The Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS) - Achievements, prospects and challenges

A consistent analysis of signal-in-space ranging errors (SISREs) is presented for all current satellite navigation systems, considering both global average values and worst-user-location statistics. The analysis is based on 1 year of broadcast ephemeris messages of the Global Positioning System (GPS), GLONASS, Galileo, BeiDou and QZSS collected with a near-global receiver network. Position and clock values derived from the navigation data are compared against precise orbit and clock products provided by the International GNSS Service and its multi-GNSS experiment. Satellite laser ranging measurements are used for a complementary and independent assessment of the orbit-only SISRE contribution. The need for proper consideration of antenna offsets is highlighted and block-/constellation-specific radial antenna offset values for the center-of-mass correction of broadcast orbits are derived. Likewise, the need for application of differential code biases in the comparison of broadcast and precise clock products is emphasized. For GPS, the analysis of the legacy navigation message is complemented by a discussion of the CNAV message performance based on the first CNAV test campaign in June 2013. Global average SISRE values for the individual constellations amount to 0.7 ± 0.02 m (GPS), 1.5 ± 0.1 m (BeiDou), 1.6 ± 0.3 m (Galileo), 1.9 ± 0.1 m (GLONASS), and 0.6 ± 0.2 m (QZSS) over a 12-month period in 2013/2014.

Broadcast versus precise ephemerides: a multi-GNSS perspective

Multi-GNSS signal-in-space range error assessment – Methodology and results

Five new-generation BeiDou-3 experimental satellites, called BeiDou-3e, have been launched into inclined geosynchronous orbit (IGSO) and medium orbit (MEO) since March 2015. In addition to newly designed signals and intersatellite links, different satellite buses, updated rubidium atomic frequency standards (RAFSs), and new passive hydrogen masers (PHMs) have been used. Using 15 stations, mainly in the Asia–Pacific region, we determined orbits and clock for both the BeiDou-3e and the regional BeiDou-2 satellites using the Extend CODE (Center for Orbit Determination in Europe) Orbit Model (ECOM). The orbit consistency, indicated by 3D orbit boundary discontinuity, is 50–70 and 40–60 cm for BeiDou-3e IGSO and MEO satellites, respectively, and better than 15 cm in radial component. Satellite laser ranging (SLR) validation gives about 17 and 10 cm for BeiDou-3e IGSO and MEO satellites. The BeiDou-3e satellites orbits show slightly better performance than the BeiDou-2 satellites as indicated by SLR. However, errors depending on the sun elongation angle were identified in SLR residuals for the BeiDou-3e IGSO C32 satellite, while such errors did not exist for BeiDou-2 IGSO/MEO and BeiDou-3e MEO satellites. No orbit accuracy degeneration for BeiDou-3e IGSO and MEO satellites was observed when the elevation angle (β angle) of the sun above the orbital plane was between − 4° and + 4°. In that case, the BeiDou-2 IGSO and MEO satellites are in orbit normal (ON) mode. An analysis of the yaw attitude identified that BeiDou-3e satellites did not use the ON mode, but experienced midnight- and noon-point maneuvers when the β angle is approximately between − 3° and + 3°. Compared with BeiDou-2 satellites, the onboard clocks of the BeiDou-3e IGSO satellites showed dramatic improved performance. The stability of BeiDou-3e IGSO satellites can be compared to the latest type of RAFSs employed onboard the GPS IIF satellites as well as the PHMs used onboard the Galileo satellites.

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Precise orbit and clock determination for BeiDou-3 experimental satellites with yaw attitude analysis

The main objective of this research was to examine the feasibility of Multi-GNSS precise point positioning (PPP) in precision agriculture (PA) through a series of experiments with different working modes (i.e. stationary and moving) under different observation conditions (e.g. open sky, with buildings or with canopy). For the stationary test carried out in open space in the UK, the positioning accuracy achieved was 13.9 mm in one dimension by a PPP approach, and the repeatability of positioning results was improved from 19.0 to 6.0 mm by using Multi-GNSS with respect to GPS only. For the moving test carried out in similar location in the UK, almost the same performance was achieved by GPS-only and by Multi-GNSS PPP. However, for a moving experiment carried out in China with obstruction conditions, Multi-GNSS improved the accuracy of baseline length from 126.0 to 35.0 mm and the repeatability from 110.0 mm to 49.0 mm, The results suggested that the addition of the BeiDou, Galileo and GLONASS systems to the standard GPS-only processing improved the positioning repeatability, while a positioning accuracy was achieved at about 20 mm level in the horizontal direction with an improvement against the GPS-only PPP results. In space-constrained and harsh environments (e.g. farms surrounded with dense trees), the availability and reliability of precise positioning decreased dramatically for the GPS-only PPP results, but limited impacts were observed for Multi-GNSS PPP. In addition, compared to real time kinematic (RTK) GNSS, which is currently most commonly used for high precision PA applications, similar accuracy has been achieved by PPP. In contrast to RTK GNSS, PPP can provide high accuracy positioning with higher flexibility and potentially lower capital and running costs. Hence, PPP might be a great opportunity for agriculture to meet the high accuracy requirements of PA in the near future.

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Multi-GNSS precise point positioning for precision agriculture

In order to simplify the attitude control for inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) satellites of the BeiDou Navigation Satellite System (BDS) in eclipse seasons, two attitude modes, namely yaw-steering (YS) and orbit-normal (ON) mode are used. Significant accuracy degradation is observed for the orbits determined with the purely empirical CODE solar radiation pressure (SRP) model when these satellites switch to the ON mode. In addition, even though BDS IGSO satellites are in the YS mode, the orbits determined with the CODE SRP model show undesirable systematic errors that depend on the elevation angle β of the sun above the satellite orbit plane and on the argument angle μ of satellite with respect to the midnight point in the orbit plane as identified from satellite laser ranging residuals. We present the yaw attitude model used for the bus of BDS IGSO and MEO satellites, and constrain the mode-switch conditions by the β and μ angles. In order to overcome the deficiency of the purely empirical CODE SRP model for precise orbit determination (POD) of BDS IGSO and MEO satellites in the ON mode, an additional constant acceleration bias with tight constraint of 1.0 × 10ź10 m/s2 in the along-track direction has been introduced to the CODE SRP model, and it is denoted as the C5a model. Although the orbit accuracy of IGSO and MEO satellites is significantly improved in the ON mode, the β- and μ-dependent systematic orbit errors of BDS IGSO are not reduced. Hence, with the presented yaw attitude model of the satellite bus and two assumed orientations of solar panels, the adjustable box-wing (ABW) model has been modified. Two modified ABW models are compared with the purely empirical CODE and C5a model. Based on the analysis of real data of 2014, the C5a model shows the best performance in the ON mode among the four SRP models. Although two modified ABW models show a rather worse performance for POD in the ON mode, particularly in the cross-track and radial direction, the β- and μ-dependent systematic orbit errors of BDS IGSO satellites are reduced. This provides a new insight and a possible way to improve the orbits of BDS IGSO and MEO satellites.

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Comparison of solar radiation pressure models for BDS IGSO and MEO satellites with emphasis on improving orbit quality

In 2020, the BeiDou navigation satellite system (BDS) initiated a real-time service (RTS) for precise point positioning (PPP) using the B2b signal for users in China and its surrounding areas. A decimeter-level accuracy is expected to be achieved using a single receiver. In this study, the PPP-B2b service is experimentally analyzed based on 7 days of corrections and compared with the RTS provided by the Centre National d'Etudes Spatiales (CNES). The availability and completeness of these two RTS products are first evaluated based on the quality of the observation-specific bias (OSB), the satellite orbit and clock offset products. The signal-in-space ranging error (SISRE) is also calculated and evaluated. PPP-B2b can provide stable service in Asia and has better availability and completeness for BDS-3 than does CNES, though the opposite is true for GPS. The analysis reveals a nonnegligible constant satellite-specific bias in the PPP-B2b clock offset for GPS and a smaller bias for BDS-3; this bias is absent in the CNES products. The SISREs of the PPP-B2b products are affected by this bias, but the SISRE STD is comparable to that of the CNES products. Positioning experiments are carried out for the PPP-B2b and CNES products using six stations evenly distributed across China. The kinematic PPP results of BDS-3-only positioning, achieving accuracy at the centimeter level using PPP-B2b, are in good agreement with the GPS-only results using CNES. The abnormal average convergence time exceeding 60 min for GPS confirms that the satellite-specific bias in the PPP-B2b clock offset degrades the pseudorange accuracy, which should be improved in the near future.

Initial Assessment of the BDS-3 PPP-B2b RTS compared with the CNES RTS

It has been noted that the satellite laser ranging (SLR) residuals of the Quasi-Zenith Satellite System (QZSS) Michibiki satellite orbits show very marked dependence on the elevation angle of the Sun above the orbital plane (i.e., the $$\beta $$
 angle). It is well recognized that the systematic error is caused by mismodeling of the solar radiation pressure (SRP). Although the error can be reduced by the updated ECOM SRP model, the orbit error is still very large when the satellite switches to orbit-normal (ON) orientation. In this study, an a priori SRP model was established for the QZSS Michibiki satellite to enhance the ECOM model. This model is expressed in ECOM’s D, Y, and B axes (DYB) using seven parameters for the yaw-steering (YS) mode, and additional three parameters are used to compensate the remaining modeling deficiencies, particularly the perturbations in the Y axis, based on a redefined DYB for the ON mode. With the proposed a priori model, QZSS Michibiki’s precise orbits over 21 months were determined. SLR validation indicated that the systematic $$\beta $$
 -angle-dependent error was reduced when the satellite was in the YS mode, and better than an 8-cm root mean square (RMS) was achieved. More importantly, the orbit quality was also improved significantly when the satellite was in the ON mode. Relative to ECOM and adjustable box-wing model, the proposed SRP model showed the best performance in the ON mode, and the RMS of the SLR residuals was better than 15 cm, which was a two times improvement over the ECOM without a priori model used, but was still two times worse than the YS mode.

An a priori solar radiation pressure model for the QZSS Michibiki satellite

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

In this paper, the accuracy of the trial operation stage BeiDou Navigation Satellite System (BDS) navigation message was analyzed and evaluated from January to December in 2012. The main content of the Beidou performance assessment was briefly introduced together with availability of Beidou precise ephemeris. Then, according to the Beidou mixed multi-satellite constellation characteristics, calculation formula of signal in space was derived, which is exactly suitable for Beidou system. Based on the Beidou precise ephemeris which derived from Position And Navigation Data Analysis software (PANDA) and BeiDou Experimental Tracking Stations (BETS), the accuracy of Beidou broadcast ephemeris, clock errors, Beidou system ionospheric correction model (BeiDou Klobuchar) and the pseudorange Single Point Positioning (SPP) were analyzed in details.

Guo Chen

Papers

Comparison of solar radiation pressure models for BDS IGSO and MEO satellites with emphasis on improving orbit quality

Initial Assessment of the BDS-3 PPP-B2b RTS compared with the CNES RTS

An a priori solar radiation pressure model for the QZSS Michibiki satellite

Multi-GNSS Combined Orbit and Clock Solutions at iGMAS

An Initial Evaluation About BDS Navigation Message Accuracy