Abstract Since the first pair of BeiDou satellites was deployed in 2000, China has made continuous efforts to establish its own independent BeiDou Navigation Satellite System (BDS) to provide the regional radio determination satellite service as well as regional and global radio navigation satellite services, which rely on the high quality of orbit and clock products. This article summarizes the achievements in the precise orbit determination (POD) of BDS satellites in the past decade with the focus on observation and orbit dynamic models. First, the disclosed metadata of BDS satellites is presented and the contribution to BDS POD is addressed. The complete optical properties of the satellite bus as well as solar panels are derived based on the absorbed parameters as well the material properties. Secondly, the status and tracking capabilities of the L-band data from accessible ground networks are presented, while some low earth orbiter satellites with onboard BDS tracking capability are listed. The topological structure and measurement scheme of BDS Inter-Satellite-Link (ISL) data are described. After highlighting the progress on observation models as well as orbit perturbations for BDS, e.g., phase center corrections, satellite attitude, and solar radiation pressure, different POD strategies used for BDS are summarized. In addition, the urgent requirement for error modeling of the ISL data is emphasized based on the analysis of the observation noises, and the incompatible characteristics of orbit and clock derived with L-band and ISL data are illuminated and discussed. The further researches on the improvement of phase center calibration and orbit dynamic models, the refinement of ISL observation models, and the potential contribution of BDS to the estimation of geodetic parameters based on L-band or ISL data are identified. With this, it is promising that BDS can achieve better performance and provides vital contributions to the geodesy and navigation. 

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Precise orbit determination for BDS satellites

As of December 2019, the core constellation of BeiDou Navigation Satellite System with global coverage (BDS-3) has been fully deployed with 24 MEO, 3 IGSO and 1 GEO satellites. In addition to the legacy B1I and B3I signals, BDS-3 satellites are capable of transmitting several new navigation signals, including B1C, B2a, B2b and B2a + b. The multi-frequency signals of BDS-3 bring new opportunities for fast ambiguity resolution (AR) of BDS precise point positioning (PPP). In this contribution, the BDS five-frequency PPP AR method was developed and the benefits of BDS-3 multi-frequency signals for precise positioning were investigated. The multi-frequency uncalibrated phase delay (UPD) products were estimated firstly using observations from 222 Multi-GNSS Experiment stations. The extra-wide-lane, wide-lane and narrow-lane UPDs of BDS-3 exhibit high stability with standard deviations less than 0.1 cycle. With the derived UPD products, five-frequency PPP AR was conducted at 12 static stations and a moving vehicle. The time to first fix of BDS PPP AR was shortened to 25.5 min with multi-frequency observations, showing improvement of 25.4% when compared to dual-frequency PPP AR. Moreover, instantaneous PPP wide-lane ambiguity resolution (WAR) can be achieved with success rate of over 90%. A fast decimeter-level accuracy can be achieved for BDS five-frequency PPP WAR with positioning accuracy improved by 68%-82% compared to PPP float solutions. The vehicle-borne experiment further demonstrates that BDS PPP WAR is potential to maintain decimeter-level positioning accuracy even in a complex environment.

BDS multi-frequency PPP ambiguity resolution with new B2a/B2b/B2a + b signals and legacy B1I/B3I signals

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The BeiDou satellite navigation system (BDS) is different from other global navigation satellite systems (GNSSs) because of its special constellation, which consists of satellites in geostationary earth orbit, inclined geosynchronous earth orbit (IGSO), and medium earth orbit (MEO). Compared to MEO satellites, the observations of IGSO satellites cover only a small range of nadir angles. Therefore, the estimation of phase center offsets (PCOs) suffers from high correlation with other estimation parameters. We have estimated the phase center offsets for BeiDou IGSO and MEO satellites with a direct PCO parameters model, and constraints are applied to cope with the correlation between the PCOs and other parameters. Validation shows that the estimated PCO parameters could be used to improve the accuracy of orbit and clock offset overlaps. Compared with the Multi-GNSS Experiment antenna phase center correction model, the average improvements of the proposed method for along-track, cross-track, and radial components are 19 mm (31%), 5 mm (14%), and 2 mm (15%) for MEO satellites, and 13 mm (17%), 12 mm (21%), and 5 mm (19%) for IGSO satellites. For clock offset overlaps, average improvements of standard deviation and root mean square (RMS) are 0.03 ns (20%) and 0.03 ns (12%), respectively. The RMS of precise coordinates in the BDS-only positioning was also improved significantly with a level of 24 mm (30%) in the up-direction. Finally, the overall uncertainty of the estimated results is discussed.

Estimation of antenna phase center offset for BDS IGSO and MEO satellites

Differential code biases (DCBs) are important parameters that must be estimated accurately and reliably for high-precision GNSS applications. For optimal operational service performance of the Beidou navigation system (BDS), continuous monitoring and constant quality assessment of the BDS satellite DCBs are crucial. In this study, a global ionospheric model was constructed based on a dual system BDS/GPS combination. Daily BDS DCBs were estimated together with the total electron content from 23 months’ multi-GNSS observations. The stability of the resulting BDS DCB estimates was analyzed in detail. It was found that over a long period, the standard deviations (STDs) for all satellite B1–B2 DCBs were within 0.3 ns (average: 0.19 ns) and for all satellite B1–B3 DCBs, the STDs were within 0.36 ns (average: 0.22 ns). For BDS receivers, the STDs were greater than for the satellites, with most values $$<$$
 2 ns. The DCBs of different receiver families are different. Comparison of the statistics of the short-term stability of satellite DCBs over different time intervals revealed that the difference in STD between 28- and 7-day intervals was small, with a maximum not exceeding 0.06 ns. In almost all cases, the difference in BDS satellite DCBs between two consecutive days was $$<$$
 0.8 ns. The main conclusion is that because of the stability of the BDS DCBs, they only require occasional estimation or calibration. Furthermore, the 30-day averaged satellite DCBs can be used reliably for the most demanding BDS applications.

Estimation of differential code biases for Beidou navigation system using multi-GNSS observations: How stable are the differential satellite and receiver code biases?

Interoperability of GNSS Open Services is a significant trend in the development of all the satellite navigation systems, and its performance will directly affect the users' security and reliability. Therefore, the monitoring and assessment of GNSS Open Services has become a focus of attention for all providers and users of GNSS. In this paper the elements and methods for the monitoring and assessment of GNSS Open Services are investigated first. Then the schemes designed for an international GNSS Monitoring and Assessment System (iGMAS) are proposed. The schemes are based on omni-directional antennas, multi-beam antennas and a high-gain paraboloid antenna to achieve Quadruple-overlap and Single-overlap coverage and sophisticated analysis respectively. Moreover, the scheme for the deployment of world-wide monitoring stations is also proposed. Finally, some related works that have been conducted to monitor and assess Beidou Open Services are introduced, which verifies the feasibility of the proposed system.

Monitoring and Assessment of GNSS Open Services

Global navigation services from the quad-constellation of GPS, GLONASS, BDS, and Galileo are now available. The international GNSS monitoring and assessment system (iGMAS) aims to evaluate the navigation performance of the current quad systems under a unified framework. In order to assess impact of orbit and clock errors on the positioning accuracy, the user range error (URE) is always taken as a metric by comparison with the precise products. Compared with the solutions from a single analysis center, the combined solutions derived from multiple analysis centers are characterized with robustness and reliability and preferred to be used as references to assess the performance of broadcast ephemerides. In this paper, the combination method of iGMAS orbit and clock products is described, and the performance of the combined solutions is evaluated by various means. There are different internal precisions of the combined orbit and clock for different constellations, which indicates that consistent weights should be assigned for individual constellations and analysis centers included in the combination. For BDS-3, Galileo, and GLONASS combined orbits of iGMAS, the root-mean-square error (RMSE) of 5 cm is achieved by satellite laser ranging (SLR) observations. Meanwhile, the SLR residuals are characterized with a linear pattern with respect to the position of the sun, which indicates that the solar radiation pressure (SRP) model adopted in precise orbit determination needs further improvement. The consistency between combined orbit and clock of quad-constellation is validated by precise point positioning (PPP), and the accuracies of simulated kinematic tests are 1.4, 1.2, and 2.9 cm for east, north, and up components, respectively.

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Multi-GNSS Combined Orbit and Clock Solutions at iGMAS

Interoperability of GNSS Open Services have already been a significant tendency in developing all Satellite Navigation Systems, and its performance will directly affect the security and reliability of its usages. Therefore, monitoring and assessment of GNSS Open Services have become an attention focus for all providers and users of GNSS. This paper begins to illuminate the elements and methods for monitoring and assessing GNSS Open Services. Then according to the requirements, the architecture of an international GNSS Monitoring and Assessment System (iGMAS) is designed to achieve the 4-overlap and 1-overlap coverage and sophisticated analysis respectively. Here, this iGMAS is based on omni-directional antennas, multi-beam antennas and a high-gain paraboloid antenna. In the meantime, the configuration scheme of world-wide monitoring stations is provided. Finally, some related works that have been done to monitor and assess BeiDou Open Service are introduced, which can be used to verify the feasibility of this proposed system.

Monitoring and assessment of GNSS open services

In traditional cesium beam clocks, cesium atoms are deflected by strong inhomogeneous magnetic fields. The distribution of the detectable atoms, which is critical to the short-term frequency stability, is hard to describe with analytical functions. In this paper, we numerically analyze the beam optics performance of cesium beam tubes based on the magnetic-state-selected and fluorescence detection scheme. To accurately model the cesium beam tube, we apply the Monte Carlo sampling directly inside the collimator. The finite element method is also applied to model the magnetic field. Upon the high dimensional distribution space, two key parameters are selected as indicators of the short-term performance of the cesium beam tube, the effective velocity distribution, and the normalized density difference of atoms in [Formula: see text] and [Formula: see text]. The influence of the configuration of the collimator is analyzed. Experiments are carried out with two manufactured beam tubes. The results show good agreement with the simulation model. We also discuss limitations of the simulation method when applied to designing cesium beam tubes.

Beam optics analysis on magnetic-state-selected atomic clocks with optical detection

High-stability optical frequency comparison over fiber link enables the establishment of ultrastable optical clock networks, having the potential to promote a series of applications, including metrology, geodesy, and astronomy. In this article, we theoretically analyze and experimentally demonstrate a time-delayed local two-way (TD-LTW) optical frequency comparison scheme with improved comparison stability, showing that the fractional instability of optical frequency comparison over a 50-km transfer link can be reduced from <inline-formula><tex-math notation="LaTeX">$1.30\times 10^{-15}$</tex-math></inline-formula> to <inline-formula><tex-math notation="LaTeX">$5.25\times 10^{-16}$</tex-math></inline-formula> at the 1 s integration time with an improvement factor of 2.48. Additionally, we also for the first time model and experimentally verify the effect of the inhomogeneous phase noise along the fiber link on the system performance. We believe that the theory and technique proposed here will be helpful in developing the high-stability optical clock networks over large-area fiber links.

Wenhai Jiao

Papers

Monitoring and Assessment of GNSS Open Services

Multi-GNSS Combined Orbit and Clock Solutions at iGMAS

Monitoring and assessment of GNSS open services

Beam optics analysis on magnetic-state-selected atomic clocks with optical detection

Enhanced Phase Noise Reduction in Localized Two-Way Optical Frequency Comparison