Analysis of the code and phase between-receiver inter-system biases of the overlapping frequencies for GPS/Galileo/BDS

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 integer-estimable 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 25km in the European Permanent GNSS Network (EPN) and the Multi-GNSS Experiment (MGEX) for the overlapping frequencies L1-E1 (L1), L5-E5a (L5) and E5b-B2b (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.     

BDS-3 PPP模糊度固定实现及精度评估

精密单点定位(PPP)模糊度固定(AR)能够显著提升精密定位的收敛速度和精度。通过在BDS-2和BDS-3之间添加系统间偏差的方法实现BDS-3的模糊度固定,并基于全球MGEX测站静态、仿动态数据和车载实验数据全面评估了BDS-3模糊度固定的效果。结果表明,相对于浮点解,BDS-3 PPP模糊度固定能够显著提升PPP的精度,在东北天3个方向上静态解算精度提升依次为37.4%、26.2%和20.1%;仿动态解算精度提升依次为38.3%、27.2%和11.1%;车载动态实验BDS-3模糊度固定精度在三维方向上综合提升为40.4%。此外,模糊度固定后,以浮点解稳定后的两倍定位精度为基准,在东北天方向上,静态定位时间提升程度依次为63.5%、64.0%和40.3%;仿动态定位时间提升程度依次为58.7%、56.8%和25.4%;车载实验在三维方向的收敛时间为30.0 min。以上结果证明了所提方法的有效性及BDS-3模糊度固定的性能提升。     

BDS-2/BDS-3 uncalibrated phase delay estimation considering the intra-system bias

Intra-system biases (ISBs) between BDS-2 and BDS-3 are of critical importance when combining observations from the BDS-2 and BDS-3 systems, which is meaningful to fully take advantage of the BDS positioning capability. Meanwhile, ISBs should also be considered in the estimation of BDS uncalibrated phase delays (UPDs). In this research, we present a BDS-2/BDS-3 joint-processing scheme, as well as a method for estimating BDS UPDs. The characteristics of ISBs and the quality of BDS UPDs are analyzed based on 30-day data from 130 multi-GNSS experimental (MGEX) stations. Our results indicate that the ISBs are related to the type and version of the receiver. The ISBs can be regarded as constant across the course of a given day, and the mean standard deviation (STD) values of ISBs over one month for different types of receivers are generally within 0.2 m. Moreover, to assess the quality of UPD products, the residuals of the estimated UPDs and the utilization rates of the observation data are computed. The results show that the quality of BDS UPDs can be improved by correcting the satellite-induced pseudo-range variations, and by estimating the wide-lane (WL) UPD difference between BDS-2 and BDS-3. The average RMS values of the estimated residuals of WL UPD and narrow-lane (NL) UPD are 0.07 and 0.09 cycles, respectively; moreover, the utilization rate of the observation data of WL UPD and NL UPD can reach above 90 %. The performance of BDS precise point positioning (PPP) and PPP ambiguity resolution (PPP-AR) is analyzed in terms of positioning accuracy and convergence performance in both the static and kinematic modes. Compared with PPP ambiguity-float solutions, the positioning accuracy of PPP-AR is significantly improved, especially in the east direction. The impact of ISBs on PPP and PPP-AR is also analyzed, and the results indicate that ISBs can improve the convergence speed of float PPP, but can be disregarded in PPP-AR.