Analysis and comparisons of the BDS/Galileo quad-frequency PPP models performances

doi:10.11947/j.AGCS.2020.20200236

Abstract

Abstract: Chinese BeiDou navigation satellite system (BDS) and Galileo system can provide the services of quad-frequency observations. In this paper, we assess the BDS/Galileo quad-frequency precise point positioning (PPP) models, i.e., PPP model with two ionosphere-free combinations (QF1), PPP model with one ionosphere-free combination (QF2), undifferenced uncombined PPP model (QF3) and ionosphere-constrained undifferenced uncombined PPP model (QF4), by comparing the dual-frequency ionosphere-free PPP model (DF). The equivalence of the QF1, QF2 and QF3 models is theoretically demonstrated by the equivalence principle. The static and simulated kinematic PPP performances are evaluated and investigated with one-month period observations from the network stations and the kinematic PPP performances are verified with a kinematic experiment in the campus. The results show that the pseudorange noises of BDS-3 B1C and B2a signals are larger than the B1I and B3I signals and the pseudorange noises differences for the Galileo quad-frequency signals are not obvious. The performances of the QF1, QF2 and QF3 models are basically consistent for the static and simulated kinematic PPP. By adding the external ionospheric constraint, the quad-frequency PPP performances are affected. Compared to the QF1, QF2 and QF3 models, the mean convergence time of the static BDS (BDS-2+BDS-3) model are reduced by 4.4%, 4.4% and 5.4%, respectively. The mean convergence time of static Q4 model increases 16.8 minutes when compared to the QF3 model. Compared to the dual-frequency PPP, the quad-frequency kinematic PPP performances are obviously improved. The three-dimensional positioning accuracy of BDS and Galileo QF4 models are improved by 11.4% and 31.4%, respectively, when compared to the QF1 models. Furthermore, the BDS/Galileo kinematic PPP models perform better than the single-system solutions.

Key words: BDS, Galileo, precise point positioning, equivalence validation, quad-frequency

CLC Number:

P228

SU Ke, JIN Shuanggen. Analysis and comparisons of the BDS/Galileo quad-frequency PPP models performances[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(9): 1189-1201.

References

[1] JIN Shuanggen, SU Ke. Co-seismic displacement and waveforms of the 2018 Alaska earthquake from high-rate GPS PPP velocity estimation[J]. Journal of Geodesy, 2019, 93(9):1559-1569.
[2] ZAVOROTNY V U, GLEASON S, CARDELLACH E, et al. Tutorial on remote sensing using GNSS bistatic radar of opportunity[J]. IEEE Geoscience and Remote Sensing Magazine, 2014, 2(4):8-45.
[3] PÍRIZ R, GARCÍA Á M, TOBÍAS G, et al. GNSS interoperability:offset between reference time scales and timing biases[J]. Metrologia, 2008, 45(6):S87.
[4] LI X X, LI X, YUAN Y, et al. Multi-GNSS phase delay estimation and PPP ambiguity resolution:GPS, BDS, GLONASS, Galileo[J]. Journal of Geodesy, 2018,92(6):579-608.
[5] YANG Y, MAO Y, SUN B. Basic performance and future developments of BeiDou global navigation satellite system[J]. Satellite Navigation, 2020, 1(1):1-8.
[6] 陈秋丽, 杨慧, 陈忠贵, 等. 北斗卫星太阳光压解析模型建立及应用[J]. 测绘学报, 2019, 48(2):169-175. DOI:10.11947/j.AGCS.2019.20180097. CHEN Qiuli, YANG Hui, CHEN Zhonggui, et al. Solar radiation pressure modeling and application of BDS satellite[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(2):169-175. DOI:10.11947/j.AGCS.2019.20180097.
[7] DIESSONGO T H, SCHVLER T, JUNKER S. Precise position determination using a Galileo E5 single-frequency receiver[J]. GPS Solutions, 2014, 18(1):73-83.
[8] ZUMBERGE J F, HEFLIN M B, JEFFERSON D C, et al. Precise point positioning for the efficient and robust analysis of GPS data from large networks[J]. Journal of Geophysical Research:Solid Earth, 1997, 102(B3):5005-5017.
[9] GUO Fei, ZHANG Xiaohong, WANG Jinling, et al. Modeling and assessment of triple-frequency BDS precise point positioning[J]. Journal of Geodesy, 2016, 90(11):1223-1235.
[10] LOU Yidong, ZHENG Fu, GU Shengfeng, et al. Multi-GNSS precise point positioning with raw single-frequency and dual-frequency measurement models[J]. GPS Solutions, 2016, 20(4):849-862.
[11] ZHANG Zhiteng, LI Bofeng, NIE Liangwei, et al. Initial assessment of BeiDou-3 global navigation satellite system:signal quality, RTK and PPP[J]. GPS Solutions, 2019, 23(4):111.
[12] JIAO Guoqiang, SONG Shuli, GE Yulong, et al. Assessment of BeiDou-3 and multi-GNSS precise point positioning performance[J]. Sensors, 2019, 19(11):2496.
[13] JIN Shuanggen, SU Ke. PPP models and performances from single- to quad-frequency BDS observations[J]. Satellite Navigation, 2020, 1(1):16.
[14] ZHANG Pengfei, TU Rui, GAO Yuping, et al. Performance of Galileo precise time and frequency transfer models using quad-frequency carrier phase observations[J]. GPS Solutions, 2020, 24(2):40.
[15] LEICK A, RAPOPORT L, TATARNIKOV D. GPS satellite surveying[M]. 4th ed. Hoboken, New Jersey:John Wiley & Sons, 2015.
[16] CLOSAS P, FERNÁNDEZ-PRADES C, FERNÁNDEZ-RUBIO J A. Maximum likelihood estimation of position in GNSS[J]. IEEE Signal Processing Letters, 2007, 14(5):359-362.
[17] 李博峰, 葛海波, 沈云中. 无电离层组合、Uofc和非组合精密单点定位观测模型比较[J]. 测绘学报, 2015, 44(7):734-740. DOI:10.11947/j.AGCS.2015.20140161. LI Bofeng, GE Haibo, SHEN Yunzhong. Comparison of ionosphere-free, Uofc and uncombined PPP observation models[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(7):734-740. DOI:10.11947/j.AGCS.2015.20140161.
[18] XU Guochang, XU Yan. GPS:theory, algorithms and applications[M]. 3rd ed. Berlin:Springer, 2016.
[19] SU Ke, JIN Shuanggen, GE Yulong. Rapid displacement determination with a stand-alone multi-GNSS receiver:GPS, BeiDou, GLONASS, and Galileo[J]. GPS Solutions, 2019, 23(2):54.
[20] SU Ke, JIN Shuanggen. Triple-frequency carrier phase precise time and frequency transfer models for BDS-3[J]. GPS Solutions, 2019, 23(3):86.
[21] SU Ke, JIN Shuanggen, HOQUE M M. Evaluation of ionospheric delay effects on multi-GNSS positioning performance[J]. Remote Sensing, 2019, 11(2):171.
[22] WANG Chen, ZHAO Qile, GUO Jing, et al. The contribution of intersatellite links to BDS-3 orbit determination:Model refinement and comparisons[J]. Navigation, 2019, 66(1):71-82.
[23] LI Z, WANG N, WANG L, et al. Regional ionospheric TEC modeling based on a two-layer spherical harmonic approximation for real-time single-frequency PPP[J]. Journal of Geodesy, 2019, 93(9):1659-1671.
[24] LIU T, YUAN Y, ZHANG B, et al. Multi-GNSS precise point positioning (MGPPP) using raw observations[J]. Journal of Geodesy, 2017, 91(3):253-268.
[25] WU J T, WU S C, HAJJ G A, et al. Effects of antenna orientation on GPS carrier phase[C]//Proceedings of Astrodynamics 1991 the AAS/AIAA Astrodynamics Conference. San Diego, CA:Univelt, Inc., 1992:1647-1660.
[26] SU Ke, JIN Shuanggen. Improvement of multi-GNSS precise point positioning performances with real meteorological data[J]. The Journal of Navigation, 2018, 71(6):1363-1380.
[27] LANDSKRON D, BÖHM J. VMF3/GPT3:refined discrete and empirical troposphere mapping functions[J]. Journal of Geodesy, 2018, 92(4):349-360.
[28] FAN Haopeng, SUN Zhongmiao, ZHANG Liping, et al. A two-step estimation method of troposphere delay with consideration of mapping function errors[J]. Journal of Geodesy and Geoinformation Science, 2020, 3(1):76-84. DOI:10.11947/j.JGGS.2020.0108.
[29] HAUSCHILD A, MONTENBRUCK O, SLEEWAEGEN J M, et al. Characterization of compass M-1 signals[J]. GPS Solutions, 2012, 16(1):117-126.