附加历元间约束的滑动窗单频实时精密单点定位算法

doi:10.11947/j.AGCS.2022.20210207

测绘学报 ›› 2022, Vol. 51 ›› Issue (5): 648-657.doi: 10.11947/j.AGCS.2022.20210207

附加历元间约束的滑动窗单频实时精密单点定位算法

杨凯淳¹, 吕志平^1,2, 李林阳^1,3, 邝英才¹, 许炜¹, 郑茜⁴

1. 信息工程大学地理空间信息学院, 河南郑州 450001;
2. 哈尔滨工业大学(深圳)空间科学与应用技术研究院, 广东深圳 518055;
3. 中国科学院精密测量科学与技术创新研究院大地测量与地球动力学国家重点实验室, 湖北武汉 430077;
4. 西安科技大学测绘科学与技术学院, 陕西西安 710054

收稿日期:2021-04-22 修回日期:2022-01-17 出版日期:2022-05-20 发布日期:2022-05-28
通讯作者: 李林阳 E-mail:lilinyang810810@163.com
作者简介:杨凯淳(1997-),男,硕士生,研究方向为GNSS数据处理。E-mail:413729378@qq.com
基金资助:
国家自然科学基金（42104033）；深圳市科技计划（KQTD20180410161218820）；广东省基础与应用基础研究基金（2021A1515012600）；河南省重点研发与推广专项（科技攻关）（212102310428）

Sliding window single-frequency real time precise point positioning algorithm with epoch constraints

YANG Kaichun¹, LV Zhiping^1,2, LI Linyang^1,3, KUANG Yingcai¹, XU Wei¹, ZHENG Xi⁴

1. Institute of Surveying and Mapping, Information Engineering University, Zhengzhou 450001, China;
2. Institute of Space Science and Applied Technology, Harbin Institute of Technology, Shenzhen 518055, China;
3. State Key Laboratory of Geodesy and Earth's Dynamics, Innovation Academy for Precision Measurement Science and Technology, Wuhan 430077, China;
4. Xi'an University of Science and Technology, College of Geomatics, Xi'an 710054, China

Received:2021-04-22 Revised:2022-01-17 Online:2022-05-20 Published:2022-05-28
Supported by:
The National Natural Science Foundation of China (No. 42104033);Shenzhen Science and Technology Program (No. KQTD20180410161218820);Guangdong Basic and Applied Basic Research Foundation (No. 2021A1515012600);The Key Specialized Research and Development Breakthrough in Henan Province (No. 212102310428)

摘要/Abstract

摘要： 针对同时估计电离层延迟导致的单频精密单点定位解算秩亏问题，提出了一种附加历元间约束的多历元递推算法。该算法根据无周跳时前后历元模糊度不变的特性，在每一组多历元联合数据解算时，每颗卫星只设置一个模糊度参数，不需要外部先验信息约束即可解决秩亏问题。另外，本文算法同时考虑了参数及观测值之间的时间相关性，采用附加约束的平方根信息滤波对部分参数进行历元间约束，克服多历元算法的病态性，提高了算法的可靠性。试验采用全球分布的15个IGS跟踪站14 d的数据，静态定位精度优于3 cm，仿动态解约为1.5 dm。与同时估计电离层延迟的单频PPP方法相比，收敛速度提高了24%，与双频无电离层组合PPP的收敛速度基本一致，定位精度提高了30%，高程分量定位精度提高更为明显。

关键词: 多历元递推算法, 单频精密单点定位, 约束条件, 病态性, 电离层延迟

Abstract: To solve the rank deficiency problem of single-frequency precise point positioning (PPP) caused by calculating ionospheric delay simultaneously, an algorithm using multi-epoch observations is proposed in this paper. Based on the characteristic that the ambiguity is invariable without cycle slip, only one ambiguity parameter is set in the multi-epoch joint data, so as to solve the rank deficiency without the constraint of external prior information. In addition, the time correlation between parameters and observations are considered, and the square root information filtering (SRIF) with additional constraints to some parameters between epochs is utilized to overcome the ill-conditioned nature and obtain more reliable results. 14 days observation data from 15 IGS stations are used in the experiment,the static positioning accuracy is better than 3 cm, and the simulated dynamic solution is 1.5 dm. Compared with the single-frequency PPP method which estimates the ionospheric delay, the convergence speed is increased by 24%, and approximately reaches the level of the dual-frequency ionospheric-free PPP algorithm. The positioning accuracy is improved by 30%, and especially a significant increase in the vertical component.

Key words: multi-epoch recursion algorithm, single-frequency precise point positioning, constraints, ill condition, ionospheric delay

中图分类号:

P228

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.

YANG Kaichun, LV Zhiping, LI Linyang, KUANG Yingcai, XU Wei, ZHENG Xi. Sliding window single-frequency real time precise point positioning algorithm with epoch constraints[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(5): 648-657.

参考文献 27

[1]	许承权. 单频GPS精密单点定位算法研究与程序实现[D]. 武汉:武汉大学, 2008. XU Chengquan. Research and program implementation of single-frequency GPS precise point positioning algorithm[D]. Wuhan:Wuhan University, 2008.
[2]	匡翠林, 张晋升, 卢辰龙, 等. GPS单双频混合方法在地表形变监测中的应用[J].武汉大学学报(信息科学版), 2016, 41(5):692-697. KUANG Cuilin, ZHANG Jinsheng, LU Chenlong, et al. Single- and dual-frequency mixed mode GPS network for ground deformation monitoring[J]. Geomatics and Information Science of Wuhan University, 2016, 41(5):692-697.
[3]	高永飞. 单频GPS低轨卫星精密轨道确定[D]. 长沙:国防科学技术大学, 2014. GAO Yongfei. Precise orbit determination for LEO based on single frequency measurement[D]. Changsha:National University of Defense Technology, 2014.
[4]	SU Ke, JIN Shuanggen, JIANG Jintao, et al. Ionospheric VTEC and satellite DCB estimated from single-frequency BDS observations with multi-layer mapping function[J/OL]. GPS Solutions, 2021, 25:68. https://doi.org/10.1007/s10291-021-01102-5.
[5]	HE Haibo, LI Jinlong, YANG Yuanxi, et al. Performance assessment of single- and dual-frequency BeiDou/GPS single-epoch kinematic positioning[J]. GPS Solutions, 2014, 18(3):393-403.
[6]	ZHAO Chuanbao, ZHANG Baochen, ZHANG Xiao. Supreme:an open-source single-frequency uncombined precise point positioning software[J/OL]. GPS Solutions, 2021, 25:86. https://doi.org/10.1007/s10291-021-01131-0.
[7]	陈正生, 张清华, 李林阳, 等. 电离层延迟变化自模型化的载波相位平滑伪距算法[J]. 测绘学报, 2019, 48(9):1107-1118. DOI:10.11947/j.AGCS.2019.20180404. CHEN Zhengsheng, ZHANG Qinghua, LI Linyang, et al. An improved carrier phase smoothing pseudorange algorithm with self-modeling of ionospheric delay variation[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(9):1107-1118. DOI:10.11947/j.AGCS.2019.20180404.
[8]	GAO Yangjun, LV Zhiwei, ZHOU Pengjin, et al. Adaptive robust filtering algorithm for BDS medium and long baseline three carrier ambiguity resolution[J]. Journal of Geodesy and Geoinformation Science, 2020, 3(2):53-61.
[9]	LE Anhquan, TIBERIUS Christian. Single-frequency precise point positioning with optimal filtering[J]. GPS Solutions. 2007, 11(11):61-69.
[10]	ZHANG Xiaohong, REN Xiaodong, WU Fengbo, et al. Short-term prediction of ionospheric TEC based on ARIMA model[J]. Journal of Geodesy and Geoinformation Science, 2019, 2(1):9-16.
[11]	畅鑫, 左翔, 张伟.动态PPP模糊度固定方法及试验分析[J].武汉大学学报(信息科学版), 2014, 39(3):275-278. CHANG Xin, ZUO Xiang, ZHANG Wei. The experiment and analysis of zero-difference ambiguity resolution for kinematic PPP[J]. Geomatics and Information Science of Wuhan University, 2014, 39(3):275-278.
[12]	阮仁桂. 高精度GNSS网数据处理关键技术研究[D]. 郑州:信息工程大学, 2018. RUAN Rengui. Research on key technologies of precise data processing for GNSS networks[D]. Zhengzhou:Information Engineering University, 2018.
[13]	涂锐, 张勤, 黄观文. 单频精密单点定位电离层延迟处理方法研究[J]. 大地测量与地球动力学, 2010, 30(2):99-103. TU Rui, ZHANG Qin, HUANG Guanwen. On ionospheric delay processing methods for single frequency precise point positioning[J]. Journal of Geodesy and Geodynamics, 2010, 30(2):99-103.
[14]	王利, 张勤, 涂锐, 等. 基于原始观测值的单频精密单点定位算法[J]. 测绘学报, 2015, 44(1):19-25. DOI:10.11947/j.AGCS.2015.20130315. WANG Li, ZHANG Qin, TU Rui, et al. A kind of single-frequency precise point positioning algorithm based on the raw observations[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(1):19-25. DOI:10.11947/j.AGCS.2015.20130315.
[15]	阮仁桂, 吴显兵, 冯来平, 等. 同时估计电离层延迟的单频精密单点定位方法[J]. 测绘学报, 2012, 41(4):490-495. RUAN Rengui, WU Xianbing, FENG Laiping, et al. Single-frequency precise point positioning with simultaneous ionospheric delay estimation[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(4):490-495.
[16]	ZHANG Baocheng, TEUNISSEN P. J. G., YUAN Yunbin, et al. Joint estimation of vertical total electron content (VTEC) and satellite differential code biases (SDCBs) using low-cost receivers[J]. Journal of Geodesy, 2018, 92(4):401-413.
[17]	涂锐, 黄观文, 张勤, 等. 基于利用单基准站改正信息和电离层参数估计的单频PPP算法[J]. 武汉大学学报(信息科学版), 2012, 37(2):170-173. TU Rui, HUANG Guanwen, ZHANG Qin, et al. PPP algorithm of single frequency based on corrections of single-base station and ionospheric parameters estimation[J]. Geomatics and Information Science of Wuhan University, 2012, 37(2):170-173.
[18]	姜卫平, 邹璇, 唐卫明. 基于CORS网络的单频GPS实时精密单点定位新方法[J]. 地球物理学报, 2012, 55(5):1549-1556. JIANG Weiping, ZOU Xuan, TANG Weiming. A new kind of real-time PPP method for GPS single-frequency receiver using VORS network[J]. Chinese Journal of Geophysics, 2012, 55(5):1549-1556.
[19]	张宝成, 欧吉坤, 袁运斌, 等. 基于GPS双频原始观测值的精密单点定位算法及应用[J]. 测绘学报, 2010, 39(5):478-483. ZHANG Baocheng, OU Jikun, YUAN Yunbin, et al. Precise point positioning algorithm based on original dual-frequency GPS code and carrier-phase observations and its application[J]. Acta Geodaetica et Cartographica Sinica, 2010, 39(5):478-483.
[20]	伍冠滨, 陈俊平, 伍晓勐, 等. 基于非差非组合PPP-RTK的大气改正模型及其性能验证[J]. 测绘学报, 2020, 49(11):1407-1418. DOI:10.11947/j.AGCS.2020.20200103. WU Guanbin, CHEN Junping, WU Xiaomeng, et al. Modeling and assessment of regional atmospheric corrections based on undifferenced and uncombined PPP-RTK[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(11):1407-1418. DOI:10.11947/j.AGCS.2020.20200103.
[21]	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. 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):61-70. DOI:10.11947/j.AGCS.2021.20200146.
[22]	张辉, 郝金明, 谢建涛, 等. 多系统非差非组合精密单点定位电离层延迟约束权阵的确定[J]. 测绘学报, 2018, 47(3):308-315. DOI:10.11947/j.AGCS.2018.20170151. ZHANG Hui, HAO Jinming, XIE Jiantao, et al. The weight matrix determination of ionospheric delay constraint for multi-GNSS precise point positioning using raw observations[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(3):308-315. DOI:10.11947/j.AGCS.2018.20170151.
[23]	李博峰, 章浙涛. 时间相关观测的几种动态数据处理方法[J].测绘学报, 2018, 47(12):1563-1570. DOI:10.11947/j.AGCS.2018.20180192. LI Bofeng, ZHANG Zhetao. Several kinematic data processing methods for time-correlated observations[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(12):1563-1570. DOI:10.11947/j.AGCS.2018.20180192.
[24]	JONGE P J. A processing strategy for the application of the GPS in networks[D]. Delft:Delft University of Technology, 1998:238.
[25]	ZANG Nan, LI Bofeng, NIE Liangwei, et al. Inter-system and inter-frequency code biases:simultaneous estimation, daily stability and applications in multi-GNSS single-frequency precise point positioning[J]. GPS Solutions, 2020, 24(18).
[26]	杨凯淳, 吕志平, 李林阳, 等.多普勒积分辅助的动态单频周跳探测[J/OL]. 武汉大学学报(信息科学版):1-18. https://doi.org/10.13203/j.whugis20200424. YANG Kaichun, LV Zhiping, LI Linyang, et al. Doppler integration aided kinematic single-frequency cycle-slip detection[J/OL]. Geomatics and Information Science of Wuhan University:1-18. https://doi.org/10.13203/j.whugis20200424.
[27]	张小红, 左翔, 李盼, 等. BDS/GPS精密单点定位收敛时间与定位精度的比较[J]. 测绘学报, 2015, 44(3):250-256. DOI:10.11947/j.AGCS.2015.20130771. ZHANG Xiaohong, ZUO Xiang, LI Pan, et al. Convergence time and positioning accuracy comparison between BDS and GPS precise point positioning[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(3):250-256. DOI:10.11947/j.AGCS.2015.20130771.

附加历元间约束的滑动窗单频实时精密单点定位算法

Sliding window single-frequency real time precise point positioning algorithm with epoch constraints

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