SSR products from BKG, CNE, DLR, ESA, GFZ, GMV, WHU, and IGS. A multi-frequency and multi-GNSS RT PPP time transfer experiment was conducted by selecting data from four stations, BRUX, PTBB, ONSA and SPT0, with precise atomic clocks mounted for one week. The accuracy of various SSR products in RT PPP time transfer was compared, and the performance of BDS/Galileo combination dual-frequency to penta-frequency RT UD PPP time transfer was evaluated. The experimental results show that the standard deviation and frequency stability difference of RT PPP time transfer among each SSR product is relatively small, especially after combining multi-systems. The frequency stability tends to be entirely consistent. In general, the WHU, GFZ, GMV, and WHU SSR products offer notable advantages in terms of accuracy and frequency stability for GPS, GLONASS, Galileo, and BDS RT PPP time transfer, respectively. Multi-GNSS and multi-frequency signals have both enhanced RT PPP time transfer performance, with a particularly noticeable improvement in terms of accuracy and short-term frequency stability. The effect of multi-GNSS on RT PPP time transfer is more pronounced than that of multi-frequency alone. Considering the higher costs associated with multi-frequency GNSS receivers, prioritizing multi-GNSS for RT PPP time transfer is recommended.

With the rapid upgrade of global navigation satellite system (GNSS) single-frequency (SF) receivers and the increasing market demand for low-cost hardware, SF precise point positioning (PPP) technology has been widely applied in the time and frequency field. The five-frequency signals provided by the whole constellation of Galileo bring more opportunities for the application of SF PPP in time and frequency transfer. In this contribution, using Galileo’s multi-frequency observations, three SF PPP time and frequency transfer models, i.e., the un-combined (UC) model, the ionosphere-free-half (IFH) model, and the ionosphere-weighted constraints (IWCs) model are established. SF PPP time and frequency transfer performance with Galileo E1, E5a, E5b, E5, and E6 multi-frequency observations is evaluated using four links (947.7 km to 1331.6 km) with five external high-precision atomic clocks stations. The results show that the time and frequency transfer performance of SF-UC and SF-IWC is better than that of SF-IFH, and the timing accuracy of SF-UC and SF-IWC is similar. SF PPP time and transfer performance with E5, E5a, E5b, and E6 signals is improved compared with traditional E1 signal. Among them, the frequency stability of E5 improves the most (about 58%), and that of E6 improves the least (about 14%). In addition, the difference in frequency stability between SF and double-frequency (DF) PPP decreases gradually with an increase in average time, and the frequency stability difference between SF and DF PPP can reach 2 × 10⁻¹⁶ in 120,000 s, indicating that SF PPP has the potential to achieve DF PPP frequency stability. Considering the possible frequency data loss during actual observation, the cost of the GNSS SF receiver, and the advantages of Galileo multi-frequency observations, SF PPP can also meet the long-time time and frequency transfer requirements, and the SF-IWC model based on Galileo E5 observations is more recommended.

Galileo four-frequency cycle slip detection and repair (CDR) is susceptible to the noise of pseudo-range observations. In this study, the Galileo four-frequency carrier phase smoothed pseudo-range (CPSP) assisted CDR method was proposed. Such method was conducted in three steps in sequence. First, the four linear independent combinations of the Galileo four-frequency observation were taken for CDR. Second, the non-divergent Hatch filter was employed to carry out the pseudo-range observation smoothly. Third, the true cycle slip was determined by rounding the float value using the least square method. To take the optimal combination of the CDR and verify the feasibility of the proposed method, the Galileo observations with satellites in different types were performed. According to the experimental results, (1) the four linear independent combinations of the geometry-free carrier phase combination (0, 1, 0, -1), (1, 1, -1, -1), (1, 2, -2, -1) and geometry-free and ionosphere-free combination (0, 0, 1, -1) were adopted for the cycle slip detection; (2) The success rate of cycle slip repair reached over 99.99% after four-frequency CPSP processing. With the CPSP assisted CDR method, the differences of the root mean square (RMS) between float and true values were down-regulated by 79.61%, 70.03%, 66.25% and 72.75%, respectively. (3) The differences of the root mean square (RMS) between float and true values were down-regulated by 13.62%, 10.67%, 10.67% and 10.67% after smoothing, respectively. In summary, the Galileo four-frequency CDR was effectively performed by the proposed method in active ionospheric area.