Refining of BDS Differential Code Bias Model

Abstract. The differential code bias (DCB) of the Global Navigation Satellite System (GNSS) is an important error source in ionospheric modeling, which was generally estimated as constants every day. However, the receiver DCB may be changing due to the varying spatial environments and temperatures. In this paper, a method based on the global ionospheric map (GIM) of the Center for Orbit Determination in Europe (CODE) is presented to estimate the BeiDou Navigation Satellite System (BDS) receiver DCB with epoch-by-epoch estimates. The BDS receiver DCBs are analyzed from 30 d of Multi-GNSS Experiment observations. The comparison of estimated receiver DCB of BDS with the DCB provided by the German Aerospace Center (DLR) and the Chinese Academy of Sciences (CAS) shows a good agreement. The root-mean-square (rms) values of receiver DCB are 0.43 and 0.80 ns with respect to the DLR and CAS estimates, respectively. In terms of the intraday variability of receiver DCB, most of the receiver DCBs show relative stability within 1 d with the intraday standard deviation (SD) of less than 1 ns. However, larger fluctuations with more than 2 ns of intraday receiver DCB are found. Besides, the intraday stability of receiver DCB calculated by the third-generation BDS (BDS-3) and the second-generation BDS (BDS-2) observations is compared. The result shows that the intraday stability of BDS-3 receiver DCB is better than that of BDS-2 receiver DCB.

This paper proposes an enhanced algorithm to estimate the differential code biases (DCB) on three frequencies of the BeiDou Navigation Satellite System (BDS) satellites. By forming ionospheric observables derived from uncombined precise point positioning and geometry-free linear combination of phase-smoothed range, satellite DCBs are determined together with ionospheric delay that is modeled at each individual station. Specifically, the DCB and ionospheric delay are estimated in a weighted least-squares estimator by considering the precision of ionospheric observables, and a misclosure constraint for different types of satellite DCBs is introduced. This algorithm was tested by GNSS data collected in November and December 2013 from 29 stations of Multi-GNSS Experiment (MGEX) and BeiDou Experimental Tracking Stations. Results show that the proposed algorithm is able to precisely estimate BDS satellite DCBs, where the mean value of day-to-day scattering is about 0.19 ns and the RMS of the difference with respect to MGEX DCB products is about 0.24 ns. In order to make comparison, an existing algorithm based on IGG: Institute of Geodesy and Geophysics, China (IGGDCB), is also used to process the same dataset. Results show that, the DCB difference between results from the enhanced algorithm and the DCB products from Center for Orbit Determination in Europe (CODE) and MGEX is reduced in average by 46 % for GPS satellites and 14 % for BDS satellites, when compared with DCB difference between the results of IGGDCB algorithm and the DCB products from CODE and MGEX. In addition, we find the day-to-day scattering of BDS IGSO satellites is obviously lower than that of GEO and MEO satellites, and a significant bias exists in daily DCB values of GEO satellites comparing with MGEX DCB product. This proposed algorithm also provides a new approach to estimate the satellite DCBs of multiple GNSS systems.

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.

It is foreseeable that the BeiDou navigation satellite system with global coverage (BDS-3) and the BeiDou navigation satellite (regional) system (BDS-2) will coexist in the next decade. Care should be taken to minimize the adverse impact of the receiver-related biases, including inter-system biases (ISBs), differential code biases (DCB), and differential phase biases (DPB) on the positioning, navigation, and timing (PNT) provided by global navigation satellite systems (GNSS). Therefore, it is important to ascertain the intrinsic characteristics of receiver-related biases, especially in the context of the combination of BDS-3 and BDS-2, which have some differences in their signal level. We present a method that enables time-wise retrieval of between-receiver ISBs, DCB, and DPB from multi-frequency multi-GNSS observations. With this method, the time-wise estimates of the receiver-related biases between BDS-3 and BDS-2 are determined using all five frequencies available in different receiver pairs. Three major findings are suggested based on our test results. First, code ISBs are significant on the two overlapping frequencies B1II and B2b/B2I between BDS-3 and BDS-2 for a baseline with non-identical receiver pairs, which disrupts the compatibility of the two constellations. Second, epoch-wise DCB estimates of the same type in BDS-3 and BDS-2 can show noticeable differences. Thus, it is unreasonable to treat them as one constellation in PNT applications. Third, the DPB of BDS-3 and BDS-2 may have significant short-term variations, which can be attributed to, on the one hand, receivers composing baselines, and on the other hand, frequencies.

The code-phase divergences, which are minimal for GPS, GLONASS, and Galileo satellites, are commonly found in BeiDou Navigation Satellite System (BDS) Geostationary Orbit (GEO), Inclined GeoSynchronous Orbit (IGSO) and Medium Earth Orbit (MEO) satellites. Several precise positioning applications which use code observations are severely affected by these code biases. We present an analysis of code bias based on multipath (MP) combination observations. To mitigate the effect of BDS code bias on precise positioning, we proposed a periodical correction method using a low-pass filter for BDS GEO, IGSO and MEO satellites. The auto-correlation of MP series over long periods is analyzed to obtain the periods of the dominant repeating components for three types of BDS satellites. The periods of the dominant daily repeating components are close to 86,160 s for BDS GEO and IGSO satellites while 603,120 s for MEO satellites. The zero phase-shift low-pass filter was used to extract the low-frequency components of MP series and then low-frequency components are applied to mitigate the code bias periodically. The developed correction methods can make a more remarkable improvement for the accuracy of MP series, compared to the current elevation-dependent correction models. Data sets collected at 50 Global Navigation Satellite System (GNSS) ground stations including 15 of the International GNSS Monitoring and Assessment System (iGMAS) and 35 of the Multi-GNSS Experiment (MGEX) stations are employed for this study. To analyze the influence of code bias on precise positioning and validate the effectiveness of the correction methods, some applications such as single point positioning (SPP), wide-lane (WL) ambiguity analysis and Uncalibrated Phase Delays (UPDs) estimation are conducted. After applying the proposal correction method to the code observations, SPP solutions outperform the uncorrected ones in term of positioning accuracy. The positioning accuracy decreased by 0.28 and 0.1 m in the north and east components and the improvements are more significant for the U components decreased by 0.42 m. In addition, the systematic variations of Melbourne-Wübbena (MW) combination are greatly removed and the convergence time of the MW series are decreased. Moreover, significant improvement is also achieved in terms of the usage rate and residuals of UPDs estimation.

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.

Differential code bias estimation based on uncombined PPP with LEO onboard GPS observations

Because of the special design of BeiDou navigation satellite system (BDS) constellation, the effects of ionospheric scintillation on operational BDS generally are more serious than on the global positioning system (GPS). As BDS is currently providing global services, it is increasingly important to seek strategies to mitigate the scintillation effects on BDS navigation and positioning services. In this study, an improved cycle-slip threshold model is proposed to decrease the high false-alarm rate of cycle-slips under scintillation conditions, thus avoiding the frequent unnecessary ambiguity resets in BDS precise point positioning (PPP) solution. We use one-year (from 23 March 2015 to 23 March 2016) BDS dataset from Hong Kong Sha Tin (HKST) station (22.4°N, 114.2°E; geomagnetic latitude: 15.4°N) to model the cycle-slip threshold and try to make it suitable for three types of BDS satellites and multiple scintillation levels. The availability of our mitigation strategy is validated by using three months (from 1 September 2015 to 30 November 2015) BDS dataset collected at 10 global navigation satellite system (GNSS) stations in Hong Kong. Positioning results demonstrate that our mitigated BDS PPP can prevent the sudden fluctuations of positioning errors induced by the ionospheric scintillation. Statistical results of BDS PPP experiments show that the mitigated solution can maintain an accuracy of about 0.08 m and 0.10 m in the horizontal and vertical components, respectively. Compared with standard BDS PPP, the accuracy of mitigated PPP can be improved by approximately 24.1%, 38.2%, and 47.9% in the east, north, and up directions, respectively. Our study demonstrates that considering different scintillation levels to establish appropriate cycle-slip threshold model in PPP processing can efficiently mitigate the ionospheric scintillation effects on BDS PPP.

In-orbit performance of GNOS on-board FY3-C and the enhancements for FY3-D satellite

The utilization of Global Navigation Satellite System (GNSS) is becoming an attractive navigation approach for geostationary orbit (GEO) satellites. A high-sensitivity receiver compatible with Global Position System (GPS) developed by the United States and BeiDou Navigation Satellite System (BDS) developed by China has been used in a GEO satellite named TJS-5 to demonstrate feasibility of real-time navigation. According to inflight data, the GNSS signal characteristics including availability, position dilution of precision (PDOP), carrier-to-noise ratio (C/N0), observations quantity and accuracy are analyzed. The mean number of GPS and GPS + BDS satellites tracked are 7.4 and 11.7 and the mean PDOP of GPS and GPS + BDS are 10.24 and 3.91, respectively. The use of BDS significantly increases the number of available navigation satellites and improves the PDOP. The number of observations with respect to C/N0 is illustrated in detail. The standard deviation of the pseudorange noises are less than 4 m, and the corresponding carrier phase noises are mostly less than 8 mm. We present the navigation performance using only GPS observations and GPS + BDS observations combination at different weights through comparisons with the precision reference orbits. When GPS combined with BDS observations, the root mean square (RMS) of the single-epoch least square position accuracy can improve from 32.1 m to 16.5 m and the corresponding velocity accuracy can improve from 0.238 m/s to 0.165 m/s. The RMS of real-time orbit determination position accuracy is 5.55 m and the corresponding velocity accuracy is 0.697 mm/s when using GPS and BDS combinations. Especially, the position accuracy in x-axis direction reduced from 7.24 m to 4.09 m when combined GPS with BDS observations.

Differential Code Biases (DCBs) are systematic errors, or biases, between two Global Navigation Satellite System (GNSS) code observations at the same or different frequencies. Knowledge of DCBs is required for positioning of GNSS receivers, extracting ionosphere total electron content (TEC), and other applications. Proper knowledge of DCBs is crucial to many navigation applications but also non-navigation applications such as ionospheric analysis and time transfer. The multitude of new signals offered by modernized and new GNSS constellations, requires a comprehensive multi-GNSS bias product. And because of the multitude of GNSS signals it has become more practical to provide the DCBs, differential signal biases, as observable specific biases, OSBs.At the Navigation Support Office at ESA/ESOC we have for many years relied on the bias products (DCB and OSB) coming from the CODE analysis centre. But in the fast-developing Multi-GNSS landscape it became clear that we needed to have to capability to generate our own independent bias product. For our different GNSS projects we therefore have developed a process to generate our own OSB product with the ambition to have DCBs for all existing MGNSS signals, as long as the signals are tracked by the stations in the large IGS station network. And rather than monthly biases as typically provided and used within the IGS, we have moved to what we call a “Bias Reference Frame” (BREF). The absolute value is still determined by a zero-mean condition at a certain date. But from that point in time the biases are kept stable unless a clear jump in the satellite bias is, automatically, detected. The detectability is at the 0.25ns for well observed biases. The DCB version of the product is publicly available on our Navigation Office website. The OSB version is still under development and testing.In developing this product, we found some very interesting features of the biases when looking at the biases of the so called “interoperable” signals, which we will present and discuss. We demonstrate the importance of this product for the analysis of the Sentinel 6A data which tracks Galileo and an interesting mix of GPS signals which makes it hard to process the GPS data with the standard IGS products, in particular for PPP-AR.

We present quad-constellation (namely, GPS, GLONASS, BeiDou and Galileo) time group delay (TGD) and differential code bias (DCB) correction models to fully exploit the code observations of all the four global navigation satellite systems (GNSSs) for navigation and positioning. The relationship between TGDs and DCBs for multi-GNSS is clearly figured out, and the equivalence of TGD and DCB correction models combining theory with practice is demonstrated. Meanwhile, the TGD/DCB correction models have been extended to various standard point positioning (SPP) and precise point positioning (PPP) scenarios in a multi-GNSS and multi-frequency context. To evaluate the effectiveness and practicability of broadcast TGDs in the navigation message and DCBs provided by the Multi-GNSS Experiment (MGEX), both single-frequency GNSS ionosphere-corrected SPP and dual-frequency GNSS ionosphere-free SPP/PPP tests are carried out with quad-constellation signals. Furthermore, the author investigates the influence of differential code biases on GNSS positioning estimates. The experiments show that multi-constellation combination SPP performs better after DCB/TGD correction, for example, for GPS-only b1-based SPP, the positioning accuracies can be improved by 25.0%, 30.6% and 26.7%, respectively, in the N, E, and U components, after the differential code biases correction, while GPS/GLONASS/BDS b1-based SPP can be improved by 16.1%, 26.1% and 9.9%. For GPS/BDS/Galileo the 3rd frequency based SPP, the positioning accuracies are improved by 2.0%, 2.0% and 0.4%, respectively, in the N, E, and U components, after Galileo satellites DCB correction. The accuracy of Galileo-only b1-based SPP are improved about 48.6%, 34.7% and 40.6% with DCB correction, respectively, in the N, E, and U components. The estimates of multi-constellation PPP are subject to different degrees of influence. For multi-constellation combination SPP, the accuracy of single-frequency is slightly better than that of dual-frequency combinations. Dual-frequency combinations are more sensitive to the differential code biases, especially for the 2nd and 3rd frequency combination, such as for GPS/BDS SPP, accuracy improvements of 60.9%, 26.5% and 58.8% in the three coordinate components is achieved after DCB parameters correction. For multi-constellation PPP, the convergence time can be reduced significantly with differential code biases correction. And the accuracy of positioning is slightly better with TGD/DCB correction.

Estimation of the DCB for the BDS-3 new signals based on BDGIM constraints

Global Navigation Satellite System (GNSS) carrier phase measurement for short baseline meets the requirements of deformation monitoring of large structures. However, the carrier phase multipath effect is the main error source with double difference (DD) processing. There are lots of methods to deal with the multipath errors of Global Position System (GPS) carrier phase data. The BeiDou navigation satellite System (BDS) multipath mitigation is still a research hotspot because the unique constellation design of BDS makes it different to mitigate multipath effects compared to GPS. Multipath error periodically repeats for its strong correlation to geometry of satellites, reflective surface and antenna which is also repetitive. We analyzed the characteristics of orbital periods of BDS satellites which are consistent with multipath repeat periods of corresponding satellites. The results show that the orbital periods and multipath periods for BDS geostationary earth orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites are about one day but the periods of MEO satellites are about seven days. The Kalman filter (KF) and Rauch-Tung-Striebel Smoother (RTSS) was introduced to extract the multipath models from single difference (SD) residuals with traditional sidereal filter (SF). Wavelet filter and Empirical mode decomposition (EMD) were also used to mitigate multipath effects. The experimental results show that the three filters methods all have obvious effect on improvement of baseline accuracy and the performance of KT-RTSS method is slightly better than that of wavelet filter and EMD filter. The baseline vector accuracy on east, north and up (E, N, U) components with KF-RTSS method were improved by 62.8%, 63.6%, 62.5% on day of year 280 and 57.3%, 53.4%, 55.9% on day of year 281, respectively.

The improvement of BDS Observation Geometry with LEO constellations in Orbit Determination