Search

Carrier Smoothing Code (CSC), as a low-pass filter, has been widely used in GNSS positioning processing to reduce pseudorange noise via carrier phases. However, current CSC methods do not consider the systematic bias between the code and carrier phase observation, also known as Satellite-induced Code Bias (SICB). SICB has been identified in the BDS-2 and the bias will reduce the accuracy or reliability of the CSC. To confront bias, an improved CSC algorithm is proposed by considering SICB for GEO, IGSO, and MEO satellites in BDS constellations. The correction model of SICB for IGSO/MEO satellites is established by using a 0.1-degree interval piecewise weighted least squares Third-order Curve Fitting Method (TOCFM). The Variational Mode Decomposition combined with Wavelet Transform (VMD-WT) is proposed to establish the correction model of SICB for the GEO satellite. To verify the proposed method, the SICB model was established by collecting 30 Multi-GNSS Experiment (MGEX) BDS stations in different seasons of a year, in which the BDS data of ALIC, KRGG, KOUR, GCGO, GAMG, and SGOC stations were selected for 11 consecutive days to verify the effectiveness of the algorithm. The results show that there is obvious SICB in the BDS-2 Multipath (MP) combination, but the SICB in the BDS-3 MP is smaller and can be ignored. Compared with the modeling in the references, TOCFM is more suitable for IGSO/MEO SICB modeling, especially for the SICB correction at low elevation angles. After the VMD-WT correction, the Root Mean Square Error (RMSE) of SICB of B1I, B2I, and B3I in GEO satellites is reduced by 53.35%, 63.50%, and 64.71% respectively. Moreover, we carried out ionosphere-free Single Point Positioning (IF SPP), Ionosphere-free CSC SPP (IF CSC SPP), CSC single point positioning with the IGSO/MEO SICB Correction based on the TOCFA Method (IGSO/MEO SICB CSC), and CSC single point positioning with the IGSO/MEO/GEO SICB correction based on VMD-WT and TOCFA (IGSO/MEO/GEO SICB CSC), respectively. Compared to IF SPP, the average improvement of the IGSO/MEO/GEO SICB CSC algorithm in the north, east, and up directions was 24.42%, 27.94%, and 24.98%, respectively, and the average reduction in 3D RMSE is 24.54%. Compared with IF CSC SPP, the average improvement of IGSO/MEO/GEO SICB CSC is 7.03%, 6.50%, and 10.48% in the north, east, and up directions, respectively, while the average reduction in 3D RMSE was 9.86%. IGSO/MEO SICB mainly improves the U direction positioning accuracy, and GEO SICB mainly improves the E and U direction positioning accuracy. After the IGSO/MEO/GEO SICB correction, the overall improvement was about 10% and positioning improved to a certain extent. [ABSTRACT FROM AUTHOR]

The extensive use of carrier-aided smoothing code (CSC) filters has led to a reduction in the noise level of raw code measurements in GNSS positioning and navigation applications. However, the existing CSC technique is sensitive to the changes in the integer ambiguity, and then the smoothing procedure needs to be restarted in the presence of cycle slips. As the Doppler shift is instantaneously observed and immune to cycle slips, the Doppler-aided smoothing code (DSC) algorithm would be more promising in a challenged environment. Based on the Hatch filter, an optimal DSC approach is proposed with the principle of minimum variance. Meanwhile, to inhibit the effect of the integral cumulative error of the Doppler, a balance factor is adopted to adjust the contributions of raw code and DSC. The noise level of code observable is not only affected by thermal noise, but also limited by systematic bias. Satellite code bias (SCB) was identified in the raw code observable on each frequency for each BDS-2 satellite. By minimizing the sum of the absolute value of residuals, the polynomial segment fitting algorithm as a function of elevation angles is applied to establish the SCB correction model based on epoch-differenced multipath (MP) deviations. Finally, different types of experiments demonstrate the validity and efficiency of the refined DSC filter with SCB corrections on each available frequency for BDS un-GEO satellites. [ABSTRACT FROM AUTHOR]

Carrier Smoothing Code (CSC), as a low-pass filter, has been widely used in GNSS positioning processing to reduce pseudorange noise via carrier phases. However, current CSC methods do not consider the systematic bias between the code and carrier phase observation, also known as Satellite-induced Code Bias (SICB). SICB has been identified in the BDS-2 and the bias will reduce the accuracy or reliability of the CSC. To confront bias, an improved CSC algorithm is proposed by considering SICB for GEO, IGSO, and MEO satellites in BDS constellations. The correction model of SICB for IGSO/MEO satellites is established by using a 0.1-degree interval piecewise weighted least squares Third-order Curve Fitting Method (TOCFM). The Variational Mode Decomposition combined with Wavelet Transform (VMD-WT) is proposed to establish the correction model of SICB for the GEO satellite. To verify the proposed method, the SICB model was established by collecting 30 Multi-GNSS Experiment (MGEX) BDS stations in different seasons of a year, in which the BDS data of ALIC, KRGG, KOUR, GCGO, GAMG, and SGOC stations were selected for 11 consecutive days to verify the effectiveness of the algorithm. The results show that there is obvious SICB in the BDS-2 Multipath (MP) combination, but the SICB in the BDS-3 MP is smaller and can be ignored. Compared with the modeling in the references, TOCFM is more suitable for IGSO/MEO SICB modeling, especially for the SICB correction at low elevation angles. After the VMD-WT correction, the Root Mean Square Error (RMSE) of SICB of B1I, B2I, and B3I in GEO satellites is reduced by 53.35%, 63.50%, and 64.71% respectively. Moreover, we carried out ionosphere-free Single Point Positioning (IF SPP), Ionosphere-free CSC SPP (IF CSC SPP), CSC single point positioning with the IGSO/MEO SICB Correction based on the TOCFA Method (IGSO/MEO SICB CSC), and CSC single point positioning with the IGSO/MEO/GEO SICB correction based on VMD-WT and TOCFA (IGSO/MEO/GEO SICB CSC), respectively. Compared to IF SPP, the average improvement of the IGSO/MEO/GEO SICB CSC algorithm in the north, east, and up directions was 24.42%, 27.94%, and 24.98%, respectively, and the average reduction in 3D RMSE is 24.54%. Compared with IF CSC SPP, the average improvement of IGSO/MEO/GEO SICB CSC is 7.03%, 6.50%, and 10.48% in the north, east, and up directions, respectively, while the average reduction in 3D RMSE was 9.86%. IGSO/MEO SICB mainly improves the U direction positioning accuracy, and GEO SICB mainly improves the E and U direction positioning accuracy. After the IGSO/MEO/GEO SICB correction, the overall improvement was about 10% and positioning improved to a certain extent.

The extensive use of carrier-aided smoothing code (CSC) filters has led to a reduction in the noise level of raw code measurements in GNSS positioning and navigation applications. However, the existing CSC technique is sensitive to the changes in the integer ambiguity, and then the smoothing procedure needs to be restarted in the presence of cycle slips. As the Doppler shift is instantaneously observed and immune to cycle slips, the Doppler-aided smoothing code (DSC) algorithm would be more promising in a challenged environment. Based on the Hatch filter, an optimal DSC approach is proposed with the principle of minimum variance. Meanwhile, to inhibit the effect of the integral cumulative error of the Doppler, a balance factor is adopted to adjust the contributions of raw code and DSC. The noise level of code observable is not only affected by thermal noise, but also limited by systematic bias. Satellite code bias (SCB) was identified in the raw code observable on each frequency for each BDS-2 satellite. By minimizing the sum of the absolute value of residuals, the polynomial segment fitting algorithm as a function of elevation angles is applied to establish the SCB correction model based on epoch-differenced multipath (MP) deviations. Finally, different types of experiments demonstrate the validity and efficiency of the refined DSC filter with SCB corrections on each available frequency for BDS un-GEO satellites.

Similar to the antenna phase center corrections for phase measurements, group delay variations (GDV) of satellite and receiving GNSS antennas affect code pseudorange measurements. They are frequency-dependent and vary with the direction of signal transmission and reception. We present the first GDV estimates for all five Galileo and three GLONASS frequency bands based on terrestrial observations. As compared to GPS, the orbit properties of Galileo and GLONASS simplify this approach, because a single reference station can observe each Galileo and GLONASS satellite in its entire elevation angle range during one orbit repeat period. The homogenous results of three receiver antenna models for identical satellite types and a comparison to GPS Block IIF indicate mainly receiver antenna-specific GDV. They amount to 35 and 28 cm peak-to-peak for Galileo and GLONASS frequency bands E1 and G1, respectively, depending on the receiver antenna type. We show their effect on linear combinations where the code observable is used for precise applications and validate our GDV estimations by improving the height component in single-frequency precise point positioning. [ABSTRACT FROM AUTHOR]

Abstract There are code biases on the pseudo-range observations of the Beidou Navigation Satellite System (BDS) that range in size from several decimeters to larger than one meter. These biases can be divided into two categories, which are the code biases in the pseudo-range observations of Inclined Geo-Synchronous Orbit (IGSO) satellites and Medium Earth Orbit (MEO) satellites and the code biases in the pseudo-range observations of Geosynchronous Earth Orbit (GEO) satellites. In view of the code bias of the IGSO/MEO satellites, the code bias correction model is established using the weighted least square curve fitting method. After the correction, the code biases of the IGSO and MEO satellites are clearly mitigated. A methodology of correcting GEO code bias is proposed based on the empirical mode decomposition (EMD)-wavelet transform (WT) coupled model. The accuracies of the GEO multipath combination of the B1, B2 and B3 frequencies are improved by 39.9%, 17.9%, and 29.4%, respectively. Based on the corrections above, the ten days observations of three Multi-GNSS Experiment (MGEX) stations are processed. The results indicate that the convergence time of the precise point positioning (PPP) can be improved remarkably by applying a code bias. The mean convergence time can be improved by 14.67% after the IGSO/MEO code bias correction. By applying the GEO code bias, the mean convergence time can be further improved by 17.42%. [ABSTRACT FROM AUTHOR]

Thecode-phase divergences, which are absent for GPS, GLONASS, and Galileo,are com- monlyfound in BDS geostationary (GEO), Inclined GeoSynchronous Orbit (IGSO) and Medium Earth Orbit (MEO) satellites. Several precise applications that use code observations are severely affected by these code biases; therefore, it is necessary to correct biases in BDS code observations. Since the BeiDou satellite-induced code bias is confirmed to he orbit type-, frequency-, and elevation-dependent, an improved code bias correction model for IGSO and MEO satellites based on a large amount of the data was developed. To obtain the best filling results, we analyzed the effect of the number and distri­bution of stations and observation time on model estimation, and also considered the different influ­ence of multipath at different elevations. A robust estimation method controlled the observation quali­ty. A dataset from 18 stations during one year period in 2015 was employed to estimate the correction model for MEO satellites and four stations for IGSO satellite. To validate the improved correction model, the effect of the code bias on precise point positioning (PPP) l>efore and after correction is ana­lyzed and compared. Results show that systematic variations were eliminated more clearly after apply­ing the improved correction model as compared to the traditional model. After correction, the positio­ning accuracy of PPP solution was improved and the convergence time decreasedshowing a better per­formance than results using thetraditional model as proposed by Wanninger and Beer. [ABSTRACT FROM AUTHOR]

GPS code pseudorange measurements exhibit group delay variations at the transmitting and the receiving antenna. We calibrated C1 and P2 delay variations with respect to dual-frequency carrier phase observations and obtained nadir-dependent corrections for 32 satellites of the GPS constellation in early 2015 as well as elevation-dependent corrections for 13 receiving antenna models. The combined delay variations reach up to 1.0 m (3.3 ns) in the ionosphere-free linear combination for specific pairs of satellite and receiving antennas. Applying these corrections to the code measurements improves code/carrier single-frequency precise point positioning, ambiguity fixing based on the Melbourne-Wübbena linear combination, and determination of ionospheric total electron content. It also affects fractional cycle biases and differential code biases. [ABSTRACT FROM AUTHOR]

A key limitation for precise orbit determination of BeiDou satellites, particularly for satellites in geostationary orbit (GEO), is the relative weak geometry of ground stations. Fortunately, data from a low earth orbiting satellite with an onboard GNSS receiver can improve the geometry of GNSS orbit determination compared to using only ground data. The Chinese FengYun-3C (FY3C) satellite carries the GNSS Occultation Sounder equipment with both dual-frequency GPS (L1 and L2) and BeiDou (B1 and B2) tracking capacity. The satellite-induced variations in pseudoranges have been estimated from multipath observables using an elevation-dependent piece-wise linear model, in which the constant biases, i.e., ambiguities and hardware delays, have been removed. For IGSO and MEO satellites, these variations can be seen in onboard B1 and B2 code measurements with elevation above 40°. For GEO satellites, a different behavior has been observed for these signals. The GEO B2 pseudoranges variations are similar to those of IGSO satellites, but no elevation-dependent variations have been identified for GEO B1. A possible cause is contamination of the larger noise in GEO B1 signals. Two sets of precise orbits were determined for FY3C in March 2015 using onboard GPS-only data and onboard BeiDou-only data, respectively. The 3D RMS (Root Mean Square) of overlapping orbit differences (OODs) is 2.3 cm for GPS-only solution. The 3D RMS of orbit differences between BeiDou-only and GPS-only solutions is 15.8 cm. Also, precise orbits and clocks for BeiDou satellites were determined based on 97 global (termed GN) or 15 regional (termed RN) ground stations. Furthermore, also using FY3C onboard BeiDou data, two additional sets of BeiDou orbit and clock products are determined with the data from global (termed GW) or regional (termed RW) stations. In general, the OODs decrease for BeiDou satellites, particularly for GEO satellites, when the FY3C onboard BeiDou data are added. The 3D OODs reductions are 10.0 and 291.2 cm for GW and RW GEO solution with respect to GN and RN solution, respectively. Since the OODs in the along-track direction dominate the OODs reduction, no improvement has been observed by satellite laser ranging, which mainly validates the accuracy of the radial orbital component. With the GW BeiDou orbit and clock products, the FY3C orbits determined with onboard BeiDou-only data also show improvement in comparison with those determined with BeiDou GN products. [ABSTRACT FROM AUTHOR]

Since 2015, China has successfully launched five experimental BeiDou global navigation system (BDS-3) satellites for expanding the regional system to global coverage. An initial performance assessment and characterization analysis of the BDS-3 is presented. Twenty days of tracking data have been collected from eleven monitoring stations. The tracking characteristics and measurement quality are analyzed and compared with the regional BDS (BDS-2) in terms of observed carrier-to-noise density ratio, pseudo-range multipath, and noise. The preliminary results suggest that the measurement quality of BDS-3 outperforms the BDS-2 for the same type of satellites. In addition, the analysis of multipath combinations reveals that the problem of satellite-induced code biases found in BDS-2 seems to have been solved for BDS-3. Precise orbit and clock determination are carried out and evaluated. The orbit overlap comparison show a precision of 2-6 dm in 3D root mean square (RMS) and 6-14 cm in the radial component for experimental BDS-3 satellites. External validations with satellite laser ranging (SLR) show residual RMS on the level of 1-3 dm. Finally, the performance of the new-generation onboard atomic clocks is evaluated and results confirm an increased stability compared to BDS-2 satellite clocks. [ABSTRACT FROM AUTHOR]

The international GNSS monitoring and assessment system (iGMAS) tracking network has been established by China to track multi-GNSS satellites. A key feature of iGMAS stations is the capability to fully track new navigation signals from the recently deployed BDS-3 satellites. In addition to the B1I and B3I signals inherited from BDS-2 satellites, the BDS-3 satellites are capable of transmitting new open service signals, including B1C at 1575.42 MHz, B2a at 1176.45 MHz, and B2b at 1207.14 MHz. In this contribution, we present a comprehensive analysis and characterization of GNSS signals tracked by different receivers and antennas equipped in the iGMAS network, especially as they relate to BDS-3 signals. Signal characteristics are analyzed in terms of the carrier-to-noise density ratio for the different signals as measured by the receiver, as well as pseudo-range noise and multipath. Special attention is given to discussion of the satellite-induced code bias, which has been identified to exist in the code observations of BDS-2, and the inter-frequency clock bias (IFCB), which has been observed in the triple-frequency carrier phase combinations of GPS Block IIF and BDS-2 satellites. The results indicate that the satellite-induced code bias is negligible for all signals of BDS-3 satellites, while small IFCB variations with peak amplitudes of about 1 cm can be recognized in BDS-3 triple-carrier combinations.

The satellite-induced systematic biases were identified to exist in the code observations from BeiDou navigation satellite system (BDS) satellites using multipath (MP) combinations. The current correction model for satellite-induced code bias (SICB) does not take into account the consistency of MP combinations, which limits the accuracy of the developed model. Both the cycle slips and different tracking of a satellite at different stations can affect the absolute values of MP combinations, although the variations remain unchanged. An improved SICB piecewise linear correction model as a function of elevations is proposed. We estimate the model parameters for each frequency and for each satellite. The single-difference of MP combinations in the domain of elevation angles is carried out to remove the unknown ambiguities and stable hardware delays so that the SICB modeling is free of the effects of MP combination inconsistency. In addition, a denser elevation node separation of 1°, rather than the 10° usually employed by the traditional model, is used to describe the more precise SICB variations. The SICB corrections show significant differences among orbit types and frequency bands. The SICB variations have much less effect on Inclined Geosynchronous Orbit (IGSO) satellites than on Medium Earth Orbit (MEO) satellites for the regional BDS (BDS-2). The B1 signal has the largest SICB corrections, which can be up to 0.9 m close to zenith for BDS-2 MEO satellites, and the B2 signal follows. After adding the SICB corrections to the code observations, the elevation-dependent code biases vanish, and we can obtain improved code observations. After applying the improved SICB correction model, the root mean square (RMS) values of MP combination time series are reduced by 7%, 6% and 2%, and 18%, 14% and 5% on the B1, B2 and B3 frequencies for the BDS-2 IGSO and MEO satellites, respectively. For comparison, we also establish the traditional SICB correction model. With the traditional SICB correction model, the corresponding RMS MP combinations are smaller than those of uncorrected MP series, but slightly larger than those of corrected MP series using the improved SICB correction model. To validate the effectiveness and correctness of our proposed model, single-frequency precise point positioning (PPP) processing with BDS-2 MEO and IGSO satellites is conducted. An accuracy improvement of 24%, 19% and 89%, and 7%, 7% and 6% for the single-frequency PPP applying the improved SICB corrections over the case without SICB corrections and the case using the traditional SICB corrections in east, north and vertical directions is achieved, respectively. Although only centimeter-level SICB variations could be observed for the two legacy signals B1 and B3 and the three new navigation signals B1C, B2a and B2b transmitted by the satellites of global BDS demonstration system (BDS-3S), we still establish an effective SICB correction model on the B1 and B3 frequencies for BDS-3S IGSO satellites, and the RMS MP combinations are reduced by 1–4% after applying the improved SICB corrections.

The code observable of global navigation satellite systems (GNSS) is influenced by group delay variations (GDV) of transmitter and receiver antennas. For the Global Positioning System (GPS), the variations can sum up to 1 m in the ionosphere-free linear combination and thus can significantly affect precise code applications. The contribution of the GPS transmitters can amount to 0.8 m peak-to-peak over the entire nadir angle range. To verify the assumption of their time-invariance, we determined daily individual satellite GDV for GPS transmitter antennas over a period of more than two years. Dual-frequency observations of globally distributed reference stations and their multipath combination form the basis for our analysis. The resulting GPS GDV are stable on the level of a few centimeters for C1, P2, and for the ionosphere-free linear combination. Our study reveals that the inconsistencies of the GDV of space vehicle number (SVN) 55 with respect to earlier studies are not caused by temporal instabilities, but are rather related to receiver properties.

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.

Code pseudorange measurements of the Chinese GNSS BeiDou reveal variations which result in code-phase divergences of more than 1 m. We have analyzed these delay variations based on observation data of the International GNSS Service and its Multi-GNSS Experiment campaign. Our results confirm that these code variations are elevation-dependent when observed by receiving antennas on the earth's surface. In addition, we found significant differences between two groups of satellites and among carrier frequencies. These delay variations have only little effects on absolute BeiDou positioning using broadcast ephemerides due to the limited accuracy of the obtainable positions. But, all precise applications which use code measurements are severely affected. These applications include, e.g., certain algorithms used in Precise Point Positioning (PPP), especially PPP ambiguity fixing and single-frequency PPP based on the ionosphere-free code-carrier combination. We developed a correction model and determined correction parameters in order to accommodate these symptoms. Application examples demonstrate the successful mitigation of these code pseudorange variations. [ABSTRACT FROM AUTHOR]

China completed a basic COMPASS navigation network with three Geostationary and three Inclined Geosynchronous satellites in orbit in April 2011. The network has been able to provide preliminary positioning and navigation functions. We first present a quality analysis using 1-week COMPASS measurements collected in Wuhan. Satellite visibility and validity of measurements, carrier-to-noise density ratio and code noise are analyzed. The analysis of multipath combinations shows that the noise level of COMPASS code measurements is higher than that of GPS collected using the same receiver. Second, the results of positioning are presented and analyzed. For the standalone COMPASS solutions, an accuracy of 20 m can be achieved. An accuracy of 3.0 m for the vertical, 1.5 m for the North and about 0.6-0.8 m for the East component is obtained using dual-frequency code only measurements for a short baseline. More importantly, code and phase measurements of the short baseline are processed together to obtain precise relative positioning. Kinematic solutions are then compared with the ground truth. The precision of COMPASS only solutions is better than 2 cm for the North component and 4 cm for the vertical. The standard deviation of the East component is smaller than 1 cm, which is even better than that of the East component of GPS solutions. The accuracy of GPS/COMPASS combination solutions is at least 20 % better than that of GPS alone. Furthermore, the geometry-based residuals of double differenced phase and code measurements are analyzed. The analysis shows that the noise level of un-differenced phase measurements is about 2-4 mm on both B1 and B2 frequencies. For the code measurements, the noise level is less than 0.45 m for B1 CA and about 0.35 m for B2 P code. Many of the COMPASS results presented are very promising and have been obtained for the first time. [ABSTRACT FROM AUTHOR]

The international GNSS monitoring and assessment system (iGMAS) tracking network has been established by China to track multi-GNSS satellites. A key feature of iGMAS stations is the capability to fully track new navigation signals from the recently deployed BDS-3 satellites. In addition to the B1I and B3I signals inherited from BDS-2 satellites, the BDS-3 satellites are capable of transmitting new open service signals, including B1C at 1575.42 MHz, B2a at 1176.45 MHz, and B2b at 1207.14 MHz. In this contribution, we present a comprehensive analysis and characterization of GNSS signals tracked by different receivers and antennas equipped in the iGMAS network, especially as they relate to BDS-3 signals. Signal characteristics are analyzed in terms of the carrier-to-noise density ratio for the different signals as measured by the receiver, as well as pseudo-range noise and multipath. Special attention is given to discussion of the satellite-induced code bias, which has been identified to exist in the code observations of BDS-2, and the inter-frequency clock bias (IFCB), which has been observed in the triple-frequency carrier phase combinations of GPS Block IIF and BDS-2 satellites. The results indicate that the satellite-induced code bias is negligible for all signals of BDS-3 satellites, while small IFCB variations with peak amplitudes of about 1 cm can be recognized in BDS-3 triple-carrier combinations. [ABSTRACT FROM AUTHOR]

The satellite-induced systematic biases were identified to exist in the code observations from BeiDou navigation satellite system (BDS) satellites using multipath (MP) combinations. The current correction model for satellite-induced code bias (SICB) does not take into account the consistency of MP combinations, which limits the accuracy of the developed model. Both the cycle slips and different tracking of a satellite at different stations can affect the absolute values of MP combinations, although the variations remain unchanged. An improved SICB piecewise linear correction model as a function of elevations is proposed. We estimate the model parameters for each frequency and for each satellite. The single-difference of MP combinations in the domain of elevation angles is carried out to remove the unknown ambiguities and stable hardware delays so that the SICB modeling is free of the effects of MP combination inconsistency. In addition, a denser elevation node separation of 1°, rather than the 10° usually employed by the traditional model, is used to describe the more precise SICB variations. The SICB corrections show significant differences among orbit types and frequency bands. The SICB variations have much less effect on Inclined Geosynchronous Orbit (IGSO) satellites than on Medium Earth Orbit (MEO) satellites for the regional BDS (BDS-2). The B1 signal has the largest SICB corrections, which can be up to 0.9 m close to zenith for BDS-2 MEO satellites, and the B2 signal follows. After adding the SICB corrections to the code observations, the elevation-dependent code biases vanish, and we can obtain improved code observations. After applying the improved SICB correction model, the root mean square (RMS) values of MP combination time series are reduced by 7%, 6% and 2%, and 18%, 14% and 5% on the B1, B2 and B3 frequencies for the BDS-2 IGSO and MEO satellites, respectively. For comparison, we also establish the traditional SICB correction model. With the traditional SICB correction model, the corresponding RMS MP combinations are smaller than those of uncorrected MP series, but slightly larger than those of corrected MP series using the improved SICB correction model. To validate the effectiveness and correctness of our proposed model, single-frequency precise point positioning (PPP) processing with BDS-2 MEO and IGSO satellites is conducted. An accuracy improvement of 24%, 19% and 89%, and 7%, 7% and 6% for the single-frequency PPP applying the improved SICB corrections over the case without SICB corrections and the case using the traditional SICB corrections in east, north and vertical directions is achieved, respectively. Although only centimeter-level SICB variations could be observed for the two legacy signals B1 and B3 and the three new navigation signals B1C, B2a and B2b transmitted by the satellites of global BDS demonstration system (BDS-3S), we still establish an effective SICB correction model on the B1 and B3 frequencies for BDS-3S IGSO satellites, and the RMS MP combinations are reduced by 1–4% after applying the improved SICB corrections. [ABSTRACT FROM AUTHOR]

The code observable of global navigation satellite systems (GNSS) is influenced by group delay variations (GDV) of transmitter and receiver antennas. For the Global Positioning System (GPS), the variations can sum up to 1 m in the ionosphere-free linear combination and thus can significantly affect precise code applications. The contribution of the GPS transmitters can amount to 0.8 m peak-to-peak over the entire nadir angle range. To verify the assumption of their time-invariance, we determined daily individual satellite GDV for GPS transmitter antennas over a period of more than two years. Dual-frequency observations of globally distributed reference stations and their multipath combination form the basis for our analysis. The resulting GPS GDV are stable on the level of a few centimeters for C1, P2, and for the ionosphere-free linear combination. Our study reveals that the inconsistencies of the GDV of space vehicle number (SVN) 55 with respect to earlier studies are not caused by temporal instabilities, but are rather related to receiver properties. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]