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.

The Japanese Quasi-Zenith Satellite System (QZSS) has been developed as a GPS (Global Positioning System) complementary system to improve positioning accuracy in the Asia-Pacific region. However, the accuracies of ultra-rapid predicted clocks are not high enough for real-time applications, so it is still a challenge problem. This article focuses on the clock predictions of the new QZSS constellation. Based on the QZSS clock periodic characteristics, an improved clock prediction method combining the spectrum analysis model (SAM) and extreme learning machine (ELM) is proposed with abbreviation as iELM. The key parameters of iELM are selected carefully including the number of hidden layer nodes and activation function. Further, the input length of the iELM network is optimized and discussed thoroughly. For the purpose of assessing the performance of the proposed algorithm, the clock prediction accuracies are compared among GBU-P (the ultra-rapid predicted orbits/clocks provided by GFZ (Deutsches GeoForschungsZentrum)), SAM and iELM methods. It is demonstrated that iELM keeps in a high level of accuracy below 1.0ns with the predicted time increasing from 0 to 18h, and a little larger during the next six hours. And the QZO (Quasi-Zenith Orbit) satellites perform better than GEO (Geostationary Earth Orbit) satellite. Furthermore, precise point positioning (PPP) for both static and kinematic modes are experimentally studied for 13 IGS (International GNSS (Global Navigation Satellite System) Service) MGEX (Multi-GNSS Experiment) stations in the longitude range between 100°E and 180°E. In the static PPP mode, the iELM method is verified to be effective for the GPS/QZSS constellation as positioning accuracy is improved by 28.3%, 57.7% and 47.4% on average in the east, north and up component with respect to GPS/QZSS GBU-P results. Nearly 70.0% stations achieve sub-decimeter accuracy in the vertical component. As for the kinematic PPP, the iELM method based on GPS/QZSS observations performs much better than the others for shorter convergence time and better positioning accuracy. Compared with GPS/QZSS GBU-P, iELM takes at most a half time to get convergence, and the accuracy is enhanced by 27.6%, 23.7% and 13.9% on average in the east, north and up direction respectively.

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.

BDS-3 was formally put into service on July 31, 2020, and now along with BDS-2 provides the positioning, navigation and timing services. In this contribution, different techniques of dual-frequency absolute positioning using the fully serviceable BDS-2+3 constellation are evaluated and compared to the positioning performance of GPS constellation. The accuracy of BDS-3 broadcast ephemerides is significantly higher than that of BDS-2 and is comparable to that of GPS, while BDS-3 International GNSS Service (IGS) Real-Time Service (RTS) products are not as good as GPS at this stage. The static Single Point Positioning (SPP) using BDS-2+3 pseudoranges based on broadcast ephemerides attains the positioning accuracy of 0.743/0.601/1.021 m (95%) and 0.453/0.365/0.566 m (68%) in east/north/up components, while its positioning accuracy is 1.210/1.097/2.447 m (95%) and 0.660/0.586/1.264 m (68%) in kinematic mode. BDS-2+3 Precise Point Positioning (PPP) using pseudoranges with carrier-phase observations based on broadcast ephemerides is able to achieve a positioning accuracy of 0.239/0.174/0.529 m (95%) and 0.115/0.096/0.296 m (68%) in static mode, and 0.636/0.486/1.108 m (95%) and 0.304/0.242/0.556 m (68%) in kinematic mode. BDS-2+3 PPP based on final Multi-GNSS Experiment (MGEX) product can obtain the positioning accuracy of centimeter to millimeter in static mode and the centimeter-level positioning accuracy in kinematic mode. The experiment results show that the positioning performances of BDS-2+3 using broadcast ephemerides and final MGEX products are both comparable to those of GPS. However, due to the poor quality and incomeless of BDS IGS RTS product, BDS-2+3 SPP and PPP based on IGS RTS product obtain the poor positioning accuracies in both static and kinematic modes, which are obviously worse than the counterparts of GPS. Another remarkable result can be obtained that BDS-2+3 achieves a better positioning performance in Asia-Pacific region at higher cut-off elevations as compared to GPS positioning.

The multi-GNSS fusion makes positioning more reliable and accurate. Considering the signal difference of different systems, GPS + Galileo + QZSS + BDS tightly combined double-difference model (TCDDM), including function and stochastic model, is proposed. The proposed model fully utilizes the overlapping frequency signals of various systems, and thus to enhance positioning model when DISBs are known beforehand. The observations of 3 ultra-short (1~10 m) and 3 short (4~10 km) baselines were processed by self-programming software, and the single-epoch single-frequency RTK performance using different system-combined models was evaluated by ambiguity-fixed correctness rate (ACR) and positioning accuracy. It demonstrated that three- and four-system TCDDM were superior to their corresponding loosely combined double-difference model (LCDDM) for ACR and positioning accuracy especially at high cut-off elevation. Moreover, four-system TCDDM had the best RTK performance obtaining average ACRs of 100% and 97.6% even at 25° cut-off elevation for ultra-short and short baseline, respectively.