Characterization and Mitigation of BeiDou Triple-Frequency Code Multipath Bias

The differential code bias (DCB) in Global Navigation Satellite System (GNSS) satellites should be precisely determined using real ground GNSS data when designing certain applications, such as precise positioning, navigation and timing. This paper analyzed the relationship between satellite elevation angle with DSNR (difference signal to noise ratio) of BDS (BeiDou Navigation Satellite System) different orbital satellite. The experimental results showed that the DSNR of IGSO satellite was less than 5dBHz and more stable, much better than the other satellites; the change of GEO satellite DSNR was small, but the absolute value was large; MEO satellite DSNR changed frequently and big. A new algorithm to get the BDS observation weight is introduced by considering the distance between the satellite and the Earth and DSNR. The results indicated that the new weight algorithm improved the DCB accuracy and enhanced the stabilities, which improved GEO satellites 1–15 %, IGSO satellites 4.5–16 %, MEO satellites 20–22 %.

Though widely used to generate the global navigation satellite system (GNSS) ultra-rapid orbit products for real-time applications, the batch least-squares (LSQ) adjustment and precise orbit determination (POD) prediction is limited for satellites undergoing maneuvers. To generate the truly real-time orbit products, we introduce the square root information filter (SRIF) real-time POD strategy, in which a real-time satellite maneuver handling algorithm that adapts the stochastic model for irregular satellite behaviors is implemented. The performance of the SRIF POD strategy is first evaluated with 1-month of data from multi-GNSS experiment (MGEX) network and BDS experimental tracking stations (BETS). Compared with the MGEX final products provided by GFZ (GBM), the SRIF solutions show higher precision than the ultra-rapid solutions. The averaged 3D RMS of the orbit differences between the SRIF solutions and the GBM final product is about 29.1 cm and 22.5 cm for the BDS IGSO and MEO satellites. The BDS orbits generated by SRIF are continuous over all the time, while the ultra-rapid orbits exhibit obvious jumps and discontinuity at the orbit update time. Validation by satellite laser ranging (SLR) shows that for GEO satellites, the SRIF solutions have better stability and continuity, whereas the GBM final products exhibit obvious accuracy degradation around the day boundary. To evaluate the performance of maneuver handling, the proposed method is further tested on 10 maneuver cases of BDS GEO and IGSO satellites. The start and end time of all maneuver events in different cases are precisely detected, which are consistent with the officially announced ones. Using the proposed strategy, the filter avoids divergence and outputs continuous orbit solutions during the maneuver periods and restores the normal POD within about 7.5 h after the maneuver is finished.

In view of the problem of the long-term variation of code multipath error (called code multipath bias) in the IGSO and MEO satellite observable, code multipath bias of BDS is analyzed using iGMAS data of multiple earth stations. In addition, the GPS and BDS multipath error variation is analyzed comparatively. The results show that the variation of BDS multipath error is related to the elevation angle, satellite orbit type and carrier frequency, but independent with the location of the receivers. And for the carrier frequency B1, B2, and B3, the code multipath bias for MEO satellite is 1.66, 1.05 and 0.53 m, respectively. For IGSO satellite the code multipath bias is 0.65, 0.44, and 0.31 m accordingly, which are smaller than that reported by earlier papers. Especially, for IGSO at frequency B2 and B3, the code multipath bias is smaller than half of that reported earlier. At the same time, in order to reduce the multipath bias, a two-order polynomial fitting algorithm is proposed in this paper. The results show that: compared with the results of piecewise linear model with 10 correction parameters, the two-order polynomial correction algorithm with three correction parameters can correct the multipath error and reduce the RMS of the multipath error more effectively. The two-order polynomial model in this paper is more convenient considering broadcasting the correction information to the users.

The multipath error is the primary pseudorange measuring error factor in Compass system, in dual-frequency positioning mode, it is difficult to be eliminated by modeling methods, and on the contrary, it is always amplified because of the combination of measuring error. As a result, certain kind of user terminal has lower vertical positioning precision under dual-frequency mode than under single-frequency mode. This paper makes simulation of the impact of multipath error on pseudorange UERE under single-band mode and dual-band mode, obtains the interrelation of ionosphere modeling error, multipath error and the vertical positioning precision of single-band and dual-band respectively. This paper extracts multipath error in pseudorange of GEO and IGSO satellite by pseudorange carrier phase combination method, and uses the ionosphere delay calculated by dual-band carrier phase measurements as a benchmark, makes assessment of the ionosphere delay calculated by dual-band pseudorange combination method and ionospheric delay model correction method, analyses the amount of error correction brought into the Compass system by pseudorange of distinct orbit satellite. Data processing results show that, under current multipath mitigation measures, the pseudorange multipath error will cause that the error of GEO satellite ionosphere delay correction measured by dual-band is larger than by single-band, make a reasonable interpretation of the phenomena that dual-band vertical positioning accuracy is lower than single-band vertical positioning accuracy, and the ionospheric delay correction errors brought by pseudorange multipath error of GEO satellites are greater than the IGSO satellites, verify the phenomenon of “standing multipath error” brought by GEO satellite orbital characteristics.

Different from GPS, GLONASS, GALILEO and BeiDou-3, it is confirmed that the code multipath bias (CMB), which originate from the satellite end and can be over 1 m, are commonly found in the code observations of BeiDou-2 (BDS) IGSO and MEO satellites. In order to mitigate their adverse effects on absolute precise applications which use the code measurements, we propose in this paper an improved correction model to estimate the CMB. Different from the traditional model which considering the correction values are orbit-type dependent (estimating two sets of values for IGSO and MEO, respectively) and modeling the CMB as a piecewise linear function with a elevation node separation of 10°, we estimate the corrections for each BDS IGSO + MEO satellite on one hand, and a denser elevation node separation of 5° is used to model the CMB variations on the other hand. Currently, the institutions such as IGS-MGEX operate over 120 stations which providing the daily BDS observations. These large amounts of data provide adequate support to refine the CMB estimation satellite by satellite in our improved model. One month BDS observations from MGEX are used for assessing the performance of the improved CMB model by means of precise point positioning (PPP). Experimental results show that for the satellites on the same orbit type, obvious differences can be found in the CMB at the same node and frequency. Results show that the new correction model can improve the wide-lane (WL) ambiguity usage rate for WL fractional cycle bias estimation, shorten the WL and narrow-lane (NL) time to first fix (TTFF) in PPP ambiguity resolution (AR) as well as improve the PPP positioning accuracy. With our improved correction model, the usage of WL ambiguity is increased from 94.1% to 96.0%, the WL and NL TTFF of PPP AR is shorten from 10.6 to 9.3 min, 67.9 to 63.3 min, respectively, compared with the traditional correction model. In addition, both the traditional and improved CMB model have a better performance in these aspects compared with the model which does not account for the CMB correction.

Validation and evaluation on B1IB3I-based and B1CB2a-based BDS-3 precise orbits from iGMAS

As a significant part of GNSS navigation message, timing group delay is one of the main errors in GNSS applications such as navigation, positioning, timing and ionospheric estimation. DCB solution in One-TGD-fixed constraint condition is more suitable for Beidou regional satellite navigation system, in which the TGD parameter exit calibration value of a certain GEO satellite is fixed as the constraint condition. Based on the global ionospheric map provided by IGS as a reference, monthly TGD parameters in 2019 have been calculated to analyse the characteristics of satellite TGD changes. The results demonstrate that the stability of TGD parameters is from high to low in the order of GEO satellites, MEO satellites and IGSO satellites. The changes of all satellites in a year are within 1ns, and most of them are within 0.5 ns. Monthly changes in TGD-B1B2 are in -1.6 ~ 1.5ns, and TGD-B1B3 are in -1.4 ~ 1.2ns. TGD-B1B3 parameters are more stable than TGD-B1B2 parameters in monthly variation, with maximum changes in a month within 1.6ns for TGD-B1B2 and 1.3ns for TGD-B1B3, average changes in a month within 0.7ns for TGD-B1B2 and 0.5ns for TGD-B1B3.

The optimization of the inter-satellite link assignment is an important technical issue, especially, for the case that the number of inter-satellite spot-beam antennas is less than assignable links. Based on Minimum Spanning Tree (MST) theory in graph theory, this paper proposes a link assignment algorithm for the hybrid navigation constellation using GEO, IGSO and MEO satellites. Using GEO satellites as the core transfer node, this algorithm assigns inter-satellite links with lower communication costs firstly, and then assigns links at least once for all visible satellites by applying the iterative assignment. As a consequence, the integrated optimization of the inter-satellite observing and communication performance can be achieved. The simulated results show that, compared to the mesh-link assignment algorithm used for the Iridium system, the proposed link assignment algorithm can be able to improve the precision of orbit determination and reduce whole-network average communication delay.

This paper focuses on the precise point positioning (PPP) ambiguity resolution (AR) using the observations acquired from four systems: GPS, BDS, GLONASS, and Galileo (GCRE). A GCRE four-system uncalibrated phase delay (UPD) estimation model and multi-GNSS undifferenced PPP AR method were developed in order to utilize the observations from all systems. For UPD estimation, the GCRE-combined PPP solutions of the globally distributed MGEX and IGS stations are performed to obtain four-system float ambiguities and then UPDs of GCRE satellites can be precisely estimated from these ambiguities. The quality of UPD products in terms of temporal stability and residual distributions is investigated for GPS, BDS, GLONASS, and Galileo satellites, respectively. The BDS satellite-induced code biases were corrected for GEO, IGSO, and MEO satellites before the UPD estimation. The UPD results of global and regional networks were also evaluated for Galileo and BDS, respectively. As a result of the frequency-division multiple-access strategy of GLONASS, the UPD estimation was performed using a network of homogeneous receivers including three commonly used GNSS receivers (TRIMBLE NETR9, JAVAD TRE_G3TH DELTA, and LEICA). Data recorded from 140 MGEX and IGS stations for a 30-day period in January in 2017 were used to validate the proposed GCRE UPD estimation and multi-GNSS dual-frequency PPP AR. Our results show that GCRE four-system PPP AR enables the fastest time to first fix (TTFF) solutions and the highest accuracy for all three coordinate components compared to the single and dual system. An average TTFF of 9.21 min with $$7{^{\circ }}$$ cutoff elevation angle can be achieved for GCRE PPP AR, which is much shorter than that of GPS (18.07 min), GR (12.10 min), GE (15.36 min) and GC (13.21 min). With observations length of 10 min, the positioning accuracy of the GCRE fixed solution is 1.84, 1.11, and 1.53 cm, while the GPS-only result is 2.25, 1.29, and 9.73 cm for the east, north, and vertical components, respectively. When the cutoff elevation angle is increased to $$30{^{\circ }}$$ , the GPS-only PPP AR results are very unreliable, while 13.44 min of TTFF is still achievable for GCRE four-system solutions.

Establishment criteria, routing algorithms and probability of use of inter-satellite links in mixed navigation constellations

With the rapid development of the Beidou satellite navigation system (BDS), assessment of its signal quality and navigation performance becomes more and more important. The pseudo-range multipath, carrier-phase signal-to-noise ratio (SNR) and accuracy of standard point positioning are usually taken as the indicators for assessment. In this research, we compared the signal quality and navigation performance of BDS with other three Global Navigation Satellite System (GPS, GLONASS, Galileo). The results of the Asia-Pacific region show that the pseudo-range multipath error for BDS is similar with GPS whereas the GLONASS code measurements exhibit a higher level. The level of carrier-phase signal-to-noise ratio for Galileo is largest, but similar for BDS, GPS and GLONASS. The standard point navigation and positioning performance of BDS is slightly lower than GPS, but it is better than GLONASS, and the accuracy of BDS, GPS and GLONASS standard point positioning is about 10 m. The pseudo-range multipath error of BDS increases as the satellites elevation decreases, but the carrier-phase signal-to-noise ratio is opposite. The variation of pseudo-range multipath error of BDS GEO satellites is small except for low satellites elevation, but the variation of signal-to-noise ratio of GEO satellites is relatively stable. The variation of multipath and signal-to-noise ratio of BDS IGSO and MEO satellites is relatively stable when the satellites elevation is larger than a certain value.

This paper shows us the coverage performance and Doppler shift of the IGSO constellation with 2, 3 or 4 satellites, and then contrasted with the GEO satellite. The IGSO constellation is better than GEO satellite in average elevation angle and multi-satellite coverage. It is concluded after simulation and analysis that the IGSO constellation with 3 or 4 IGSO satellites can provide higher coverage performance for the Chinese areas and nearby, especially communication elevation in high latitude area, just with a small Doppler shift increase. The IGSO satellite constellation can be used more properly as the regional mobile satellite communication constellation.

In GNSS real-time high-precision monitoring, the multipath spatial correlation is weak, it is difficult to eliminate the multipath error by double difference, and the traditional method based on the sidereal filtering in the coordinate domain to mitigate multipath error of MEO satellite will no longer be applicable. Aiming at the above problem, this paper storage single difference observation residuals after ambiguity resolved in real-time baseline resolution, where storage residual information for 1d in GPS, BDS GEO, IGSO, and BDS MEO satellite for 7d. When the residual information database initialization is complete, each satellite multipath error sequence model will be established from the residual database by using the low-pass filter method, then mitigating multipath error of the corresponding satellite carrier phase observations in real time. The measured data show that, based on the mitigating multipath of observation domain, the real-time monitoring accuracy of the 3D position can be improved by about 50% after mitigating multipath error in real-time.

The precise orbit determination (POD) accuracy of the Chinese BeiDou Navigation Satellite System (BDS) is still not comparable to that of the Global Positioning System because of the unfavorable geometry of the BDS and the uneven distribution of BDS ground monitoring stations. Fortunately, low Earth orbit (LEO) satellites, serving as fast moving stations, can efficiently improve BDS geometry. Nearly all studies on Global Navigation Satellite System POD enhancement using large LEO constellations are based on simulations and their results are usually overly optimistic. The receivers mounted on a spacecraft or an LEO satellite are usually different from geodetic receivers and the observation conditions in space are more challenging than those on the ground. The noise level of spaceborne observations needs to be carefully calibrated. Moreover, spaceborne observational errors caused by space weather events, i.e., solar geomagnetic storms, are usually ignored. Accordingly, in this study, the actual spaceborne observation noises are first analyzed and then used in subsequent observation simulations. Then, the observation residuals from the actual-processed LEO POD during a solar storm on 8 September 2017 are extracted and added to the simulated spaceborne observations. The effect of the observational errors on the BDS POD augmented with different LEO constellation configurations is analyzed. The results indicate that the noise levels from the Swarm-A, GRACE-A, and Sentinel-3A satellites are different and that the carrier-phase measurement noise ranges from 2 mm to 6 mm. Such different noise levels for LEO spaceborne observations cause considerable differences in the BDS POD solutions. Experiments calculating the augmented BDS POD for different LEO constellations considering spaceborne observational errors extracted from the solar storm indicate that these errors have a significant influence on the accuracy of the BDS POD. The 3D root mean squares of the BDS GEO, IGSO, and MEO satellite orbits are 1.30 m, 1.16 m, and 1.02 m, respectively, with a Walker 2/1/0 LEO constellation, and increase to 1.57 m, 1.72 m, and 1.32 m, respectively, with a Walker 12/3/1 constellation. When the number of LEO satellites increases to 60, the precision of the BDS POD improves significantly to 0.89 m, 0.77 m, and 0.69 m for the GEO, IGSO, and MEO satellites, respectively. While 12 satellites are sufficient to enhance the BDS POD to the sub-decimeter level, up to 60 satellites can effectively reduce the influence of large spaceborne observational errors, i.e., from solar storms.

With the first phase of COMPASS/BeiDou-2 (BDS) completed, the assessment of positioning performance and the characterization of its system are analyzed and presented. Pseudo-range and carrier phase measurements modulated on B1 and B2 have been collected in Shanghai, from 00:00 to 24:00 on 28 December, 2012. Compared with GPS, visibility and measurement quality of BDS's GEO, IGSO and MEO satellites are analyzed. DOP during the whole orbital period is also analyzed the results demonstrate that BDS's HDOP is better than GPS's one, but VDOP opposite. Furthermore, the result of positioning is also presented and analyzed. Short baselines are estimated by standalone BDS and GPS's carrier phase measurement, respectively, using 48 segmentations of observations during a whole day (24 hours, each segmentation, is about 30 minutes observation). The analysis of static relative positioning demonstrates that BDS could achieve to millimeter level, corresponding to GPS. Kinematic result is produced by double differenced carrier phase observations with the ambiguities fixed under the constraint of precise short baseline.The result shows that the centimeter accuracy could be achieved. When comparing the results of kinematic baseline solutions, performance of BDS is worse than GPS on North and Up components, but oppositely on the component of East in the kinematic baseline processing.