GNSS载波相位整数等变估计及其PPP性能提升算法

doi:10.11947/j.AGCS.2022.20210371

测绘学报 ›› 2022, Vol. 51 ›› Issue (8): 1779-1786.doi: 10.11947/j.AGCS.2022.20210371

GNSS载波相位整数等变估计及其PPP性能提升算法

周锋^1,2, 杨宇泽¹, 王磊³, 徐天河⁴

1. 山东科技大学测绘与空间信息学院, 山东青岛 266590;
2. 大地测量与地球动力学国家重点实验室, 湖北武汉 430077;
3. 武汉大学测绘遥感信息工程国家重点实验室, 湖北武汉 430079;
4. 山东大学空间科学研究院, 山东威海 264209

收稿日期:2021-07-08 修回日期:2022-07-15 发布日期:2022-09-03
通讯作者: 王磊 E-mail:lei.wang@whu.edu.cn
作者简介:周锋(1985-),男,博士,讲师,研究方向为多源传感器融合导航定位。E-mail:zhouforme@163.com
基金资助:
国家自然科学基金(41904027;41904011;42074036);中国博士后科学基金(2020M673669);大地测量与地球动力学国家重点实验室开放研究基金(SKLGED2020-3-2-E);山东省自然科学基金(ZR2019QD003)

GNSS carrier phase integer equivariant estimator and its application in improving PPP performance

ZHOU Feng^1,2, YANG Yuze¹, WANG Lei³, XU Tianhe⁴

1. College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao 266590, China;
2. State Key Laboratory of Geodesy and Earth's Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China;
3. State Key Laboratory of Information Engineering in Surveying, Mapping, and Remote Sensing, Wuhan University, Wuhan 430079, China;
4. Institute of Space Science, Shandong University, Weihai 264209, China

Received:2021-07-08 Revised:2022-07-15 Published:2022-09-03
Supported by:
The National Natural Science Foundation of China (Nos.41904027;41904011;42074036);China Postdoctoral Science Foundation (No.2020M673669);The Foundation of State Key Laboratory of Geodesy and Earth's Dynamics (No.SKLGED2020-3-2-E);The Natural Science Foundation of Shandong Province of China (No.ZR2019QD003)

摘要/Abstract

摘要： 精密单点定位技术能够提供全球高精度定位结果,其主要技术瓶颈在于定位收敛时间长,载波相位模糊度固定技术是加快PPP收敛速度、改善定位精度的主要手段之一。模糊度固定的可靠性问题在PPP定位中尤为突出,因为模糊度浮点解质量取决于服务端产品质量、接收机噪声特性和观测环境等多种因素,所以高可靠PPP模糊度固定技术仍然充满巨大挑战。为了保障PPP定位的可靠性,本文将最优整数等变估计(best integer equivariant,BIE)引入PPP模糊度估计过程中。BIE法利用GNSS模糊度整数解加权融合以获得最优的浮点模糊度估计值,可有效降低模糊度错误固定风险,同时又利用了模糊度整数解信息来提升模糊度估值精度,从而提升PPP定位精度,缩短模糊度收敛时间。本文选取了105个全球分布的MGEX测站对BIE估计PPP模糊度的性能进行验证,试验结果表明,与模糊度固定解相比,采用BIE估计PPP模糊度能够进一步改善坐标三分量(东、北、垂向)定位性能,收敛时间分别减少了37%、28%与31%,收敛后定位精度分别提高了9%、8%和3%。此外,BIE估计PPP模糊度定位结果的毛刺和阶跃现象更少。

关键词: 精密单点定位, 最优整数等变, 模糊度估计, 定位性能

Abstract: Precision point positioning (PPP) technology can provide global high-precision positioning results,but its main technical bottleneck lies in the long positioning convergence time.The carrier phase ambiguity fixing technology is one of the main means to speed up PPP convergence and improve positioning accuracy.The reliability of ambiguity fixing is particularly prominent in PPP positioning,because the quality of the ambiguity-float solutions depends on the quality of the server product,various factors such as the noise characteristics of the receiver and the observation environment,making high reliability PPP ambiguity fixing technology is still full of huge challenges.In order to ensure the reliability of PPP positioning,we introduce the best integer equivariant (BIE) estimator into the PPP ambiguity estimation process.The estimator improves the estimation accuracy of float ambiguities through multiple ambiguity-fixed solution weighting methods,thereby improving the PPP positioning accuracy and shortening the ambiguity convergence time.105 globally distributed MGEX stations are selected to verify the performance of BIE in PPP ambiguity estimation.Experimental results showed that compared with the ambiguity-fixed solutions,using BIE to estimate PPP ambiguities can further improve the positioning performance of east,north and up components of the coordinates,the convergence time of which can be shortened by 37%,28% and 31%,and the positioning accuracy of which is improved by 9%,8% and 3%,respectively.Furthermore,there are fewer glitches and steps in the positioning results derived from BIE-based PPP.

Key words: precise point positioning, best integer equivariant, ambiguity estimation, positioning performance

中图分类号:

P227

周锋, 杨宇泽, 王磊, 徐天河. GNSS载波相位整数等变估计及其PPP性能提升算法[J]. 测绘学报, 2022, 51(8): 1779-1786.

ZHOU Feng, YANG Yuze, WANG Lei, XU Tianhe. GNSS carrier phase integer equivariant estimator and its application in improving PPP performance[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(8): 1779-1786.

参考文献

[1] MALYS S, JENSEN P A. Geodetic point positioning with GPS carrier beat phase data from the CASA UNO experiment[J]. Geophysical Research Letters, 1990, 17(5):651-654. DOI:10.1029/GL017i005p00651.
[2] 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, 1997, 102(B3):5005-5017. DOI:10.1029/96JB03860.
[3] 张小红,李星星,李盼. GNSS精密单点定位技术及应用进展[J].测绘学报, 2017, 46(10):1399-1407. DOI:10.11947/j.AGCS.2017.20170327. ZHANG Xiaohong, LI Xingxing, LI Pan. Review of GNSS PPP and its application[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(10):1399-1407. DOI:10.11947/j.AGCS.2017.20170327.
[4] 张小红,胡家欢,任晓东. PPP/PPP-RTK新进展与北斗/GNSS PPP定位性能比较[J].测绘学报, 2020, 49(9):1084-1100. DOI:10.11947/j.AGCS.2020.20200328. ZHANG Xiaohong, HU Jiahua, REN Xiaodong. New progress of PPP/PPP-RTK and positioning performance comparison of BDS/GNSS PPP[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(9):1084-1100. DOI:10.11947/j.AGCS.2020.20200328.
[5] 杨元喜,许扬胤,李金龙,等.北斗三号系统进展及性能预测——试验验证数据分析[J].中国科学:地球科学, 2018, 48(5):584-594. DOI:10.1360/N072017-00434. YANG Yuanxi, XU Yangyin, LI Jinlong, et al. Progress and performance evaluation of BeiDou global navigation satellite system:data analysis based on BDS-3 demonstration system[J]. Science China Earth Sciences, 2018, 48(5):584-594. DOI:10.1360/N072017-00434.
[6] 蔡洪亮,孟轶男,耿长江,等.北斗三号全球导航卫星系统服务性能评估:定位导航授时、星基增强、精密单点定位、短报文通信与国际救援[J].测绘学报, 2021, 50(4):427-435. DOI:10.11947/j.AGCS.2021.20200549. CAI Hongliang, MENG Yinan, GENG Changjiang, et al. BDS-3 performance assessment:PNT, SBAS, PPP, SMC and SAR[J]. Acta Geodaetica et Cartographica Sinica, 2021, 50(4):427-435. DOI:10.11947/j.AGCS.2021.20200549.
[7] 张宝成,欧吉坤,袁运斌,等.利用非组合精密单点定位技术确定斜向电离层总电子含量和站星差分码偏差[J].测绘学报, 2011, 40(4):447-453. ZHANG Baocheng, OU Jikun, YUAN Yunbin, et al. Calibration of slant total electron content and satellite-receiver's differential code biases with uncombined precise point positioning technique[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(4):447-453.
[8] GE M, GENDT G, ROTHACHER M, et al. Resolution of GPS carrier-phase ambiguities in precise point positioning (PPP) with daily observations[J]. Journal of Geodesy, 2008, 82(7):389-399. DOI:10.1007/s00190-007-0187-4.
[9] LAURICHESSE D, MERCIER F, BERTHIAS J. Real time precise GPS constellation orbits and clocks estimation using zero-difference integer ambiguity fixing[C]//Proceedings of 2009 ION ITM. California, USA:IEEE, 2009.
[10] COLLINS P, BISNATH S, LAHAVE F, et al. Undifferenced GPS ambiguity resolution using the decoupled clock model and ambiguity datum fixing[J]. Navigation, 2010, 57(2):123-135. DOI:10.1002/j.2161-4296.2010.tb01772.x.
[11] TEUNISSEN P, KHODABANDEH A. Review and principles of PPP-RTK methods[J]. Journal of Geodesy,2015, 89:217-240. DOI:10.1007/s00190-014-0771-3.
[12] 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.
[13] 耿江辉,常华,郭将,等.面向城市复杂环境的3种多频多系统GNSS单点高精度定位方法及性能分析[J].测绘学报, 2020, 49(1):1-13. DOI:10.11947/j.AGCS.2020.20190106. GENG Jianghui, CHANG Hua, GUO Jiang, et al. Three multi-frequency and multi-system GNSS high-precision point positioning methods and their performance in complex urban environment[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(1):1-13. DOI:10.11947/j.AGCS.2020.20190106.
[14] VERHAGEN S. Integer ambiguity validation:an open problem?[J]. GPS Solutions, 2004, 8(1):36-43. DOI:10.1007/s10291-004-0087-5.
[15] LI Pan, ZHANG Xiaohong, REN Xiaodong, et al. Generating GPS satellite fractional cycle bias for ambiguity-fixed precise point positioning[J]. GPS Solutions, 2016, 20:771-782. DOI:10.1007/s10291-015-0483-z.
[16] TEUNISSEN P. Theory of integer equivariant estimation with application to GNSS[J]. Journal of Geodesy, 2003, 77(7-8):402-410. DOI:10.1007/s00190-003-0344-3.
[17] TEUNISSEN P. Best integer equivariant estimation for elliptically contoured distributions[J]. Journal of Geodesy, 2020, 94:82. DOI:10.1007/s00190-020-01407-2.
[18] WEN Z, HENKEL P, BRACK A, et al. Best integer equivariant estimation for precise point positioning[C]//Proceedings of the 54th International Symposium. Zadar, Croatia:[s.n.], 2012:279-282.
[19] DUONG V, HARIMA K, CHOY S, et al. GNSS best integer equivariant estimation using multivariant t-distribution:a case study for precise point positioning[J]. Journal of Geodesy, 2021(95):10. DOI:10.1007/s00190-020-01461-w.
[20] WANG Lei, VERHAGEN S. A new ambiguity acceptance test threshold determination method with controllable failure rate[J]. Journal of Geodesy, 2015, 89(4):361-375. DOI:10.1007/s00190-014-0780-2.
[21] TEUNISSEN P. On the computation of the best integer equivariant estimator[J]. Artificial Satellites, 2005, 40(3):161-171.
[22] 李博峰,沈云中,张兴福.纳伪概率可控的四舍五入法及其在RTK模糊度固定中的应用[J].测绘学报, 2012, 41(4):483-489. LI Bofeng, SHEN Yunzhong, ZHAGN Xingfu. Error probability controllable integer rounding method and its application to RTK ambiguity resolution[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(4):483-489.
[23] ODOLINSKI R, TEUNISSEN P. Best integer equivariant estimation:performance analysis using real data collected by low-cost, single-and dual-frequency, multi-GNSS receivers for short-to long-baseline RTK positioning[J]. Journal of Geodesy, 2020, 94:91. DOI:10.1007/s00190-020-01423-2.
[24] 周锋,徐天河. GPS/BDS/Galileo三频精密单点定位模型及性能分析[J].测绘学报, 2021, 50(1):61-67. DOI:10.11947/j.AGCS.2021.20200146. ZHOU Feng, XU Tianhe. Modeling and assessment of GPS/BDS/Galileo triple-frequency precise point positioning[J]. Acta Geodaetica et Cartographica Sinica, 2021, 50(1):61-67. DOI:10.11947/j.AGCS.2021.20200146.
[25] WANG Lei, FENG Yanming, GUO Jiming, et al. Impact of decorrelation on success rate bounds of ambiguity estimation[J]. Journal of Navigation, 2016, 69(5):1061-1081. DOI:10.1017/S0373463316000047.
[26] ZHOU Feng, DONG Danan, LI Weiwei, et al. GAMP:an open-source software of multi-GNSS precise point positioning using undifferenced and uncombined observations[J]. GPS Solutions, 2018, 22:33. DOI:10.1007/s10291-018-0699-9.
[27] WANG Lei, FENG Yanming, GUO Jiming. Reliability control of single-epoch RTK ambiguity resolution[J]. GPS Solutions, 2017, 21(2):591-604. DOI:10.1007/s10291-016-0550-0.
[28] ZHOU Feng, DONG Danan, GE Maorong, et al. Simultaneous estimation of GLONASS pseudorange inter-frequency biases in precise point positioning using undifferenced and uncombined observations[J]. GPS Solutions, 2018, 22:19. DOI:10.1007/s10291-017-0685-7.
[29] ZHOU Feng, CAO Xinyun, GE Yulong, et al. Assessment of the positioning performance and tropospheric delay retrieval with precise point positioning using products from different analysis centers[J]. GPS Solutions, 2020, 24:12. DOI:10.1007/s10291-019-0925-0.

GNSS载波相位整数等变估计及其PPP性能提升算法

GNSS carrier phase integer equivariant estimator and its application in improving PPP performance

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	袁运斌, 刘帅, 潭冰峰. 基于钟差解耦的GNSS精密单点定位模糊度固定模型及效果分析[J]. 测绘学报, 2022, 51(8): 1669-1679.
[2]	刘根友, 高铭, 尹翔飞, 肖恭伟, 吕栋, 王生亮, 王润. 基于GNSS精密单点定位的高精度云平台授时[J]. 测绘学报, 2022, 51(8): 1736-1743.
[3]	施闯, 辜声峰, 楼益栋, 郑福, 宋伟, 张东, 毛飞宇. 广域实时精密定位与时间服务系统[J]. 测绘学报, 2022, 51(7): 1206-1214.
[4]	金双根, 汪奇生, 史奇奇. 单频到五频多系统GNSS精密单点定位参数估计与应用[J]. 测绘学报, 2022, 51(7): 1239-1248.
[5]	杨凯淳, 吕志平, 李林阳, 邝英才, 许炜, 郑茜. 附加历元间约束的滑动窗单频实时精密单点定位算法[J]. 测绘学报, 2022, 51(5): 648-657.
[6]	蔡洪亮, 孟轶男, 耿长江, 高为广, 张天桥, 李罡, 邵搏, 辛洁, 卢红洋, 毛悦, 袁海波, 刘成, 胡小工, 楼益栋. 北斗三号全球导航卫星系统服务性能评估:定位导航授时、星基增强、精密单点定位、短报文通信与国际搜救[J]. 测绘学报, 2021, 50(4): 427-435.
[7]	房亚男, 朱俊, 李杰, 王冲, 王家松, 张少愚. 北斗混合星座分层约束下的精密定轨方法[J]. 测绘学报, 2021, 50(4): 466-474.
[8]	张兵兵, 牛继强, 王正涛, 徐丰, 田坤俊. Swarm系列卫星非差运动学厘米级精密定轨[J]. 测绘学报, 2021, 50(1): 27-36.
[9]	周锋, 徐天河. GPS/BDS/Galileo三频精密单点定位模型及性能分析[J]. 测绘学报, 2021, 50(1): 61-70.
[10]	张小红, 胡家欢, 任晓东. PPP/PPP-RTK新进展与北斗/GNSS PPP定位性能比较[J]. 测绘学报, 2020, 49(9): 1084-1100.
[11]	苏珂, 金双根. BDS/Galileo四频精密单点定位模型性能分析与比较[J]. 测绘学报, 2020, 49(9): 1189-1201.
[12]	杜祯强, 柴洪洲, 向民志, 尹潇, 刘春鹤. 3种PPP模型的统一模糊度固定方法[J]. 测绘学报, 2020, 49(7): 824-832.
[13]	周乐韬, 黄丁发, 袁林果, 冯威, 龚晓颖, 田玉淼, 张熙, 赵英豪. 基于状态和残差的北斗基准站观测数据表达与信息分级[J]. 测绘学报, 2020, 49(10): 1265-1274.
[14]	陈俊平, 王阿昊, 张益泽, 周建华, 王兵浩, 王解先. 北斗广域差分分米级定位的分区切换算法[J]. 测绘学报, 2019, 48(7): 822-830.
[15]	吕大千, 曾芳玲, 欧阳晓凤, 于合理. 时频传递的改进整数相位钟方法[J]. 测绘学报, 2019, 48(7): 889-897.