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Journal Pre-proofs Analysis of the code and phase between-receiver inter-system biases of the overlapping frequencies for GPS/Galileo/BDS Yumiao Tian, Linguo Yuan, Dingfa Huang, Letao Zhou, Xueyang Chen, Shaoguang Xu, Wei Feng, Xiaoying Gong PII: DOI: Reference:
S0273-1177(19)30830-0 https://doi.org/10.1016/j.asr.2019.11.022 JASR 14546
To appear in:
Advances in Space Research
Received Date: Revised Date: Accepted Date:
2 September 2019 14 November 2019 15 November 2019
Please cite this article as: Tian, Y., Yuan, L., Huang, D., Zhou, L., Chen, X., Xu, S., Feng, W., Gong, X., Analysis of the code and phase between-receiver inter-system biases of the overlapping frequencies for GPS/ Galileo/BDS, Advances in Space Research (2019), doi: https://doi.org/10.1016/j.asr.2019.11.022
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Analysis of the code and phase between-receiver inter-system biases of the overlapping frequencies for GPS/Galileo/BDS Yumiao Tian1,3, Linguo Yuan1,3, Dingfa Huang1,3, Letao Zhou1,3, Xueyang Chen2, Shaoguang Xu1,3, Wei Feng1,3, Xiaoying Gong1,3 1
Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu, Sichuan, 611756, China 2 Chongqing Geomatics and Remote Sensing Center, Chongqing, 611756, China 3 State-Province Joint Engineering Laboratory of Spatial Information Technology for High-Speed Railway Safety, Chengdu, Sichuan, 610031, China * Correspondence: [email protected] Email address: Yumiao Tian: [email protected]; Linguo Yuan: [email protected]; Dingfa Huang: [email protected]; Letao Zhou: [email protected]; Xueyang Chen: [email protected]; Shaoguang Xu : [email protected]; Wei Feng: [email protected]; Xiaoying Gong: [email protected]
Abstract: The overlapping-frequency signals from different GNSS constellations are interoperable and can be integrated as one constellation in multi-GNSS positioning when inter-system bias (ISB) is properly disposed. The look-up table method for ISB calibration can enhance the model strength, maximize the number of integerestimable ambiguities, and thus is preferred. However, the characteristics and magnitudes of the receiver code ISB and phase fractional ISB (F-ISB) are not well known and the wrong values of the biases can seriously degrade the positioning results. In this contribution, we first estimate the between-receiver code ISB and phase F-ISB of hundreds of the baselines up to around 25 km in the European Permanent GNSS Network (EPN) and the Multi-GNSS Experiment (MGEX) for the overlapping frequencies L1-E1 (L1), L5-E5a (L5) and E5bB2b(L7). The data collected from 1st January 2016 to 1st January 2019. Second, the receiver-type and firmware-version combinations for the receivers of Trimble, Leica, Javad, Septentrio and NovAtel are carefully classified. Results show that the Septentrio receivers have consistent code and phase ISB values for the three overlapping frequencies i.e. only one value for each frequency and no receivers are different. The Leica, Trimble and Javad receivers have two or more ISB values for at least one of the three frequencies. A few receivers with biases to the groups are also found and listed. Third, the code ISB and phase F-ISB of the groups are adjusted by the least-squares method. The root mean square errors (RMSE) of the least square adjustment are 0.240 m, 0.250 m and 0.200 m for code of L1, L5 and L7 frequencies, respectively, and are 0.0009 m, 0.0015 m and 0.0031 m for phase of L1, L5 and L7 frequencies, respectively. Finally, the effects of code ISB errors on code positing are investigated with the zero-baseline MAT1_MATZ. The distance root mean square error (DRMS) of L1-E1 code positioning can be reduced by 48.2% with 5 GPS and Galileo satellites and the DRMS degrades quickly when the code ISB error is larger. Keywords: Multi-GNSS; Inter system bias (ISB); code ISB; Carrier phase ISB
1. Introduction Global Navigation Satellite System (GNSS) positioning benefits enormously from the integration of multiGNSS systems as more satellites are available. The method that integrates the signals from different GNSS constellations including GPS/GLONASS/Galileo/BDS by the interoperability of the overapplying frequencies or narrowly-spaced frequencies can lower the PDOP, ADOP, improve the success rate of ambiguity fixing and the accuracy of the results (Odolinski et al., 2014; Li et al., 2015; Tian et al., 2018; Kubo et al., 2018; Chen et al., 2019; Wu et al., 2019a). Due to the different paths of hardware and digital signal processing, the signals of overlapped frequencies for GPS/ Galileo/BDS can be misaligned in the receivers, leading to between-receiver inter-system bias (ISB). 1 / 19
Those biases need to be dealt carefully in multi-GNSS data processing so that the benefits of the observations from different systems can be fully exploited. The phase ISB is separated into two parts, the integer parts which are neglectable and the fractional part (F-ISB) which need to be accurately calibrated (Odolinski et al., 2014; Paziewski and Wielgosz, 2015, 2017; Paziewski et al., 2015). The code ISB has no periodic characteristics and the entire value needs to be calibrated in the code models. The estimation of ISB in multi-GNSS integration has been investigated in the past years. Basically, the estimation approaches require additional unknown parameters (Paziewski and Wielgosz, 2015; Gao et al., 2017, 2018) or reduced number of integer-estimable ambiguities (Odijk and Teunissen, 2013a, 2013b) or increased computation efforts (Tian et al., 2017, 2018). If the code ISB or phase F-ISB are known, the look-up table method calibrating the ISB in advance can be used. The known ISB values brings the benefits of strengthened estimation model and maximized integer-estimable ambiguities (Khodabandeh and Teunissen, 2016; Odijk et al., 2016). The knowledge such as the characteristics and magnitudes of code ISB and phase F-ISB which is critical to the reliability of the look-up table method should be thoroughly investigated. Odijk and Teunissen (2013a, 2013b) investigated the characteristics of between-receiver phase F-ISB and the baselines with the receivers of identical receiver types are considered to be free of the bias, but the baselines formed by different receiver types are usually with significant ISB values. Those values are stable and can be calibrated in GPS/Galileo integration. The values of GPS L1 and Galileo E1, GPS L5 and Galileo E5 of several receiver brands were given and they indicated that the values should be validated with more data. Paziewski and Wielgosz (2015), Paziewski et al. (2015) and Dong et al. (2018) showed that the F-ISB is stable with several baselines of different receiver types. Besides, the effects of the firmware upgrade on the ISB of the receivers such as Trimble and Javad were reported (Dong et al., 2018; Nadarajah et al., 2015; Zhang and Teunissen, 2016; Liu et al., 2017; Wu et al., 2019b). Zhang and Teunissen (2016) also found that the between-receiver ISB may also be affected by the daily maximum temperature. Tian et al. (2019b) estimated the between-receiver ISB with eight baselines and analyzed the characteristics. Besides, the multi-GNSS observation types are supposed to have an impact on the ISB values. For example, the Galileo L5I, L5Q which are in phase and quadrature phase observations, respectively, are supposed to have a bias of 1/4 circles. This has been noticed and the phase shift values are given in the data file format RINEX since version 3.02 (Rinex 3.02, 2013; Rinex 3.04, 2018). Obviously, the observation types should also be considered in the analysis of the phase F-ISB characteristics. Besides, the Multi-GNSS Experiment (MGEX) is specially launched for the investigation of the GNSS satellite signals and receiver states, as well as multi-GNSS software development (Montenbruck et al., 2017; Li et al., 2019). The stations from MGEX plus the stations of the European Permanent GNSS Network (EPN) (Bruyninx et al, 2001) bring a large amount of multi-GNSS observation data allowing us to thoroughly analyze both the code and phase between-receiver ISB. This investigation focuses on the magnitudes of the ISB and their classifications instead of the estimation and correction methodology. the code ISB and phase F-ISB of hundreds of baselines with length up to around 25 km are estimated and analyzed. The RINEX 3 data of the MGEX and EPN collected on the days distributed over the last three years since day of year (DOY) 001 (1st January) 2016 are employed. The estimates of the overlapping frequencies including GPS L1-Galileo E1 (L1), GPS L5- Galileo E5a (L5), Galileo E5b-GPS B2b (L7) of the receivers are grouped and then the ISB values of the groups are adjusted for refinement. It is shown how the phase F-ISB and code ISB changes over different receiver-types and firmware-versions, how stable the ISB is over time, and how individual receivers agree for each group. Also, the benefits brought by the code ISB look-up table are analyzed. In the follows, the employed previous published method for code ISB and phase F-ISB is briefly introduced in section 2. The data from MGEX and EPN are described in section 3. Section 4 presents the estimates and analysis of code ISB and phase F-ISB, as well as an investigation of the code ISB error effects on positioning. Conclusions are given in section 5. 2. Estimation of the code ISB and phase F-ISB The between-receiver ISB can be parameterized in the double difference models of GNSS relative positioning. The general forms of the DD models can be found in the reference (Tian et al., 2019). In the relative data processing, both the receiver and satellite clocks are eliminated. In this study, the baselines are up to around 25 km and the tropospheric and ionospheric delays are simply corrected by empirical models instead of being 2 / 19
parameterized. The code and phase observations models of GPS L1 and GPS L2 are included in the ISB estimations of all the three frequencies and can be expressed as
PabL1L1,ij abL1L1,ij abL1L1 PabL 2 L 2,ij abL 2L 2,ij abL 2L 2 L1 L1L1,ij abL1L1,ij L1 N abL1L1,ij abL1L1 ab L 2abL 2 L 2,ij abL 2L 2,ij L 2 N abL 2 L 2,ij abL 2 L 2
(1)
where P and are the code and phase observations, respectively. a and b are the two stations. i and j are the two observed GPS satellites. L1 and L 2 indicates the two carriers. is the carrier wavelength. N is the integer ambiguities.
and
are the noises for the code and phase observations, respectively.
For the GPS L1 and Galileo E1, the inter-system DD observation models are
PabL1E1,ik abL1E1,ik d abL1E1 abL1E1 L1 L1E1,ik abL1E1 abL1E1 L1 N abL1E1,ik abL1E1 ab
(2)
PabL 5 E 5 a ,ik abL 5 E 5 a ,ik d abL 5 E 5 a abL 5 E 5 a L 5 L 5 E 5 a ,ik abL 5 E 5 a abL 5 E 5 a L 5 N abL 5 E 5 a ,ik abL 5 E 5 a ab
(3)
where d is the between-receiver code ISB and is the between-receiver phase F-ISB. The inter-system DD observation models of the overlapping frequency GPS L5 and Galileo E5a named as L5 in the RINEX 3 format can be formed in a similar way as
Also, the inter-system DD models of the overlapping frequency Galileo E5b and BDS B2b named as L7 in the RINEX 3 format are
PabE 5bB 2b ,ik abE 5bB 2b ,ik d abE 5bB 2b abE 5bB 2b E 5b E 5bB 2b ,ik abE 5bB 2b abE 5bB 2b E 5b N aEb5bB 2b ,ik abE 5bB 2b ab
(4)
After the other errors are eliminated or reduced by empirical models, the code ISB can be estimated directly by the combination of the above equations, such as the combinations of Eq. (1) and Eq. (2), Eq. (1) and Eq. (3), Eq. (1) and Eq. (4) for the code ISB estimation of L1/E1, L5/E5a and E5b/B2b, respectively. The phase F-ISB are estimated with particle-filtering-based estimation approach presented in the research (Tian et al., 2017). This approach can fully exploit the multi-GNSS observations by fixing the maximized number of integer ambiguities. First, the F-ISB values sampled over the initial range with length of one wavelength are generated, and each sample is assigned the initial weights. Second, each F-ISB value is used to calibrate the FISB in the inter-system model and both the inter- and intra-system DD ambiguities are fixed by LAMBDA method (Teunissen, 1995). After the corresponding RATIO values are calculated, the weight of each F-ISB value is updated according to the RATIO value (Euler and Schaffrin, 1991; Verhagen, 2005; Verhagen and Teunissen, 2013) and the F-ISB value is derived by the weighted F-ISB samples. Third, the F-ISB values are resampled so that each F-ISB values have similar weights again. Although the approach has a relatively large computation load, it is not a problem in this study. After the between-receiver code ISB and phase F-ISB are estimated, the receiver-type and firmware-version combinations are classified into different groups according to the their ISB magnitudes. Then the ISB estimates are adjusted by least-squares method with difference models to refine the ISB values. In the adjustment calculation, the number of the unknown parameters which representing the ISB of each group is one larger than the rank of the equations, and thus an additional equation setting the ISB of the reference group to a reference value is added. After the adjustment, the between-receiver ISB estimates are transformed into single-receiver ISB relatives to the reference receiver group. It should be noted that only the difference between single-receiver ISB matters and the single-receiver ISB of the reference group can be set as an arbitrary value. The adjustment models can be 3 / 19
expressed as
v = Bx - l
(5)
where
est12 1，， 0 ， 0 x1 -1， est x -1，， 0 ， 13 2 0 1， x= l= B= 0 -1， 1 ，， est( n1) n 0， ref xn 0， 0 1 , ，， ,
v is the residuals, x
is the single-receiver ISB parameters for each receiver group and
n
is the number of
the receiver groups, est is the code ISB or phase F-ISB estimate for each baseline and ref is the reference value assigned to the reference receiver group. The row of the equation equals the number of the ISB estimates for hybrid-receiver baselines plus one. The elements in vector x can be transformed into between-receiver ISB in applications and are the study objective in the following sections. 3. Data employed The MGEX and EPN provide a large amount of data for the analysis of satellite signals and receiver qualities for multi-GNSS interation. The data collected on DOY 001 and 180 of 2016, 2017 and 2018, DOY 001 of 2019 which cover a time period of more than three years are downloaded. Those data are collected by receivers of 6 brands and the numbers of each brand receivers are shown in Fig. 1. The proportion of each brand on DOY 001 2019 presented in table 1. The most equipped receivers are Trimble (TRIM), Leica (LEIC), Javad (JAVA) and Septentrio (SEPT) with increasing numbers over the last three years, while the receivers from TPS and NovAtel (NOV) are much less without station-number increment since DOY 001 2017. Besides, most TPS stations do not provide Galileo and BDS data but with only one exception CAG1 using TPS NET-G5 receiver. However, station CAG1 is lack of recorded data to calculate any ISB parameter and thus all TPS receivers are excluded. The NOV receiver is equipped on only one station and has observations of L1 and L5 but not L7.
Figure 1. Numbers of the receivers employed by MGEX and EPN stations over the last three years. The receivers include Trimble (TRIM), Leica (LEIC), Javad (JAVA), Septentrio (SEPT), TPS and NovAtel (NOV).
The observation types of the receivers are listed in table 1 and are consistent for each receiver brand with very few exceptions. For example, the observation type for L5 is L5Q for most stations which are equipped with Leica receivers from type GR10 to type GR50 but is L5X for the only one station equipped with GRX1200+GNSS receiver. The different observation types may have phase shifts which can be a factor affecting the Phase F-ISB by values presented in RINEX format since version 3.02 (Rinex 3.02, 2013) 4 / 19
Table 1. Number of stations and observation types of both code and phase for MGEX and EPN network on DOY 001 of 2019
Receiver brands LEIC SEPT TRIM JAVA TPS NOV
# stations 105 72 130 98 23 1
Proportio n (%) 24.5 16.8 30.3 22.8 5.4 0.2
L1 C1C C1C C1C C1C C1C C1C
E1 C1C C1C C1X C1X C1B C1C
L5 C5Q C5Q C5X C5X C5Q C5Q
code E5a C5Q C5Q C5X C5X C5X C5Q
E5b C7Q C7Q C7X C7X C7I
B2b C7I C7I C7I C7I C7I
L1 L1C L1C L1C L1C L1C L1C
E1 L1C L1C L1X L1X L1B L1C
phase L5 E5a L5Q L5Q L5Q L5Q L5X L5X L5X L5X L5Q L5X L5Q L5Q
E5b L7Q L7Q L7X L7X L7I
The short baselines of the data are almost free of tropospheric and ionospheric delays and are ideal for the analysis of between-receiver ISB. The number of the baselines shorter than around 25 km and the number of the receivers for each brand are listed in table 2. The sum of the receiver number is smaller than twice of the baseline number because some of the baselines share the same stations. For example, a total of 17 baselines are employed on DOY 001 2016 and the baselines are composed by 25 stations equipped with 4 Leica receivers, 3 Septentrio receivers, 8 Trimble receivers, 8 Javad receivers and 2 NovAtel receivers. The employed data pairs are globally distributed and the locations of the data pairs on DOY 001 2019 are shown as red dots in Fig. 2. Table 2. Number of short baselines and receiver stations employed in the calculations
Year and DOY 2016 001 2016 180 2017 001 2017 180 2018 001 2018 180 2019 001 sum
# Baselines 17 33 44 60 60 73 110 391
# LEIC 4 12 14 17 20 22 75 164
# SEPT 3 7 10 13 14 19 43 109
# TRIM 8 17 20 27 26 27 66 191
# JAVA 8 10 17 20 16 23 61 155
#NOV 2 1 1 1 1 1 1 8
Figure 2. Geographical distribution of the baselines (red dots) employed in the experiments
4. ISB refinement and analysis The baselines described in Table 2 are employed to analyze the code ISB and phase F-ISB of the overlapping frequencies L1-E1, L5-E5a and E5b-B2b. Some baselines which cannot provide precise positioning results such as baseline FAA1_THTG on DOY 001 2018 are excluded. The code ISB and phase F-ISB of the remaining receivers are estimated and the receiver-type and firmware-version combinations are separated into different groups. The receivers of each group are from the same manufactures and have similar code ISB or phase F-ISB value. 5 / 19
B2b L7I L7I L7I L7I L7I
4.1 Code ISB estimation results The code ISBs of L1/E1, L5/E5a, E5b/B2a are estimated by the combination of the code models described in section 2. The receiver-type and firmware-version combinations are then grouped according to their code ISB estimates and the group contents are given in appendix from table 1 to table 3. The receiver ISB of each group are then refined by Eq. (5). Since the group LEIC2 has code ISB of a smaller value, we select this group as the reference group and set its code ISB to zero value for all the three frequencies. The selection of the reference group is not important because only the differences between every two groups are our interest. The refined code ISB of L1 and L5 are listed in table 3 and the code ISB of L7 are given in table 4. The code ISB results plus the residuals are plotted in Fig. 3 and the histogram of the adjustment residuals are plotted in Fig. 4. The residual standard deviations (STD) of the adjustment are 0.240 m, 0.250 m and 0.200 m for L1, L5 and L7, respectively. The comparisons of the code ISB for L1-E1 and L5-E5a, L1- E1 and E5b- B2b are shown in Fig. 5a and 5b, respectively. Table 3. Code ISB of each group for GPS L1-Galileo E1 and GPS L5-Galileo E5a after adjustment calculation (unit: m)
L1/E1 L5/E5a
LEIC1
LEIC_S
LEIC2
SEPT
TRIM
TRIM_S
JAVA
NOV
28.1 29.5
23.1 25.4
0.0 0.0
6.0 6.0
4.3 0.0
6.1 1.5
6.2 6.0
28.1 30.0
Table 4. Code ISB of each group for Galileo E5b-BDS B2b after adjustment calculation (unit: m)
E5b/B2a
LEIC1 21.4
LEIC_S 16.2
LEIC2 0.0
SEPT 0.0
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TRIM1 -1.4
TRIM_S 0.4
TRIM2 -4.3
JAVA 0.2
Figure 3. Code ISB estimates plus the residuals of the adjustment for GPS L1-Galileo E1 (a), GPS L5-Galileo E5a (b) and Galileo E5b-BDS B2b (c) for the short baselines of the 7 DOYs over the last three years.
Figure 4. Code ISB residuals of the adjustment for the three frequencies, GPS L1-Galileo E1 (a), GPS L5-Galileo E5a (b) and Galileo E5b-BDS B2b (c)
Figure 5. Comparison of the code ISBs for GPS L1-Galileo E1 and GPS L5-Galileo E5a (a), and GPS L1-Galileo E1 and Galileo E5b-BDS B2b (b).
The receiver-type and firmware-version combinations of Leica receivers are divided into two different groups including receivers before GR 25 belong to group LEIC1 and the receivers after GR 30 belong to group LEIC2. The two groups have different ISB values for all the three overlapping frequencies as shown in Fig. 3. Besides, the group LEIC1 has the exceptional stations MARS, GUIP, TLMF, MLVL on DOY 180 2016 and station KOUG on DOY 001 2016, all with firmware version 3.11. Those stations as well as station GOP6 7 / 19
equipped with LEICA GRX1200+GNSS 9.20 form a subgroup named LEIC_S shown in table 5 with smaller code ISB than that of the main group LEIC1. Table 5. Stations belong to subgroup LEIC_S where GOP6 equipped with LEICA GRX1200+GNSS 9.20, while the others with firmware version of 3.11.
Year and DOY 2016 001 2016 180 2018 001 2018 180
L1/E1 KOUG MARS GUIP TLMF MLVL GOP6 GOP6
L5/E5a KOUG MARS GUIP TLMF MLVL GOP6 GOP6
E5b/B2b KOUG MARS GUIP TLMF MLVL
The Trimble receiver has also a subgroup listed in table 6 which has code ISB values larger than the rest stations of the main groups. This Trimble subgroup is named TRIM_S in Table 3 and Fig. 3. The stations of TRIM_S have code ISB different from the main group until the latest data collected on DOY 001 2019. Besides, the subgroup TRIM_S for L1 and the subgroup TRIM_S for L5 include different combinations of receiver-type and firmware-version as shown in the Fig. 5a. Except for the stations in TRIM_S, the Trimble receivers are consistent for both L1 and L5 frequencies but are separated into two groups for L7. The code ISB of Galileo E2b and BDS B2b (L7) for Trimble receivers with firmware versions before 5.15 and after 5.20 are significantly different. The Septentrio and Javad receivers have very similar code ISB for all receivers. Septentrio receivers have consistent code ISB for every frequency i.e. all the SEPT receivers have the same code ISB for each of the three frequencies. The code ISBs of Javad receivers are also consistent for each of L1 and L5 frequencies but has an exception of one station WTZZ for L7 with code ISB about 1.0 m larger. The data of the only NOV station shows that the NOV OEM6 receiver has code ISB of L1 and L5 almost the same as LEIC1. The station is lack of BDS data and thus the analysis for L7 is missing. Table 6. Stations belong to TRIM_S for the three overlapping frequencies
Year and DOY 2016 180 2017 001 2017 180 2018 001
L1/E1 DUND, SIN1 CEU1, DUND, UCAL DUND, STR2, UCAL DUND, STR2, UCAL
L5/E5a DUND, SIN1 UCAL STR2, UCAL STR2, DUND, UCAL
E5b/B2b STR2 STR2
2018 180
DUND, SCTB, SIN1, STR2, UCAL
DUND, STR2
SCTB, SIN1, STR2
2019 001
DUND, SCTB, SIN1, STR2, UCAL
DUND, SCTB
SCTB, SIN1, STR2
4.2. Phase F-ISB estimation results For the phase F-ISB, all the Leica and Septentrio receivers are consistent between the receivers of the same brand, and each of Trimble and Javad receiver brands can be separated into two groups with different phase FISB values. For Trimble receivers, the second group TRIM2 is composed by firmware versions of 4.85 and 5.01. The Javad receiver groups include a lot of firmware versions and the details can be found in the appendix tables from 4 to 6. The only Nov station has phase F-ISB of L1 and L5 the same as LEIC. The phase F-ISB of the Leica receivers is selected as the reference group with reference F-ISB values of 0.000 m, 0.127 m (1/2 cycles of L5) and 0.062 m (1/4 cycles of L7) for the frequencies of L1, L5 and L7, respectively. The phase F-ISB values refined by least-squares method are listed in tables 7 and are plotted in Fig. 6 after plus the residuals. The residual STD of the adjustment are 0.9 mm, 1.5 mm and 3.1 mm for L1, L5 and L7, respectively. The histograms of the residuals for the three frequencies are drawn in Fig. 7 and the comparison of L1 and L5, L1 and L7 are shown in Fig. 8a and 8b, respectively.
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Table 7. Phase F-ISB of each group for GPS L1-Galileo E1, GPS L5-Galileo E5a and Galileo E5b-BDS B2b after adjustment calculation (unit: m)
Frequency L1/E1 L5/E5a E5b/B2b
LEIC
SEPT
TRIM1
TRIM2
JAVA1
JAVA2
NOV
0.000 0.127 0.062
0.095 0.128 0.062
0.095 0.128 0.125
0.055 0.008 0.084
0.095 0.127 0.063
0.000 0.001 0.001
0.002 0.124 ---
Figure 6. Phase F-ISB estimates plus the residuals of the adjustment for GPS L1-Galileo E1 (a), GPS L5-Galileo E5a (b) and Galileo E5b-BDS B2b (c) for the short baselines of the 7 DOYs over the last three years.
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Figure 7. Phase F-ISB residuals of the adjustment for the three frequencies, GPS L1-Galileo E1 (a), GPS L5Galileo E5a (b) and Galileo E5b-BDS B2b (c)
Figure 8. Comparison of the phase F-ISB for GPS L1-Galileo E1 and GPS L5-Galileo E5a (a), and GPS L1Galileo E1 and Galileo E5b-BDS B2b (b)
The L1X observations of some Javad receivers such as at stations LPGS, AREG on DOY 001 of 2019 are shifted by 1/2 cycles probably to align the observations to L1B and the shift is marked in the head of the RINEX 3 files, while L1X observations of the other Javad receivers such as WUH2, HRAG on DOY 001 of 2019 are not shifted. Those phase shifts are calibrated back in advance before being grouped, otherwise, the phase F-ISB of the combinations of receiver-type and firmware-version are not consistent. The phase shifts are not a problem for L5 and L7 because their shifts happen rarely and the observations of both GNSSs are shifted at the same time when happen. However, the station PRDS marks a phase shift of 1/4 cycles for L5 on DOY 180 of 2017, but the receivers are consistent with the main group before being shifted back. It is better to make the phase shift the same at least for the same receiver brands and mark the shift in the head of the RINEX 3 files carefully. The group JAVA1 of L1 include some receivers belonging to JAVA 2 of L5 as shown in Fig. 8, indicating the groups for JAVA1 of L1 and JAVA1 of L5 are not the same, so is the case for L7. Both Trimble and Javad receivers have subgroups composed by the stations with station-related different phase ISB. In the experiments, the phase F-ISB of those stations are identified and calibrated in advance before the adjustment. The Trimble stations with station-related phase ISB are listed in table 8, the L1 phase F-ISB of which should be added by +0.047 to equal that of the main groups. It seems this difference exist regardless of the firmware version. For example, the station TLSE on DOY 180 of 2016 is installed with the firmware of 5.01 belong to TRIM2, and the L1 phase F- ISB equals the value of TRIM2 minus +0.047 m. The station KIR8 is installed with firmware of 5.10 belong to TRIM1 and the L1 phase F-ISB equals the value of TRIM1 minus +0.047 m. This phase F-ISB difference has been noticed in the research (Tian et al., 2017) and disappears in the data files of 10 / 19
RINEX 2 from IGS website. This difference equals a quarter of L1 wavelength, and no phase shift is recorded in the file heads. Fortunately, the unrecorded shifts are not observed for the data of recent two years. Javad receivers also have some station-related F-ISB values which are different from the main group and are listed in Table 9. The differences from the main group JAVA1 or JAVA2 are only several millimeters. The fact that the code ISB and phase F-ISB can be classified into several groups with small residuals by receiver types and firmware versions indicates that the values are stable overtime. It also indicates that the remaining atmospheric delays of the baselines are small and do not affect the analysis even they may not be completely mitigated when the baselines length reaches 25 km. The zero-baselines are ideal for ISB estimation and analysis, but the number of such baselines in EPN and MGEX are too small to draw any conclusion. Table 8. TRIM stations with F-ISB difference of -0.047 from the main TRIM groups for GPS L1 and Galileo E1
Year and DOY 2016 001 2016 180 2017 001 2017 180
Stations JFNG, RGDG KIR8, TLSE, JFNG, RGDG KIR8 KIR8
Table 9. JAVA stations with F-ISB different from the main JAVA groups for L5 and L7 (unit: m)
Year and DOY 2016 001 2016 180 2017 001 2017 180
L1/E1 -0.004 UNBD UNBD UNBD
2018 001
UNBD
2018 180
UNBD
2019 001
L5/E5a
+0.007
WTZZ FFMJ, HELG WTZZ FFMJ, HELG WTZZ FFMJ, HELG WTZZ FFMJ WTZZ
+0.004
-0.007
WTZZ WTZZ WTZZ
ZIMJ ZIMJ
WTZZ
ZIMJ
WTZZ
ZIMJ
WTZZ
ZIMJ
4.3. Applications of the estimated ISB values The code ISB and phase F-ISB groups can be separated into two types, type I groups are consistent and type II groups include a few receivers with station-related constant bias values for the latest data. The groups of the two types are listed in Table 10. It’s high likely that the station-related constant bias values for type II groups are caused by the station-related data processing instead of the effects of receiver types and firmware versions and require further investigations in the future. Type I groups may be used directly in multi-GNSS integration and type II need to be checked in advance or be used as initial ISB values in ISB estimation. Table 10. group classification for code ISB and phase F-ISB of the three overlapping frequencies L1/E1, L5/E5a and E5b/B2b
Observation types Code
Frequencies
type I
type II
L1/E1
LEIC1, LEIC2, SEPT, JAVA, NOV
TRIM
L5/E5a
LEIC1, LEIC2, SEPT, JAVA, NOV
TRIM
E5b/B2b
LEIC1, LEIC2, SEPT, NOV, TRIM2
TRIM1, JAVA
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phase
L1/E1
LEIC, SEPT, TRIM1, TRIM2, NOV
JAVA1, JAVA2
L5/E5a
LEIC, SEPT, TRIM1, TRIM2, NOV
JAVA1, JAVA2
E5b/B2b
LEIC, SEPT, TRIM1, TRIM2, JAVA1, JAVA2
When the code ISB and phase F-ISB values in tables 3, 4 and 7 are used in multi-GNSS integration, the observations from different constellations can be regarded as from one constellation. The advantages by employing known phase F-ISB have been demonstrated in the previous research (Tian et al., 2019a). The benefits brought by the known code ISB from Table 3 and Table 4 are demonstrated by comparison with method of parameterizing code ISB. The GPS L1 and Galileo E1 code integration of zero-baseline MAT1_MATZ with data collected on DOY 001 2019 is taken as an example. Both the atmosphere delays and multipath effects are mitigated, and the code positioning results are only affected by the code ISB. The baseline MAT1_MATZ is equipped with receivers of LEICA GR30 4.20 belong to group LEIC2 and SEPT POLARX5TR 5.2.0 belong to group SEPT. The code ISB of L1-E1 for the group LEIC2 and group SEPT in Table 3 are 0.0 m and 6.0 m, respectively, with difference of 6.0 m and the difference should be subtracted from the inter-system double difference code observations. Assuming 4 GPS and 1 Galileo satellites are observed at each epoch, the code relative single-epoch positioning is implemented in two ways. In the first way, the code ISB is parametrized in the observation models as unknown variables. A total of 4 code double difference equations can be formed and 4 unknown parameters including 3 coordinate and 1 code ISB parameters need to be solved. The solutions of the whole day are drawn in Fig.9a. In the second way, the value 6.0 m is used to calibrate the code ISB in advance and thus only 3 coordinate parameters need to be solved. The solutions of the whole day are shown in Fig.9b. The distance root mean squares (DRMS) calculated by Eq. (6) for the two ways are 1.487 m and 0.770 m, respectively, with reduction of 48.2% by the known code ISB. N DRMS = ∑i = 1(∆ei2 + ∆ni2 + ∆ui2)/N (6) where e,n,u are the solution errors in the direction of east, north and up direction in local coordinate system, N is the number of epochs.
Figure 9. Code positioning results with 4 GPS satellites and 1 Galileo satellites in the case of parameterized code ISB (a) and known code ISB (b) for zero-baseline MAT1_MATZ with data collected on DOY 001 2019.
The code positioning benefits more from known code ISB when the number of satellites is smaller. As an example, different errors from -2.0 m to 2.0 m with 0.01 m interval are added to the known value in code ISB calibration and the corresponding DRMS of the code positioning with zero-baseline MAT1_MATZ are calculated and compared with observed satellites of three cases. The first case is with 3 GPS and 1 Galileo satellites, the second case is with one more GPS satellite and the third case is with all observed GPS and Galileo satellites. The DRMS of the first case are drawn in Fig.10a. If the code ISB is parameterized, the code positioning will fail as the equations are rank-deficient. Therefore, the code positioning benefits from the known code ISB 12 / 19
as long as the DRMS is acceptable. The DRMS of the second case are drawn in Fig.10b. The code positioning with parameterized code ISB also succeeds and the DRMS are shown in the panel with blue line. We can see that if the errors of the known ISB are too large, the DRMS may be even larger than the code positioning with parameterized ISB. When the known code ISB is within the range with length of 1.375 m i.e. the length of the blue line within the two intersection points in Fig.10b, the DRMS with known code ISB will be smaller. The DRMS of the third case are drawn in Fig.10c. The code positioning can hardly benefit from the known code ISB. The range length within the two intersection points is 0.285 m which is much shorter.
Figure 10. DRMS of the code positioning with 3 GPS and 1 Galileo satellites (a), with 4 GPS and 1 Galileo satellites (b) and with all observed GPS and Galileo satellites (c). The red line is the results with known code ISB and the blue line is that with parameterized code ISB.
5. Conclusions This study analyzes the between-receiver code ISB and phase F-ISB of the overlapping frequencies L1-E1, L5-E5a and E5b-B2b based on the EPN and MGEX baselines up to around 25 km. The baseline data are collected since DOY 001 2016 and recorded in format RINEX 3. After the code ISB and phase F-ISB of the baselines are estimated, the combinations of the receiver-type and firmware-version for Trimble, Leica, Javad, Septentrio and NovAtel receivers are clustered into several groups according to their ISB estimates. Then, the values of the code ISB and phase F-ISB of the groups are refined by least-squares method and are presented in tables. Results show that the Septentrio receivers have consistent code and phase ISB values for the three overlapping frequencies L1-E1, L5-E5a and E5b-B2b i.e. only one value for each frequency and no Septentrio receivers are different. Other receiver brands including Leica, Trimble and Javad have two or more ISB values for at least one frequency. The only NovAtel receiver has the code ISB value similar with Leica receivers before Leica GR25 and has the phase F-ISB value similar with Septentrio receivers for L1-E1 and L5-E5a. Besides, the groups of phase F-ISB may include different receiver-type and firmware-version combinations with that of the code ISB. For example, Leica has only one group for phase F-ISB while two groups for code ISB. Trimble receivers have two groups for both code ISB and phase F-ISB but including different firmware versions. Besides, Trimble and Javad receivers include a few stations with code ISB or phase F-ISB different form the main groups by constant values which requires further investigations. Some of the data files with Javad receiver implement non-zero phase shift which are marked in the head of the RINEX 3 files while others not. The non-zero phase shifts need to be shifted back in the analysis to keep consistency and should be considered in L1/E1 integration and the files for Leica, Septentrio and Trimble do not have non-zero phase shift. The phase shift values directly affect the phase F-ISB and should be more carefully disposed in MGEX and EPN multi-GNSS data processing. The ISB errors can seriously affect the performance of the positioning especially when the number of the observed satellites is small. For example, the code ISB error can degraded the positioning performance to the extent that the results are worse than the positioning without known code ISB when 5 or more satellites from different constellations are observed. The experiments of the single-epoch code positioning with the data of zerobaseline MAT1_MATZ collected on DOY 001 2019 show that the distance RMSE can be reduced by 48.2% from 1.487 m to 0.770 m with accurate code ISB when a total of 5 GPS and Galileo satellites are observed. The distance RMSE significantly increases when the code ISB error is larger. 13 / 19
Acknowledgments: The authors thank IGS MGEX and EPN for providing multi-GNSS data.
Appendix Table 1. Main groups of code ISB for GPS L1-Galileo E1
Receiver groups
Approximate ISB (m) 6
0
LEIC GR10 3.22, 4.02, 4.11, 4.20; LEIC GR25 3.11, 3.22, 4.00, 4.02, 4.11, 4.30, 4.31
LEIC1
LEIC2
28
LEIC GR30 4.11, 4.20; LEIC GR50 4.11, 4.20, 4.30, 4.31
SEPT
SEPT P4 2.5.2, 2.9.0, 2.9.3, 2.9.5, 2.9.6; SEPT P5 5.0.3, 5.10, 5.1.1, 5.1.2, 5.2.0, 5.2.2; SEPT A3 3.4.0
TRIM
TRIM R9 4.85, 5.01, 5.03, 5.10, 5.14, 5.15, 5.20, 5.22, 5.30, 5.33, 5.37; TRIM SPS855 5.32; TRIM AY 5.37
JAVA
JAVA 3 3.6.8, 3.7.2, 3.7.3, 3.7.4, JAVA 3TH 3.5.1, 3.6.1, 3.6.2, 3.6.3, 3.6.4, 3.6.6, 3.6.7, 3.6.9, 3.7.1, 3.7.2, 3.7.3, 3.7.4, 3.7.5; JAVA 3n 3.6.1, 3.6.9; JAVA G2T 3.6.1, 3.6.2
NOV
NOV OEM6
Note: LEIC = LEICA; SEPT P = SEPT POLARX; TRIM R9 = TRIMBLE NETR9; JAVA 3 = JAVAD TRE_3 DELTA; JAVA 3TH = JAVAD TRE_3TH DELTA
Table 2. Main groups of code ISB for GPS L5-Galileo E5a
Receiver groups
0
Approximate ISB (m) 6
LEIC1
LEIC2
LEIC GR30 4.10, 4.11, 4.20; LEIC GR50 4.11, 4.20, 4.30, 4.31 SEPT P4 2.9.0, 2.5.2, 2.9.3, 2.9.5, 2.9.6; SEPT P5 5.0.3, 5.10, 5.1.1, 5.1.2, 5.2.0; SEPT A3 3.4.0
SEPT
TRIM
JAVA
TRIM R9 4.85, 5.01, 5.03, 5.10, 5.14, 5.15, 5.20, 5.22, 5.30, 5.32, 5.33, 5.37; TRIM SPS855 5.32; TRIM AY 5.37 JAVA 3.7.4, 3.5.1, 3.6.4, 3.7.1,
3 3.6.8, 3.7.2, 3.7.5; JAVA 3.6.1, 3.6.2, 3.6.7, 3.6.6, 3.7.2, 3.7.3,
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3.7.3, 3TH 3.6.3, 3.6.9, 3.7.4,
30 LEIC GR10 4.00, 4.02, 4.11, 4.20; LEIC GR25 3.11, 3.22, 4.02, 4.11, 4.30, 4.31
3.7.5; JAVA 3n 3.6.1, 3.6.9; JAVA G2T 3.6.1, 3.6.2, 3.7.5
NOV
NOV OEM6
Table 3. Main groups of code ISB for Galileo E5b-BDS B2b
Receiver groups
Approximate ISB (m) 0
-4
22 LEIC GR10 3.22, 4.02 LEIC GR10 4.11, 4.20; LEIC GR25 3.11, 3.22, 4.02, 4.11, 4.30
LEIC1 LEIC GR30 4.11, 4.20; LEIC GR50 4.11, 4.20, 4.31 SEPT P4 2.9.0, 2.9.3, 2.9.5, 2.9.6; SEPT P5 5.0.3, 5.10, 5.1.1, 5.1.2
LEIC2 SEPT
TRIM R9 5.20, 5.22, 5.32, 5.33, 5.37; TRIM AY 5.37; TRIM R9 5.30
TRIM1 TRIM2
TRIM R9 4.85, 5.01, 5.03, 5.10, 5.14, 5.15 JAVA 3 3.7.2, 3.7.3, 3.7.4; JAVA 3TH 3.6.8, 3.6.6, 3.6.9, 3.7.1, 3.7.2, 3.7.3, 3.7.4, 3.7.5
JAVA
Table 4. Main groups of phase F-ISB for GPS L1-Galileo E1
Receiver groups
LEIC
Approximate F-ISB (m) 0.00
0.06
0.10
LEIC GR10 4.02, 4.11, 4.20; LEIC GR25 3.11, 3.22, 4.02, 4.11, 4.30, 4.31; GR30 4.20; LEIC GR50 4.30, 4.20, 4.31; LEICA GRX1200 9.20 SETP A3 3.4.0; SETP P4 2.9.0, 2.9.3, 2.9.5, 2.9.6; SETP P5 5.2.0, 5.0.3, 5.10, 5.1.1, 5.1.2 TRIM R9 5.10, 5.14, 5.15, 5.20, 5.22, 5.30, 5.33, 5.37; TRIM A 5.37; TRIM S855 5.32
SEPT
TRIM1
TRIM2
TRIM R9 5.01; 4.85 JAVA 3 3.6.8; JAVA 3TH 3.4.9, 3.5.1, 3.6.1, 3.6.2, 3.6.3, 3.6.4, 3.6.6, 3.6.7, 3.6.9, 3.7.2; JAVA G2 3.6.1, 3.6.2; JAVA 3N 3.6.1, 3.6.9
JAVA1
JAVA2
JAVA 3 3.6.4, 3.7.2, 3.7.3, 3.7.4, 3.7.5; JAVA 3TH 3.7.1, 3.7.3, 3.7.4, 3.7.5; JAVA G2 3.7.5
NOV
NOV OEM6 15 / 19
Table 5. Main groups of phase F-ISB for GPS L5-Galileo E5a
Approximate F-ISB (m)
Receiver groups
0.00
0.12 LEIC GR10 4.00, 4.20; LEIC GR25 3.11, 3.22, 4.00, 4.02, 4.11, 4.30, 4.31; LEIC GR30 4.20; LEIC GR50 4.20, 4.31;
LEIC
LEIC GRX1200 9.20 SEPT
SEPT P4 2.9.0, 2.9.3, 2.9.5, 2.9.6; SEPT P5 5.0.3, 5.10, 5.1.1, 5.1.2, 5.2.0; SEPT A3 3.4.0
TRIM1
TRIM R9 5.03, 5.10, 5.14, 5.15, 5.20, 5.22, 5.30, 5.33, 5.37; TRIM A 5.37; TRIM S855 5.32
TRIM2
TRIM R9 5.01, 4.85 JAVA 3 3.6.8, 3.7.2, 3.7.3, 3.7.4, 3.7.5; JAVA 3TH 3.7.2, 3.7.3, 3.7.4, 3.7.5; JAVA 3N 3.6.1, 3.6.9; JAVA G2 3.7.5
JAVA1
JAVA2
JAVA 3TH 3.4.9, 3.5.1, 3.6.1, 3.6.2, 3.6.3, 3.6.4, 3.6.6, 3.6.7, 3.6.9, 3.7.1; JAVA G2 3.6.1, 3.6.2
NOV
NOV OEM6
Table 6. Main groups of phase F-ISB for Galileo E5b-BDS B2b
Receiver groups
0.00
LEIC
LEIC LEIC 4.02, LEIC LEIC 4.31
Approximate F-ISB (m) 0.06 0.08 GR10 4.20, 4.11; GR25 3.11, 3.22, 4.11, 5.11, 4.30; GR30 4.11, 4.20; GR50 4.11, 4.20,
SEPT P4 2.9.0, 2.9.3, 2.9.5, 2.9.6; SEPT P5 5.0.3, 5.10, 5.1.1, 5.1.2, 5.2.0
SEPT
TRIM R9 5.10, 5.14, 5.15, 5.20. 5.22, 5.30, 5.33; TRIM AY 5.30, 5.37; TRIM SPS855 5.32
TRIM1
TRIM R9 4.85, 5.01
TRIM2 JAVA1 JAVA2
0.12
JAVAD 3TH 3.6.6, 3.6.9 JAVAD 3TH 3.7.2 JAVAD 3 3.7.2, 3.7.3, 3.7.4
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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
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S0273-1177(19)30830-0 https://doi.org/10.1016/j.asr.2019.11.022 JASR 14546
To appear in:
Advances in Space Research
Received Date: Revised Date: Accepted Date:
2 September 2019 14 November 2019 15 November 2019
Please cite this article as: Tian, Y., Yuan, L., Huang, D., Zhou, L., Chen, X., Xu, S., Feng, W., Gong, X., Analysis of the code and phase between-receiver inter-system biases of the overlapping frequencies for GPS/ Galileo/BDS, Advances in Space Research (2019), doi: https://doi.org/10.1016/j.asr.2019.11.022
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Analysis of the code and phase between-receiver inter-system biases of the overlapping frequencies for GPS/Galileo/BDS Yumiao Tian1,3, Linguo Yuan1,3, Dingfa Huang1,3, Letao Zhou1,3, Xueyang Chen2, Shaoguang Xu1,3, Wei Feng1,3, Xiaoying Gong1,3 1
Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu, Sichuan, 611756, China 2 Chongqing Geomatics and Remote Sensing Center, Chongqing, 611756, China 3 State-Province Joint Engineering Laboratory of Spatial Information Technology for High-Speed Railway Safety, Chengdu, Sichuan, 610031, China * Correspondence: [email protected] Email address: Yumiao Tian: [email protected]; Linguo Yuan: [email protected]; Dingfa Huang: [email protected]; Letao Zhou: [email protected]; Xueyang Chen: [email protected]; Shaoguang Xu : [email protected]; Wei Feng: [email protected]; Xiaoying Gong: [email protected]
Abstract: The overlapping-frequency signals from different GNSS constellations are interoperable and can be integrated as one constellation in multi-GNSS positioning when inter-system bias (ISB) is properly disposed. The look-up table method for ISB calibration can enhance the model strength, maximize the number of integerestimable ambiguities, and thus is preferred. However, the characteristics and magnitudes of the receiver code ISB and phase fractional ISB (F-ISB) are not well known and the wrong values of the biases can seriously degrade the positioning results. In this contribution, we first estimate the between-receiver code ISB and phase F-ISB of hundreds of the baselines up to around 25 km in the European Permanent GNSS Network (EPN) and the Multi-GNSS Experiment (MGEX) for the overlapping frequencies L1-E1 (L1), L5-E5a (L5) and E5bB2b(L7). The data collected from 1st January 2016 to 1st January 2019. Second, the receiver-type and firmware-version combinations for the receivers of Trimble, Leica, Javad, Septentrio and NovAtel are carefully classified. Results show that the Septentrio receivers have consistent code and phase ISB values for the three overlapping frequencies i.e. only one value for each frequency and no receivers are different. The Leica, Trimble and Javad receivers have two or more ISB values for at least one of the three frequencies. A few receivers with biases to the groups are also found and listed. Third, the code ISB and phase F-ISB of the groups are adjusted by the least-squares method. The root mean square errors (RMSE) of the least square adjustment are 0.240 m, 0.250 m and 0.200 m for code of L1, L5 and L7 frequencies, respectively, and are 0.0009 m, 0.0015 m and 0.0031 m for phase of L1, L5 and L7 frequencies, respectively. Finally, the effects of code ISB errors on code positing are investigated with the zero-baseline MAT1_MATZ. The distance root mean square error (DRMS) of L1-E1 code positioning can be reduced by 48.2% with 5 GPS and Galileo satellites and the DRMS degrades quickly when the code ISB error is larger. Keywords: Multi-GNSS; Inter system bias (ISB); code ISB; Carrier phase ISB
1. Introduction Global Navigation Satellite System (GNSS) positioning benefits enormously from the integration of multiGNSS systems as more satellites are available. The method that integrates the signals from different GNSS constellations including GPS/GLONASS/Galileo/BDS by the interoperability of the overapplying frequencies or narrowly-spaced frequencies can lower the PDOP, ADOP, improve the success rate of ambiguity fixing and the accuracy of the results (Odolinski et al., 2014; Li et al., 2015; Tian et al., 2018; Kubo et al., 2018; Chen et al., 2019; Wu et al., 2019a). Due to the different paths of hardware and digital signal processing, the signals of overlapped frequencies for GPS/ Galileo/BDS can be misaligned in the receivers, leading to between-receiver inter-system bias (ISB). 1 / 19
Those biases need to be dealt carefully in multi-GNSS data processing so that the benefits of the observations from different systems can be fully exploited. The phase ISB is separated into two parts, the integer parts which are neglectable and the fractional part (F-ISB) which need to be accurately calibrated (Odolinski et al., 2014; Paziewski and Wielgosz, 2015, 2017; Paziewski et al., 2015). The code ISB has no periodic characteristics and the entire value needs to be calibrated in the code models. The estimation of ISB in multi-GNSS integration has been investigated in the past years. Basically, the estimation approaches require additional unknown parameters (Paziewski and Wielgosz, 2015; Gao et al., 2017, 2018) or reduced number of integer-estimable ambiguities (Odijk and Teunissen, 2013a, 2013b) or increased computation efforts (Tian et al., 2017, 2018). If the code ISB or phase F-ISB are known, the look-up table method calibrating the ISB in advance can be used. The known ISB values brings the benefits of strengthened estimation model and maximized integer-estimable ambiguities (Khodabandeh and Teunissen, 2016; Odijk et al., 2016). The knowledge such as the characteristics and magnitudes of code ISB and phase F-ISB which is critical to the reliability of the look-up table method should be thoroughly investigated. Odijk and Teunissen (2013a, 2013b) investigated the characteristics of between-receiver phase F-ISB and the baselines with the receivers of identical receiver types are considered to be free of the bias, but the baselines formed by different receiver types are usually with significant ISB values. Those values are stable and can be calibrated in GPS/Galileo integration. The values of GPS L1 and Galileo E1, GPS L5 and Galileo E5 of several receiver brands were given and they indicated that the values should be validated with more data. Paziewski and Wielgosz (2015), Paziewski et al. (2015) and Dong et al. (2018) showed that the F-ISB is stable with several baselines of different receiver types. Besides, the effects of the firmware upgrade on the ISB of the receivers such as Trimble and Javad were reported (Dong et al., 2018; Nadarajah et al., 2015; Zhang and Teunissen, 2016; Liu et al., 2017; Wu et al., 2019b). Zhang and Teunissen (2016) also found that the between-receiver ISB may also be affected by the daily maximum temperature. Tian et al. (2019b) estimated the between-receiver ISB with eight baselines and analyzed the characteristics. Besides, the multi-GNSS observation types are supposed to have an impact on the ISB values. For example, the Galileo L5I, L5Q which are in phase and quadrature phase observations, respectively, are supposed to have a bias of 1/4 circles. This has been noticed and the phase shift values are given in the data file format RINEX since version 3.02 (Rinex 3.02, 2013; Rinex 3.04, 2018). Obviously, the observation types should also be considered in the analysis of the phase F-ISB characteristics. Besides, the Multi-GNSS Experiment (MGEX) is specially launched for the investigation of the GNSS satellite signals and receiver states, as well as multi-GNSS software development (Montenbruck et al., 2017; Li et al., 2019). The stations from MGEX plus the stations of the European Permanent GNSS Network (EPN) (Bruyninx et al, 2001) bring a large amount of multi-GNSS observation data allowing us to thoroughly analyze both the code and phase between-receiver ISB. This investigation focuses on the magnitudes of the ISB and their classifications instead of the estimation and correction methodology. the code ISB and phase F-ISB of hundreds of baselines with length up to around 25 km are estimated and analyzed. The RINEX 3 data of the MGEX and EPN collected on the days distributed over the last three years since day of year (DOY) 001 (1st January) 2016 are employed. The estimates of the overlapping frequencies including GPS L1-Galileo E1 (L1), GPS L5- Galileo E5a (L5), Galileo E5b-GPS B2b (L7) of the receivers are grouped and then the ISB values of the groups are adjusted for refinement. It is shown how the phase F-ISB and code ISB changes over different receiver-types and firmware-versions, how stable the ISB is over time, and how individual receivers agree for each group. Also, the benefits brought by the code ISB look-up table are analyzed. In the follows, the employed previous published method for code ISB and phase F-ISB is briefly introduced in section 2. The data from MGEX and EPN are described in section 3. Section 4 presents the estimates and analysis of code ISB and phase F-ISB, as well as an investigation of the code ISB error effects on positioning. Conclusions are given in section 5. 2. Estimation of the code ISB and phase F-ISB The between-receiver ISB can be parameterized in the double difference models of GNSS relative positioning. The general forms of the DD models can be found in the reference (Tian et al., 2019). In the relative data processing, both the receiver and satellite clocks are eliminated. In this study, the baselines are up to around 25 km and the tropospheric and ionospheric delays are simply corrected by empirical models instead of being 2 / 19
parameterized. The code and phase observations models of GPS L1 and GPS L2 are included in the ISB estimations of all the three frequencies and can be expressed as
PabL1L1,ij abL1L1,ij abL1L1 PabL 2 L 2,ij abL 2L 2,ij abL 2L 2 L1 L1L1,ij abL1L1,ij L1 N abL1L1,ij abL1L1 ab L 2abL 2 L 2,ij abL 2L 2,ij L 2 N abL 2 L 2,ij abL 2 L 2
(1)
where P and are the code and phase observations, respectively. a and b are the two stations. i and j are the two observed GPS satellites. L1 and L 2 indicates the two carriers. is the carrier wavelength. N is the integer ambiguities.
and
are the noises for the code and phase observations, respectively.
For the GPS L1 and Galileo E1, the inter-system DD observation models are
PabL1E1,ik abL1E1,ik d abL1E1 abL1E1 L1 L1E1,ik abL1E1 abL1E1 L1 N abL1E1,ik abL1E1 ab
(2)
PabL 5 E 5 a ,ik abL 5 E 5 a ,ik d abL 5 E 5 a abL 5 E 5 a L 5 L 5 E 5 a ,ik abL 5 E 5 a abL 5 E 5 a L 5 N abL 5 E 5 a ,ik abL 5 E 5 a ab
(3)
where d is the between-receiver code ISB and is the between-receiver phase F-ISB. The inter-system DD observation models of the overlapping frequency GPS L5 and Galileo E5a named as L5 in the RINEX 3 format can be formed in a similar way as
Also, the inter-system DD models of the overlapping frequency Galileo E5b and BDS B2b named as L7 in the RINEX 3 format are
PabE 5bB 2b ,ik abE 5bB 2b ,ik d abE 5bB 2b abE 5bB 2b E 5b E 5bB 2b ,ik abE 5bB 2b abE 5bB 2b E 5b N aEb5bB 2b ,ik abE 5bB 2b ab
(4)
After the other errors are eliminated or reduced by empirical models, the code ISB can be estimated directly by the combination of the above equations, such as the combinations of Eq. (1) and Eq. (2), Eq. (1) and Eq. (3), Eq. (1) and Eq. (4) for the code ISB estimation of L1/E1, L5/E5a and E5b/B2b, respectively. The phase F-ISB are estimated with particle-filtering-based estimation approach presented in the research (Tian et al., 2017). This approach can fully exploit the multi-GNSS observations by fixing the maximized number of integer ambiguities. First, the F-ISB values sampled over the initial range with length of one wavelength are generated, and each sample is assigned the initial weights. Second, each F-ISB value is used to calibrate the FISB in the inter-system model and both the inter- and intra-system DD ambiguities are fixed by LAMBDA method (Teunissen, 1995). After the corresponding RATIO values are calculated, the weight of each F-ISB value is updated according to the RATIO value (Euler and Schaffrin, 1991; Verhagen, 2005; Verhagen and Teunissen, 2013) and the F-ISB value is derived by the weighted F-ISB samples. Third, the F-ISB values are resampled so that each F-ISB values have similar weights again. Although the approach has a relatively large computation load, it is not a problem in this study. After the between-receiver code ISB and phase F-ISB are estimated, the receiver-type and firmware-version combinations are classified into different groups according to the their ISB magnitudes. Then the ISB estimates are adjusted by least-squares method with difference models to refine the ISB values. In the adjustment calculation, the number of the unknown parameters which representing the ISB of each group is one larger than the rank of the equations, and thus an additional equation setting the ISB of the reference group to a reference value is added. After the adjustment, the between-receiver ISB estimates are transformed into single-receiver ISB relatives to the reference receiver group. It should be noted that only the difference between single-receiver ISB matters and the single-receiver ISB of the reference group can be set as an arbitrary value. The adjustment models can be 3 / 19
expressed as
v = Bx - l
(5)
where
est12 1，， 0 ， 0 x1 -1， est x -1，， 0 ， 13 2 0 1， x= l= B= 0 -1， 1 ，， est( n1) n 0， ref xn 0， 0 1 , ，， ,
v is the residuals, x
is the single-receiver ISB parameters for each receiver group and
n
is the number of
the receiver groups, est is the code ISB or phase F-ISB estimate for each baseline and ref is the reference value assigned to the reference receiver group. The row of the equation equals the number of the ISB estimates for hybrid-receiver baselines plus one. The elements in vector x can be transformed into between-receiver ISB in applications and are the study objective in the following sections. 3. Data employed The MGEX and EPN provide a large amount of data for the analysis of satellite signals and receiver qualities for multi-GNSS interation. The data collected on DOY 001 and 180 of 2016, 2017 and 2018, DOY 001 of 2019 which cover a time period of more than three years are downloaded. Those data are collected by receivers of 6 brands and the numbers of each brand receivers are shown in Fig. 1. The proportion of each brand on DOY 001 2019 presented in table 1. The most equipped receivers are Trimble (TRIM), Leica (LEIC), Javad (JAVA) and Septentrio (SEPT) with increasing numbers over the last three years, while the receivers from TPS and NovAtel (NOV) are much less without station-number increment since DOY 001 2017. Besides, most TPS stations do not provide Galileo and BDS data but with only one exception CAG1 using TPS NET-G5 receiver. However, station CAG1 is lack of recorded data to calculate any ISB parameter and thus all TPS receivers are excluded. The NOV receiver is equipped on only one station and has observations of L1 and L5 but not L7.
Figure 1. Numbers of the receivers employed by MGEX and EPN stations over the last three years. The receivers include Trimble (TRIM), Leica (LEIC), Javad (JAVA), Septentrio (SEPT), TPS and NovAtel (NOV).
The observation types of the receivers are listed in table 1 and are consistent for each receiver brand with very few exceptions. For example, the observation type for L5 is L5Q for most stations which are equipped with Leica receivers from type GR10 to type GR50 but is L5X for the only one station equipped with GRX1200+GNSS receiver. The different observation types may have phase shifts which can be a factor affecting the Phase F-ISB by values presented in RINEX format since version 3.02 (Rinex 3.02, 2013) 4 / 19
Table 1. Number of stations and observation types of both code and phase for MGEX and EPN network on DOY 001 of 2019
Receiver brands LEIC SEPT TRIM JAVA TPS NOV
# stations 105 72 130 98 23 1
Proportio n (%) 24.5 16.8 30.3 22.8 5.4 0.2
L1 C1C C1C C1C C1C C1C C1C
E1 C1C C1C C1X C1X C1B C1C
L5 C5Q C5Q C5X C5X C5Q C5Q
code E5a C5Q C5Q C5X C5X C5X C5Q
E5b C7Q C7Q C7X C7X C7I
B2b C7I C7I C7I C7I C7I
L1 L1C L1C L1C L1C L1C L1C
E1 L1C L1C L1X L1X L1B L1C
phase L5 E5a L5Q L5Q L5Q L5Q L5X L5X L5X L5X L5Q L5X L5Q L5Q
E5b L7Q L7Q L7X L7X L7I
The short baselines of the data are almost free of tropospheric and ionospheric delays and are ideal for the analysis of between-receiver ISB. The number of the baselines shorter than around 25 km and the number of the receivers for each brand are listed in table 2. The sum of the receiver number is smaller than twice of the baseline number because some of the baselines share the same stations. For example, a total of 17 baselines are employed on DOY 001 2016 and the baselines are composed by 25 stations equipped with 4 Leica receivers, 3 Septentrio receivers, 8 Trimble receivers, 8 Javad receivers and 2 NovAtel receivers. The employed data pairs are globally distributed and the locations of the data pairs on DOY 001 2019 are shown as red dots in Fig. 2. Table 2. Number of short baselines and receiver stations employed in the calculations
Year and DOY 2016 001 2016 180 2017 001 2017 180 2018 001 2018 180 2019 001 sum
# Baselines 17 33 44 60 60 73 110 391
# LEIC 4 12 14 17 20 22 75 164
# SEPT 3 7 10 13 14 19 43 109
# TRIM 8 17 20 27 26 27 66 191
# JAVA 8 10 17 20 16 23 61 155
#NOV 2 1 1 1 1 1 1 8
Figure 2. Geographical distribution of the baselines (red dots) employed in the experiments
4. ISB refinement and analysis The baselines described in Table 2 are employed to analyze the code ISB and phase F-ISB of the overlapping frequencies L1-E1, L5-E5a and E5b-B2b. Some baselines which cannot provide precise positioning results such as baseline FAA1_THTG on DOY 001 2018 are excluded. The code ISB and phase F-ISB of the remaining receivers are estimated and the receiver-type and firmware-version combinations are separated into different groups. The receivers of each group are from the same manufactures and have similar code ISB or phase F-ISB value. 5 / 19
B2b L7I L7I L7I L7I L7I
4.1 Code ISB estimation results The code ISBs of L1/E1, L5/E5a, E5b/B2a are estimated by the combination of the code models described in section 2. The receiver-type and firmware-version combinations are then grouped according to their code ISB estimates and the group contents are given in appendix from table 1 to table 3. The receiver ISB of each group are then refined by Eq. (5). Since the group LEIC2 has code ISB of a smaller value, we select this group as the reference group and set its code ISB to zero value for all the three frequencies. The selection of the reference group is not important because only the differences between every two groups are our interest. The refined code ISB of L1 and L5 are listed in table 3 and the code ISB of L7 are given in table 4. The code ISB results plus the residuals are plotted in Fig. 3 and the histogram of the adjustment residuals are plotted in Fig. 4. The residual standard deviations (STD) of the adjustment are 0.240 m, 0.250 m and 0.200 m for L1, L5 and L7, respectively. The comparisons of the code ISB for L1-E1 and L5-E5a, L1- E1 and E5b- B2b are shown in Fig. 5a and 5b, respectively. Table 3. Code ISB of each group for GPS L1-Galileo E1 and GPS L5-Galileo E5a after adjustment calculation (unit: m)
L1/E1 L5/E5a
LEIC1
LEIC_S
LEIC2
SEPT
TRIM
TRIM_S
JAVA
NOV
28.1 29.5
23.1 25.4
0.0 0.0
6.0 6.0
4.3 0.0
6.1 1.5
6.2 6.0
28.1 30.0
Table 4. Code ISB of each group for Galileo E5b-BDS B2b after adjustment calculation (unit: m)
E5b/B2a
LEIC1 21.4
LEIC_S 16.2
LEIC2 0.0
SEPT 0.0
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TRIM1 -1.4
TRIM_S 0.4
TRIM2 -4.3
JAVA 0.2
Figure 3. Code ISB estimates plus the residuals of the adjustment for GPS L1-Galileo E1 (a), GPS L5-Galileo E5a (b) and Galileo E5b-BDS B2b (c) for the short baselines of the 7 DOYs over the last three years.
Figure 4. Code ISB residuals of the adjustment for the three frequencies, GPS L1-Galileo E1 (a), GPS L5-Galileo E5a (b) and Galileo E5b-BDS B2b (c)
Figure 5. Comparison of the code ISBs for GPS L1-Galileo E1 and GPS L5-Galileo E5a (a), and GPS L1-Galileo E1 and Galileo E5b-BDS B2b (b).
The receiver-type and firmware-version combinations of Leica receivers are divided into two different groups including receivers before GR 25 belong to group LEIC1 and the receivers after GR 30 belong to group LEIC2. The two groups have different ISB values for all the three overlapping frequencies as shown in Fig. 3. Besides, the group LEIC1 has the exceptional stations MARS, GUIP, TLMF, MLVL on DOY 180 2016 and station KOUG on DOY 001 2016, all with firmware version 3.11. Those stations as well as station GOP6 7 / 19
equipped with LEICA GRX1200+GNSS 9.20 form a subgroup named LEIC_S shown in table 5 with smaller code ISB than that of the main group LEIC1. Table 5. Stations belong to subgroup LEIC_S where GOP6 equipped with LEICA GRX1200+GNSS 9.20, while the others with firmware version of 3.11.
Year and DOY 2016 001 2016 180 2018 001 2018 180
L1/E1 KOUG MARS GUIP TLMF MLVL GOP6 GOP6
L5/E5a KOUG MARS GUIP TLMF MLVL GOP6 GOP6
E5b/B2b KOUG MARS GUIP TLMF MLVL
The Trimble receiver has also a subgroup listed in table 6 which has code ISB values larger than the rest stations of the main groups. This Trimble subgroup is named TRIM_S in Table 3 and Fig. 3. The stations of TRIM_S have code ISB different from the main group until the latest data collected on DOY 001 2019. Besides, the subgroup TRIM_S for L1 and the subgroup TRIM_S for L5 include different combinations of receiver-type and firmware-version as shown in the Fig. 5a. Except for the stations in TRIM_S, the Trimble receivers are consistent for both L1 and L5 frequencies but are separated into two groups for L7. The code ISB of Galileo E2b and BDS B2b (L7) for Trimble receivers with firmware versions before 5.15 and after 5.20 are significantly different. The Septentrio and Javad receivers have very similar code ISB for all receivers. Septentrio receivers have consistent code ISB for every frequency i.e. all the SEPT receivers have the same code ISB for each of the three frequencies. The code ISBs of Javad receivers are also consistent for each of L1 and L5 frequencies but has an exception of one station WTZZ for L7 with code ISB about 1.0 m larger. The data of the only NOV station shows that the NOV OEM6 receiver has code ISB of L1 and L5 almost the same as LEIC1. The station is lack of BDS data and thus the analysis for L7 is missing. Table 6. Stations belong to TRIM_S for the three overlapping frequencies
Year and DOY 2016 180 2017 001 2017 180 2018 001
L1/E1 DUND, SIN1 CEU1, DUND, UCAL DUND, STR2, UCAL DUND, STR2, UCAL
L5/E5a DUND, SIN1 UCAL STR2, UCAL STR2, DUND, UCAL
E5b/B2b STR2 STR2
2018 180
DUND, SCTB, SIN1, STR2, UCAL
DUND, STR2
SCTB, SIN1, STR2
2019 001
DUND, SCTB, SIN1, STR2, UCAL
DUND, SCTB
SCTB, SIN1, STR2
4.2. Phase F-ISB estimation results For the phase F-ISB, all the Leica and Septentrio receivers are consistent between the receivers of the same brand, and each of Trimble and Javad receiver brands can be separated into two groups with different phase FISB values. For Trimble receivers, the second group TRIM2 is composed by firmware versions of 4.85 and 5.01. The Javad receiver groups include a lot of firmware versions and the details can be found in the appendix tables from 4 to 6. The only Nov station has phase F-ISB of L1 and L5 the same as LEIC. The phase F-ISB of the Leica receivers is selected as the reference group with reference F-ISB values of 0.000 m, 0.127 m (1/2 cycles of L5) and 0.062 m (1/4 cycles of L7) for the frequencies of L1, L5 and L7, respectively. The phase F-ISB values refined by least-squares method are listed in tables 7 and are plotted in Fig. 6 after plus the residuals. The residual STD of the adjustment are 0.9 mm, 1.5 mm and 3.1 mm for L1, L5 and L7, respectively. The histograms of the residuals for the three frequencies are drawn in Fig. 7 and the comparison of L1 and L5, L1 and L7 are shown in Fig. 8a and 8b, respectively.
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Table 7. Phase F-ISB of each group for GPS L1-Galileo E1, GPS L5-Galileo E5a and Galileo E5b-BDS B2b after adjustment calculation (unit: m)
Frequency L1/E1 L5/E5a E5b/B2b
LEIC
SEPT
TRIM1
TRIM2
JAVA1
JAVA2
NOV
0.000 0.127 0.062
0.095 0.128 0.062
0.095 0.128 0.125
0.055 0.008 0.084
0.095 0.127 0.063
0.000 0.001 0.001
0.002 0.124 ---
Figure 6. Phase F-ISB estimates plus the residuals of the adjustment for GPS L1-Galileo E1 (a), GPS L5-Galileo E5a (b) and Galileo E5b-BDS B2b (c) for the short baselines of the 7 DOYs over the last three years.
9 / 19
Figure 7. Phase F-ISB residuals of the adjustment for the three frequencies, GPS L1-Galileo E1 (a), GPS L5Galileo E5a (b) and Galileo E5b-BDS B2b (c)
Figure 8. Comparison of the phase F-ISB for GPS L1-Galileo E1 and GPS L5-Galileo E5a (a), and GPS L1Galileo E1 and Galileo E5b-BDS B2b (b)
The L1X observations of some Javad receivers such as at stations LPGS, AREG on DOY 001 of 2019 are shifted by 1/2 cycles probably to align the observations to L1B and the shift is marked in the head of the RINEX 3 files, while L1X observations of the other Javad receivers such as WUH2, HRAG on DOY 001 of 2019 are not shifted. Those phase shifts are calibrated back in advance before being grouped, otherwise, the phase F-ISB of the combinations of receiver-type and firmware-version are not consistent. The phase shifts are not a problem for L5 and L7 because their shifts happen rarely and the observations of both GNSSs are shifted at the same time when happen. However, the station PRDS marks a phase shift of 1/4 cycles for L5 on DOY 180 of 2017, but the receivers are consistent with the main group before being shifted back. It is better to make the phase shift the same at least for the same receiver brands and mark the shift in the head of the RINEX 3 files carefully. The group JAVA1 of L1 include some receivers belonging to JAVA 2 of L5 as shown in Fig. 8, indicating the groups for JAVA1 of L1 and JAVA1 of L5 are not the same, so is the case for L7. Both Trimble and Javad receivers have subgroups composed by the stations with station-related different phase ISB. In the experiments, the phase F-ISB of those stations are identified and calibrated in advance before the adjustment. The Trimble stations with station-related phase ISB are listed in table 8, the L1 phase F-ISB of which should be added by +0.047 to equal that of the main groups. It seems this difference exist regardless of the firmware version. For example, the station TLSE on DOY 180 of 2016 is installed with the firmware of 5.01 belong to TRIM2, and the L1 phase F- ISB equals the value of TRIM2 minus +0.047 m. The station KIR8 is installed with firmware of 5.10 belong to TRIM1 and the L1 phase F-ISB equals the value of TRIM1 minus +0.047 m. This phase F-ISB difference has been noticed in the research (Tian et al., 2017) and disappears in the data files of 10 / 19
RINEX 2 from IGS website. This difference equals a quarter of L1 wavelength, and no phase shift is recorded in the file heads. Fortunately, the unrecorded shifts are not observed for the data of recent two years. Javad receivers also have some station-related F-ISB values which are different from the main group and are listed in Table 9. The differences from the main group JAVA1 or JAVA2 are only several millimeters. The fact that the code ISB and phase F-ISB can be classified into several groups with small residuals by receiver types and firmware versions indicates that the values are stable overtime. It also indicates that the remaining atmospheric delays of the baselines are small and do not affect the analysis even they may not be completely mitigated when the baselines length reaches 25 km. The zero-baselines are ideal for ISB estimation and analysis, but the number of such baselines in EPN and MGEX are too small to draw any conclusion. Table 8. TRIM stations with F-ISB difference of -0.047 from the main TRIM groups for GPS L1 and Galileo E1
Year and DOY 2016 001 2016 180 2017 001 2017 180
Stations JFNG, RGDG KIR8, TLSE, JFNG, RGDG KIR8 KIR8
Table 9. JAVA stations with F-ISB different from the main JAVA groups for L5 and L7 (unit: m)
Year and DOY 2016 001 2016 180 2017 001 2017 180
L1/E1 -0.004 UNBD UNBD UNBD
2018 001
UNBD
2018 180
UNBD
2019 001
L5/E5a
+0.007
WTZZ FFMJ, HELG WTZZ FFMJ, HELG WTZZ FFMJ, HELG WTZZ FFMJ WTZZ
+0.004
-0.007
WTZZ WTZZ WTZZ
ZIMJ ZIMJ
WTZZ
ZIMJ
WTZZ
ZIMJ
WTZZ
ZIMJ
4.3. Applications of the estimated ISB values The code ISB and phase F-ISB groups can be separated into two types, type I groups are consistent and type II groups include a few receivers with station-related constant bias values for the latest data. The groups of the two types are listed in Table 10. It’s high likely that the station-related constant bias values for type II groups are caused by the station-related data processing instead of the effects of receiver types and firmware versions and require further investigations in the future. Type I groups may be used directly in multi-GNSS integration and type II need to be checked in advance or be used as initial ISB values in ISB estimation. Table 10. group classification for code ISB and phase F-ISB of the three overlapping frequencies L1/E1, L5/E5a and E5b/B2b
Observation types Code
Frequencies
type I
type II
L1/E1
LEIC1, LEIC2, SEPT, JAVA, NOV
TRIM
L5/E5a
LEIC1, LEIC2, SEPT, JAVA, NOV
TRIM
E5b/B2b
LEIC1, LEIC2, SEPT, NOV, TRIM2
TRIM1, JAVA
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phase
L1/E1
LEIC, SEPT, TRIM1, TRIM2, NOV
JAVA1, JAVA2
L5/E5a
LEIC, SEPT, TRIM1, TRIM2, NOV
JAVA1, JAVA2
E5b/B2b
LEIC, SEPT, TRIM1, TRIM2, JAVA1, JAVA2
When the code ISB and phase F-ISB values in tables 3, 4 and 7 are used in multi-GNSS integration, the observations from different constellations can be regarded as from one constellation. The advantages by employing known phase F-ISB have been demonstrated in the previous research (Tian et al., 2019a). The benefits brought by the known code ISB from Table 3 and Table 4 are demonstrated by comparison with method of parameterizing code ISB. The GPS L1 and Galileo E1 code integration of zero-baseline MAT1_MATZ with data collected on DOY 001 2019 is taken as an example. Both the atmosphere delays and multipath effects are mitigated, and the code positioning results are only affected by the code ISB. The baseline MAT1_MATZ is equipped with receivers of LEICA GR30 4.20 belong to group LEIC2 and SEPT POLARX5TR 5.2.0 belong to group SEPT. The code ISB of L1-E1 for the group LEIC2 and group SEPT in Table 3 are 0.0 m and 6.0 m, respectively, with difference of 6.0 m and the difference should be subtracted from the inter-system double difference code observations. Assuming 4 GPS and 1 Galileo satellites are observed at each epoch, the code relative single-epoch positioning is implemented in two ways. In the first way, the code ISB is parametrized in the observation models as unknown variables. A total of 4 code double difference equations can be formed and 4 unknown parameters including 3 coordinate and 1 code ISB parameters need to be solved. The solutions of the whole day are drawn in Fig.9a. In the second way, the value 6.0 m is used to calibrate the code ISB in advance and thus only 3 coordinate parameters need to be solved. The solutions of the whole day are shown in Fig.9b. The distance root mean squares (DRMS) calculated by Eq. (6) for the two ways are 1.487 m and 0.770 m, respectively, with reduction of 48.2% by the known code ISB. N DRMS = ∑i = 1(∆ei2 + ∆ni2 + ∆ui2)/N (6) where e,n,u are the solution errors in the direction of east, north and up direction in local coordinate system, N is the number of epochs.
Figure 9. Code positioning results with 4 GPS satellites and 1 Galileo satellites in the case of parameterized code ISB (a) and known code ISB (b) for zero-baseline MAT1_MATZ with data collected on DOY 001 2019.
The code positioning benefits more from known code ISB when the number of satellites is smaller. As an example, different errors from -2.0 m to 2.0 m with 0.01 m interval are added to the known value in code ISB calibration and the corresponding DRMS of the code positioning with zero-baseline MAT1_MATZ are calculated and compared with observed satellites of three cases. The first case is with 3 GPS and 1 Galileo satellites, the second case is with one more GPS satellite and the third case is with all observed GPS and Galileo satellites. The DRMS of the first case are drawn in Fig.10a. If the code ISB is parameterized, the code positioning will fail as the equations are rank-deficient. Therefore, the code positioning benefits from the known code ISB 12 / 19
as long as the DRMS is acceptable. The DRMS of the second case are drawn in Fig.10b. The code positioning with parameterized code ISB also succeeds and the DRMS are shown in the panel with blue line. We can see that if the errors of the known ISB are too large, the DRMS may be even larger than the code positioning with parameterized ISB. When the known code ISB is within the range with length of 1.375 m i.e. the length of the blue line within the two intersection points in Fig.10b, the DRMS with known code ISB will be smaller. The DRMS of the third case are drawn in Fig.10c. The code positioning can hardly benefit from the known code ISB. The range length within the two intersection points is 0.285 m which is much shorter.
Figure 10. DRMS of the code positioning with 3 GPS and 1 Galileo satellites (a), with 4 GPS and 1 Galileo satellites (b) and with all observed GPS and Galileo satellites (c). The red line is the results with known code ISB and the blue line is that with parameterized code ISB.
5. Conclusions This study analyzes the between-receiver code ISB and phase F-ISB of the overlapping frequencies L1-E1, L5-E5a and E5b-B2b based on the EPN and MGEX baselines up to around 25 km. The baseline data are collected since DOY 001 2016 and recorded in format RINEX 3. After the code ISB and phase F-ISB of the baselines are estimated, the combinations of the receiver-type and firmware-version for Trimble, Leica, Javad, Septentrio and NovAtel receivers are clustered into several groups according to their ISB estimates. Then, the values of the code ISB and phase F-ISB of the groups are refined by least-squares method and are presented in tables. Results show that the Septentrio receivers have consistent code and phase ISB values for the three overlapping frequencies L1-E1, L5-E5a and E5b-B2b i.e. only one value for each frequency and no Septentrio receivers are different. Other receiver brands including Leica, Trimble and Javad have two or more ISB values for at least one frequency. The only NovAtel receiver has the code ISB value similar with Leica receivers before Leica GR25 and has the phase F-ISB value similar with Septentrio receivers for L1-E1 and L5-E5a. Besides, the groups of phase F-ISB may include different receiver-type and firmware-version combinations with that of the code ISB. For example, Leica has only one group for phase F-ISB while two groups for code ISB. Trimble receivers have two groups for both code ISB and phase F-ISB but including different firmware versions. Besides, Trimble and Javad receivers include a few stations with code ISB or phase F-ISB different form the main groups by constant values which requires further investigations. Some of the data files with Javad receiver implement non-zero phase shift which are marked in the head of the RINEX 3 files while others not. The non-zero phase shifts need to be shifted back in the analysis to keep consistency and should be considered in L1/E1 integration and the files for Leica, Septentrio and Trimble do not have non-zero phase shift. The phase shift values directly affect the phase F-ISB and should be more carefully disposed in MGEX and EPN multi-GNSS data processing. The ISB errors can seriously affect the performance of the positioning especially when the number of the observed satellites is small. For example, the code ISB error can degraded the positioning performance to the extent that the results are worse than the positioning without known code ISB when 5 or more satellites from different constellations are observed. The experiments of the single-epoch code positioning with the data of zerobaseline MAT1_MATZ collected on DOY 001 2019 show that the distance RMSE can be reduced by 48.2% from 1.487 m to 0.770 m with accurate code ISB when a total of 5 GPS and Galileo satellites are observed. The distance RMSE significantly increases when the code ISB error is larger. 13 / 19
Acknowledgments: The authors thank IGS MGEX and EPN for providing multi-GNSS data.
Appendix Table 1. Main groups of code ISB for GPS L1-Galileo E1
Receiver groups
Approximate ISB (m) 6
0
LEIC GR10 3.22, 4.02, 4.11, 4.20; LEIC GR25 3.11, 3.22, 4.00, 4.02, 4.11, 4.30, 4.31
LEIC1
LEIC2
28
LEIC GR30 4.11, 4.20; LEIC GR50 4.11, 4.20, 4.30, 4.31
SEPT
SEPT P4 2.5.2, 2.9.0, 2.9.3, 2.9.5, 2.9.6; SEPT P5 5.0.3, 5.10, 5.1.1, 5.1.2, 5.2.0, 5.2.2; SEPT A3 3.4.0
TRIM
TRIM R9 4.85, 5.01, 5.03, 5.10, 5.14, 5.15, 5.20, 5.22, 5.30, 5.33, 5.37; TRIM SPS855 5.32; TRIM AY 5.37
JAVA
JAVA 3 3.6.8, 3.7.2, 3.7.3, 3.7.4, JAVA 3TH 3.5.1, 3.6.1, 3.6.2, 3.6.3, 3.6.4, 3.6.6, 3.6.7, 3.6.9, 3.7.1, 3.7.2, 3.7.3, 3.7.4, 3.7.5; JAVA 3n 3.6.1, 3.6.9; JAVA G2T 3.6.1, 3.6.2
NOV
NOV OEM6
Note: LEIC = LEICA; SEPT P = SEPT POLARX; TRIM R9 = TRIMBLE NETR9; JAVA 3 = JAVAD TRE_3 DELTA; JAVA 3TH = JAVAD TRE_3TH DELTA
Table 2. Main groups of code ISB for GPS L5-Galileo E5a
Receiver groups
0
Approximate ISB (m) 6
LEIC1
LEIC2
LEIC GR30 4.10, 4.11, 4.20; LEIC GR50 4.11, 4.20, 4.30, 4.31 SEPT P4 2.9.0, 2.5.2, 2.9.3, 2.9.5, 2.9.6; SEPT P5 5.0.3, 5.10, 5.1.1, 5.1.2, 5.2.0; SEPT A3 3.4.0
SEPT
TRIM
JAVA
TRIM R9 4.85, 5.01, 5.03, 5.10, 5.14, 5.15, 5.20, 5.22, 5.30, 5.32, 5.33, 5.37; TRIM SPS855 5.32; TRIM AY 5.37 JAVA 3.7.4, 3.5.1, 3.6.4, 3.7.1,
3 3.6.8, 3.7.2, 3.7.5; JAVA 3.6.1, 3.6.2, 3.6.7, 3.6.6, 3.7.2, 3.7.3,
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3.7.3, 3TH 3.6.3, 3.6.9, 3.7.4,
30 LEIC GR10 4.00, 4.02, 4.11, 4.20; LEIC GR25 3.11, 3.22, 4.02, 4.11, 4.30, 4.31
3.7.5; JAVA 3n 3.6.1, 3.6.9; JAVA G2T 3.6.1, 3.6.2, 3.7.5
NOV
NOV OEM6
Table 3. Main groups of code ISB for Galileo E5b-BDS B2b
Receiver groups
Approximate ISB (m) 0
-4
22 LEIC GR10 3.22, 4.02 LEIC GR10 4.11, 4.20; LEIC GR25 3.11, 3.22, 4.02, 4.11, 4.30
LEIC1 LEIC GR30 4.11, 4.20; LEIC GR50 4.11, 4.20, 4.31 SEPT P4 2.9.0, 2.9.3, 2.9.5, 2.9.6; SEPT P5 5.0.3, 5.10, 5.1.1, 5.1.2
LEIC2 SEPT
TRIM R9 5.20, 5.22, 5.32, 5.33, 5.37; TRIM AY 5.37; TRIM R9 5.30
TRIM1 TRIM2
TRIM R9 4.85, 5.01, 5.03, 5.10, 5.14, 5.15 JAVA 3 3.7.2, 3.7.3, 3.7.4; JAVA 3TH 3.6.8, 3.6.6, 3.6.9, 3.7.1, 3.7.2, 3.7.3, 3.7.4, 3.7.5
JAVA
Table 4. Main groups of phase F-ISB for GPS L1-Galileo E1
Receiver groups
LEIC
Approximate F-ISB (m) 0.00
0.06
0.10
LEIC GR10 4.02, 4.11, 4.20; LEIC GR25 3.11, 3.22, 4.02, 4.11, 4.30, 4.31; GR30 4.20; LEIC GR50 4.30, 4.20, 4.31; LEICA GRX1200 9.20 SETP A3 3.4.0; SETP P4 2.9.0, 2.9.3, 2.9.5, 2.9.6; SETP P5 5.2.0, 5.0.3, 5.10, 5.1.1, 5.1.2 TRIM R9 5.10, 5.14, 5.15, 5.20, 5.22, 5.30, 5.33, 5.37; TRIM A 5.37; TRIM S855 5.32
SEPT
TRIM1
TRIM2
TRIM R9 5.01; 4.85 JAVA 3 3.6.8; JAVA 3TH 3.4.9, 3.5.1, 3.6.1, 3.6.2, 3.6.3, 3.6.4, 3.6.6, 3.6.7, 3.6.9, 3.7.2; JAVA G2 3.6.1, 3.6.2; JAVA 3N 3.6.1, 3.6.9
JAVA1
JAVA2
JAVA 3 3.6.4, 3.7.2, 3.7.3, 3.7.4, 3.7.5; JAVA 3TH 3.7.1, 3.7.3, 3.7.4, 3.7.5; JAVA G2 3.7.5
NOV
NOV OEM6 15 / 19
Table 5. Main groups of phase F-ISB for GPS L5-Galileo E5a
Approximate F-ISB (m)
Receiver groups
0.00
0.12 LEIC GR10 4.00, 4.20; LEIC GR25 3.11, 3.22, 4.00, 4.02, 4.11, 4.30, 4.31; LEIC GR30 4.20; LEIC GR50 4.20, 4.31;
LEIC
LEIC GRX1200 9.20 SEPT
SEPT P4 2.9.0, 2.9.3, 2.9.5, 2.9.6; SEPT P5 5.0.3, 5.10, 5.1.1, 5.1.2, 5.2.0; SEPT A3 3.4.0
TRIM1
TRIM R9 5.03, 5.10, 5.14, 5.15, 5.20, 5.22, 5.30, 5.33, 5.37; TRIM A 5.37; TRIM S855 5.32
TRIM2
TRIM R9 5.01, 4.85 JAVA 3 3.6.8, 3.7.2, 3.7.3, 3.7.4, 3.7.5; JAVA 3TH 3.7.2, 3.7.3, 3.7.4, 3.7.5; JAVA 3N 3.6.1, 3.6.9; JAVA G2 3.7.5
JAVA1
JAVA2
JAVA 3TH 3.4.9, 3.5.1, 3.6.1, 3.6.2, 3.6.3, 3.6.4, 3.6.6, 3.6.7, 3.6.9, 3.7.1; JAVA G2 3.6.1, 3.6.2
NOV
NOV OEM6
Table 6. Main groups of phase F-ISB for Galileo E5b-BDS B2b
Receiver groups
0.00
LEIC
LEIC LEIC 4.02, LEIC LEIC 4.31
Approximate F-ISB (m) 0.06 0.08 GR10 4.20, 4.11; GR25 3.11, 3.22, 4.11, 5.11, 4.30; GR30 4.11, 4.20; GR50 4.11, 4.20,
SEPT P4 2.9.0, 2.9.3, 2.9.5, 2.9.6; SEPT P5 5.0.3, 5.10, 5.1.1, 5.1.2, 5.2.0
SEPT
TRIM R9 5.10, 5.14, 5.15, 5.20. 5.22, 5.30, 5.33; TRIM AY 5.30, 5.37; TRIM SPS855 5.32
TRIM1
TRIM R9 4.85, 5.01
TRIM2 JAVA1 JAVA2
0.12
JAVAD 3TH 3.6.6, 3.6.9 JAVAD 3TH 3.7.2 JAVAD 3 3.7.2, 3.7.3, 3.7.4
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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
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