The core performance elements of global navigation satellite system include availability, continuity, integrity and accuracy, all of which are particularly important for the developing BeiDou global navigation satellite system (BDS-3). This paper describes the basic performance of BDS-3 and suggests some methods to improve the positioning, navigation and timing (PNT) service. The precision of the BDS-3 post-processing orbit can reach centimeter level, the average satellite clock offset uncertainty of 18 medium circular orbit satellites is 1.55 ns and the average signal-in-space ranging error is approximately 0.474 m. The future possible improvements for the BeiDou navigation system are also discussed. It is suggested to increase the orbital inclination of the inclined geostationary orbit (IGSO) satellites to improve the PNT service in the Arctic region. The IGSO satellite can perform part of the geostationary orbit (GEO) satellite’s functions to solve the southern occlusion problem of the GEO satellite service in the northern hemisphere (namely the “south wall effect”). The space-borne inertial navigation system could be used to realize continuous orbit determination during satellite maneuver. In addition, high-accuracy space-borne hydrogen clock or cesium clock can be used to maintain the time system in the autonomous navigation mode, and stability of spatial datum. Furthermore, the ionospheric delay correction model of BDS-3 for all signals should be unified to avoid user confusion and improve positioning accuracy. Finally, to overcome the vulnerability of satellite navigation system, the comprehensive and resilient PNT infrastructures are proposed for the future seamless PNT services.

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Basic performance and future developments of BeiDou global navigation satellite system

The BDS-3 preliminary system was declared functional on December 27, 2018. It enables positioning service on a global scale. This study conducts a comprehensive investigation of the BDS-3 global service from the perspective of positioning, including satellite ephemeris, benefits of the new BDS-3 satellites, and the new signal effect on three positioning modes: single-point positioning (SPP), precise-point positioning (PPP) and real-time kinematic (RTK). First, the broadcast and precise ephemeris availabilities of 18 BDS-3 Medium Earth orbit (MEO) satellites from January to June 2019 are investigated. Due to the shorter operational timespans of BDS-3 satellites, their broadcast and precise ephemeris files retrieved from Multi-GNSS Experiment (MGEX) have 1.2–19.4% and 10.9–13.77% discontinuities, respectively, while the discontinuities of BDS-2 satellite broadcast and precise ephemeris are only 0.1 and 2.1%. Second, the BDS-3 satellite orbit accuracies and clock precisions are significantly improved, i.e., below 0.5 m and 1.82 ns compared to 2 m and 2.91 ns for BDS-2 because of the inter-satellite links of BDS-3 satellites. Third, an average of 4.4–5.7 BDS satellites can be observed at stations located in North/South America, and 8.9 for the European station FFMJ located in Germany after the BDS-3 global system announcement. As a result, continuous positioning is feasible in these regions. As to four Asia–Pacific stations, their SPP accuracies are improved by 12.1–60.2% compared to those of the BDS-2-only solution. Meanwhile, the PPP and RTK convergence times of Asia–Pacific stations are also shortened. Last but not least, the new B1C signal does not bring convincing improvement to PPP and RTK positioning accuracies in this study, due to the limited number of available B1C new signals at this time.

Assessment of BDS-3 global positioning service: ephemeris, SPP, PPP, RTK, and new signal

The basic constellation of the BeiDou global satellite navigation system (BDS-3) had been successfully completed by the end of 2018. It included 18 medium earth orbit satellites and 1 geostationary orbit satellite. An initial assessment of BDS-3 broadcast orbit and clock accuracy based on 55 days of broadcast message data is presented in this contribution. Satellite positions and clock offsets derived from broadcast ephemeris are compared with precise orbit determination orbits and clock offsets. Furthermore, the corresponding signal-in-space range error (SISRE), which is of most interest to navigation users, is computed. Thanks to the new inter-satellite link payloads on BDS-3 satellites, the statistics of age-of-data-ephemeris and age-of-data-clock demonstrate that more than 98% of ephemerides and 93% of clock parameters are updated within only one hour. Experimental results show that the 3D root mean square (RMS) of broadcast orbit errors is less than 0.6 m for the overall constellation. The broadcast orbit is also assessed by satellite laser ranging measurements, giving an RMS of 7.3 cm. The orbit-only SISRE is about 0.1 m. With respect to clock errors, the timescale differences between two clock products are eliminated to assess the accuracy of broadcast clock offsets. The standard deviation value of 0.25 m shows a good performance, but the RMS value is regrettably nearly 0.5 m due to a nonzero mean bias. RMS of BDS-3 SISRE amounts to approximately 0.5 m, which is largely attributed to clock errors. Finally, a positioning experiment is conducted to analyze the accuracy of single point positioning (SPP). With 95% confidence level, the horizontal accuracy is less than 5 m, and the vertical accuracy is close to 6 m. Considering that the nonzero mean bias in clock errors may affect the performance of SPP, we correct the nonzero mean value by a satellite-specific constant to analyze the influence of clock bias on the SPP performance. The results show that improvement in the 3D position accuracy can be up to 11%, especially in the up direction.

Initial assessment of BDS-3 preliminary system signal-in-space range error

https://iopscience.iop.org/article/10.1088/1361-6501/ab41cf/pdf

Improving BDS-2 and BDS-3 joint precise point positioning with time delay bias estimation

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

Since November 2017, eight BeiDou global navigation system (BDS-3) satellites equipped with Ka-band inter-satellite link (ISL) payloads have been launched into medium earth orbit. We present the precise orbit determination (POD) for BDS-3 satellites using both L-band satellite-ground and Ka-band ISL observations. The satellite-ground tracking data are collected from the international GNSS Monitoring and Assessment System stations. The data period is DOY (day of year) 127---156, 2018. The BDS-3 ISL measurements are described by a dual one-way observation model. After transforming the dual one-way observations to the same epoch, clock-free and geometry-free observables can be obtained by the addition and subtraction of dual one-way observations. Using the geometry-free observables, the ISL measurement noise is analyzed and confirmed to be less than 10?cm. Using the clock-free observables and ground tracking data, the precise orbits are determined together with combined ISL hardware delays. For the estimates of hardware delays, the mean STD is 0.08?ns. For the satellite orbits, the ground-only POD solutions are also computed for comparison. When using 16 globally distributed ground stations, the addition of the ISLs improves the POD performance. For example, the 3D RMS of orbit overlap differences is reduced from 15.9?cm to 9.2?cm, yielding an improvement of 42% compared to ground-only POD. When only 6 stations in China are used for POD, the addition of ISLs enables the 3D RMS to be reduced from 85.4?cm to 14.8?cm with a greater improvement of 83%.

Precise orbit determination for BDS-3 satellites using satellite-ground and inter-satellite link observations

China is currently focusing on the establishment of its BDS-3 system, and a BDS-3 constellation with 18 satellites in medium Earth orbit (MEO) and one satellite in geostationary Earth orbit (GEO) has been able to provide preliminary global services since the end of 2018. These BDS-3 satellites feature the inter-satellite link (ISL) and new high-quality onboard clocks. In this study, we present the analysis of BDS-3 orbits and clocks determined by Ka-band ISL measurements from 18 MEO satellites and one GEO satellite. The ISL data of 43 days from 1 January to 12 February 2019 are used. The BDS-3 ISL measurement is described by a dual one-way ranging model. After converting bidirectional observations to the same epoch, Ka-band clock-free and geometry-free observables are obtained by the addition and subtraction of dual one-way observations, respectively. One anchor station with Ka-band bidirectional observations is introduced into the orbit determination to provide the orientation constraints. Using Ka-band clock-free observables, BDS-3 satellite orbits are determined. The ISL hardware delays are estimated together with orbits, and the resulting hardware delay estimates are quite stable with STD of about 0.03 ns. The Ka-band orbits are evaluated by orbit overlap differences, comparison with L-band precise orbits, and satellite laser ranging validation. The results indicate that the radial orbit errors are on the 2–4 cm level for MEO satellites and 8–10 cm for the GEO satellite. In addition, we investigate the ground anchoring capability by adding one anchor station and reducing the amount of data of the anchor station. Using Ka-band geometry-free observables, BDS-3 satellite clocks are estimated and the RMS of post-fit ISL residuals is about 5 cm. The Ka-band clock offsets are analyzed and compared with L-band precise clocks. Independent of orbit errors, the Allan deviation of Ka-band clocks for averaging interval longer than 5000 s is superior to that of L-band clocks. Furthermore, a pronounced bump, which appears in the Allan deviation of L-band clocks, almost vanishes in Ka-band clocks. Finally, the periodic variations are detected for L-band and Ka-band clocks.

Orbit and clock analysis of BDS-3 satellites using inter-satellite link observations

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.

/pdf/multi-gnss-combined-orbit-and-clock-solutions-at-igmas-3p9i7j19.pdf

Multi-GNSS Combined Orbit and Clock Solutions at iGMAS

For the same antenna type, numerical differences among the phase center correction (PCC) models released by different institutes can reach several millimeters, which is far beyond the nominal calibration accuracy. This contribution introduces a new method to evaluate the consistency of these PCC models. We first investigated the coupling of phase center offset (PCO) and phase center variation (PCV) through simulation experiments, and the results show that the calibrated PCO values under different strategies may result in large differences, and so do PCV values due to strong coupling with PCO. This is further confirmed by field calibration experiments. Moreover, a new datum parameter is introduced to equivalently transform the PCC models to assess the consistency of PCC models of the same antenna type calibrated under different strategies or by different facilities. It is also essential to perform consistency analysis of PCC models in the coordinate domain. We further investigated these PCC models through a simulated positioning experiment. The results show that millimeter-level consistency of PCC models will lead to the same level of positioning precision in the coordinate domain. Moreover, as a comparison, both baseline positioning and PPP were performed with an antenna-type JAV_RINGANT_G3T NONE based on real observations. Multiday results showed that the average RMS of the positioning differences between PCC models from robot and anechoic chamber calibration is less than 1 mm for the baseline solution and 4 mm for the PPP solution, although the PCC model differences can reach 6 mm in L1 and 4 mm in L2, respectively. Finally, we also investigated the distribution of position biases without PCC or with inaccurate PCC. Considering the actual GPS constellation, we found that position biases have a strong correlation with latitude, if PCV values fluctuate greatly with the users’ elevation angle.

/pdf/consistency-analysis-of-the-gnss-antenna-phase-center-ro71ommu.pdf

Consistency Analysis of the GNSS Antenna Phase Center Correction Models

The consistency of terrestrial reference frames (TRFs) realized by global navigation satellite system (GNSS) broadcast ephemerides is of great importance for multi-GNSS combined positioning. Based on BDS-3 broadcast ephemeris over 2020, we assess the coincidence level of BeiDou Coordinate System (BDCS) accessible via broadcast orbits with the newest international TRF (i.e., ITRF2014), which is also compared with the respective results of GPS and Galileo. The orbital realization of BDCS coincides with ITRF2014 at the level of 10 cm, although the broadcast orbits are constrained to BDCS only on the positions of regional stations in China. Obvious systematic errors in z-origin and orientation are found in BDS-3 broadcast orbital realized TRF, resulting in positioning errors up to 10 and 25 cm, respectively. By contrast, random errors are dominating the orbital realization of TRFs for Galileo and GPS, with an uncertainty of approximately 5 cm. The annual instability of z-origin for BDS-3 shows manufacturer- and orbit-plane-dependent characteristics, probably triggered by imperfect orbit models. A posterior model is proposed to calibrate the periodic errors in z-origin. Limited by the Monday update of earth orientation parameters prediction, the orientation stability of BDS-3 broadcast orbits degrade from Tuesday within one week, which may be amplified as no global geodetic constraints are applied. If these rotation errors are removed, the root-mean-square error of BDS-3 broadcast orbits can be reduced by 30–50% in the along and cross direction. In addition, we prove that the uncertainty of GNSS broadcast TRFs can be assessed by orbit comparison or comparisons between sets of station coordinates. Although the latter approach generally obtains larger uncertainty, results from these two approaches are at the same level.

Hongliang Cai

Papers

Precise orbit determination for BDS-3 satellites using satellite-ground and inter-satellite link observations

Orbit and clock analysis of BDS-3 satellites using inter-satellite link observations

Multi-GNSS Combined Orbit and Clock Solutions at iGMAS

Consistency Analysis of the GNSS Antenna Phase Center Correction Models

Assessment of BDS-3 terrestrial reference frame realized by broadcast ephemeris: comparison with GPS/Galileo