BDS参考站三频整周模糊度单历元确定方法

doi:10.11947/j.AGCS.2020.20200110

摘要/Abstract

摘要： 参考站载波相位整周模糊度的准确确定是实现BDS网络RTK定位的关键。本文研究了BDS参考站三频载波相位整周模糊度单历元确定方法。首先推导了参考站三频载波相位整周模糊度之间的多个整数线性关系，根据双频载波相位整周模糊度的整数线性关系，以及B1载波相位整周模糊度备选值，确定B1/B2和B1/B3载波相位整周模糊度的备选组合。然后利用不受误差影响的三频载波相位整周模糊度间整数线性关系，对整周模糊度备选值进行约束和确定。根据大气误差的空间相关性，采用以卫星高度角和方位角为依据的基准卫星选择方法，降低了对流层延迟误差残差对多频载波相位整周模糊度之间线性关系约束能力的影响。试验结果表明，本文方法能够实现参考站三频载波相位整周模糊度的单历元准确确定，且计算效率高，算法简单。

关键词: BDS参考站, 三频观测值, 载波相位整周模糊度, 整数线性关系, 单历元

Abstract: The carrier phase integer ambiguity resolution between reference stations is very important in BDS network RTK. The algorithm of determining the BDS triple-frequency carrier phase ambiguity between reference stations at single-epoch is studied in this paper. Firstly, the linear relations of triple-frequency carrier phase ambiguity between the reference stations are deduced. Then the ambiguity candidates of B1 and B2 carrier phase are selected by ambiguity candidates of B1 carrier phase ambiguity and the linear relationship of dual-frequency carrier phase ambiguities, and the same as the ambiguity candidates of B1 and B3 carrier phase. The ambiguity candidates of triple-frequency carrier phase are controlled and fixed by the linear relationship between triple-frequency carrier phase ambiguities without errors. In order to reduce the influence of tropospheric delay on the constraint ability of linear relations between multi-frequency carrier phase ambiguities, the method of selecting a reference satellite with altitude and azimuth is used by the spatial correlation of atmospheric errors. The results of test indicate that the carrier phase integer ambiguities of triple-frequency between reference stations can be fixed at single-epoch, and the algorithm is simple and efficient.

Key words: BDS reference stations, triple-frequency observations, carrier phase integer ambiguity, integer linear relationship, single epoch

中图分类号:

P288

祝会忠, 雷啸挺, 李军, 高猛, 徐爱功. BDS参考站三频整周模糊度单历元确定方法[J]. 测绘学报, 2020, 49(11): 1388-1398.

ZHU Huizhong, LEI Xiaoting, LI Jun, GAO Meng, XU Aigong. The algorithm of integer ambiguity resolution with BDS triple-frequency between reference stations at single epoch[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(11): 1388-1398.

参考文献

[1] 李金龙. 北斗/GPS多频实时精密定位理论与算法[J]. 测绘学报, 2015, 44(11):1297. DOI:10.11947/j.AGCS.2015.20150254. LI Jinlong. BDS/GPS multi-frequency real-time kinematic positioning theory and algorithms[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(11):1297. DOI:10.11947/j.AGCS.2015.20150254.
[2] 王广兴. 北斗观测值特性分析及其在PPP模糊度固定应用中的研究[D]. 武汉:武汉大学, 2016. WANG Guangxing. On the analysis of BeiDou observations' characteristics and its application in the PPP integer ambiguity resolution[D]. Wuhan:Wuhan University, 2016.
[3] TANG Weiming, DENG Chenlong, SHI Chuang, et al. Triple-frequency carrier ambiguity resolution for BeiDou navigation satellite system[J]. GPS Solutions, 2014, 18(3):335-344.
[4] ZHANG Xiaohong, HE Xiyang. Performance analysis of triple-frequency ambiguity resolution with BeiDou observations[J]. GPS Solutions, 2016, 20(2):269-281.
[5] 祝会忠. 基于非差误差改正数的长距离单历元GNSS网络RTK算法研究[J]. 测绘学报, 2015, 44(1):116. DOI:10.11947/j.AGCS.2015.20140358. ZHU Huizhong. The study of GNSS network RTK algorithm between long range at single epoch using un-difference error corrections[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(1):116. DOI:10.11947/j.AGCS.2015.20140358.
[6] GENG Jianghui, GUO Jiang, CHANG Hua, et al. Toward global instantaneous decimeter-level positioning using tightly coupled multi-constellation and multi-frequency GNSS[J]. Journal of Geodesy, 2019, 93(7):977-991.
[7] LI Bofeng, LI Zhen, ZHANG Zhiteng, et al. ERTK:extra-wide-lane RTK of triple-frequency GNSS signals[J]. Journal of Geodesy, 2017, 91(9):1031-1047.
[8] 高扬骏, 吕志伟, 周朋进, 等. 北斗中长基线三频模糊度解算的自适应抗差滤波算法[J]. 测绘学报, 2019, 48(3):295-302. DOI:10.11947/j.AGCS.2019.20180379. GAO Yangjun, LV Zhiwei, ZHOU Pengjin, et al. Adaptive robust filtering algorithm for BDS medium and long baseline three carrier ambiguity resolution[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(3):295-302. DOI:10.11947/j.AGCS.2019.20180379.
[9] 高星伟, 刘经南, 葛茂荣. 网络RTK基准站间基线单历元模糊度搜索方法[J]. 测绘学报, 2002, 31(4):305-309. DOI:10.3321/j.issn:1001-1595.2002.04.005. GAO Xingwei, LIU Jingnan, GE Maorong. An ambiguity searching method for network RTK baselines between base stations at single epoch[J]. Acta Geodaetica et Cartographica Sinica, 2002, 31(4):305-309. DOI:10.3321/j.issn:1001-1595.2002.04.005.
[10] LI Bofeng, SHEN Yunzhong, FENG Yanming, et al. GNSS ambiguity resolution with controllable failure rate for long baseline network RTK[J]. Journal of Geodesy, 2014, 88(2):99-112.
[11] 祝会忠, 刘经南, 唐卫明, 等. 长距离网络RTK基准站间整周模糊度单历元确定方法[J]. 测绘学报, 2012, 41(3):359-365. ZHU Huizhong, LIU Jingnan, TANG Weiming, et al. The algorithm of single-epoch integer ambiguity resolution between long-range network RTK base stations[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(3):359-365.
[12] 沈雪峰, 高成发, 潘树国. 基于星型结构的虚拟参考站网络实时动态测量关键算法研究[J]. 测绘学报, 2012, 41(1):33-40. SHEN Xuefeng, GAO Chengfa, PAN Shuguo. Algorithm for network RTK (VRS) based on star structure[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(1):33-40.
[13] CHU Fengyu, YANG Ming, WU Joz. A new approach to modernized GPS phase-only ambiguity resolution over long baselines[J]. Journal of Geodesy, 2016, 90(3):241-254.
[14] HU Guorong, ABBEY D A, CASTLEDEN N, et al. An approach for instantaneous ambiguity resolution for medium-to long-range multiple reference station networks[J]. GPS Solution, 2005, 9(1):1-11.
[15] 黄丁发, 李成钢, 吴耀强, 等. GPS/VRS实时网络改正数生成算法研究[J]. 测绘学报, 2007, 36(3):256-261, 339. DOI:10.3321/j.issn:1001-1595.2007.03.003. HUANG Dingfa, LI Chenggang, WU Yaoqiang, et al. Study of the real-time network correction generation approach for GPS/VRS technique[J]. Acta Geodaetica et Cartographica Sinica, 2007, 36(3):256-261, 339. DOI:10.3321/j.issn:1001-1595.2007.03.003.
[16] 周乐韬, 黄丁发, 袁林果, 等. 网络RTK参考站间模糊度动态解算的卡尔曼滤波算法研究[J]. 测绘学报, 2007, 36(1):37-42. DOI:10.3321/j.issn:1001-1595.2007.01.007. ZHOU Letao, HUANG Dingfa, YUAN Linguo, et al. A Kalman filtering algorithm for online integer ambiguity resolution in reference station network[J]. Acta Geodaetica et Cartographica Sinica, 2007, 36(1):37-42. DOI:10.3321/j.issn:1001-1595.2007.01.007.
[17] 李博峰, 沈云中, 周泽波. 中长基线三频GNSS模糊度的快速算法[J]. 测绘学报, 2009, 38(4):296-301. DOI:10.3321/j.issn:1001-1595.2009.04.003. LI Bofeng, SHEN Yunzhong, ZHOU Zebo. A new method for medium and long range three frequency GNSS rapid ambiguity resolution[J]. Acta Geodaetica et Cartographica Sinica, 2009, 38(4):296-301. DOI:10.3321/j.issn:1001-1595.2009.04.003.
[18] 姚宜斌, 胡明贤, 许超钤. 基于DREAMNET的GPS/BDS/GLONASS多系统网络RTK定位性能分析[J]. 测绘学报, 2016, 45(9):1009-1018. DOI:10.11947/j.AGCS.2016.20160133. YAO Yibin, HU Mingxian, XU Chaoqian. Positioning accuracy analysis of GPS/BDS/GLONASS network RTK based on DREAMNET[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(9):1009-1018. DOI:10.11947/j.AGCS.2016.20160133.
[19] LOU Yidong, GONG Xiaopeng, GU Shengfeng, et al. Assessment of code bias variations of BDS triple-frequency signals and their impacts on ambiguity resolution for long baselines[J]. GPS Solutions, 2017, 21(1):177-186.
[20] ZHANG Ming, LIU Hui, BAI Zhengdong, et al. Fast ambiguity resolution for long-range reference station networks with ionospheric model constraint method[J]. GPS Solutions, 2017, 21(2):617-626.
[21] 祝会忠, 徐爱功, 高猛, 等. BDS网络RTK中距离参考站整周模糊度单历元解算方法[J]. 测绘学报, 2016, 45(1):50-57. DOI:10.11947/j.AGCS.2016.20140525. ZHU Huizhong, XU Aigong, GAO Meng, et al. The algorithm of single-epoch integer ambiguity resolution between middle-range BDS network RTK reference stations[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(1):50-57. DOI:10.11947/j.AGCS.2016.20140525.
[22] 赵庆志, 姚宜斌, 姚顽强, 等. 利用ECMWF改善射线利用率的三维水汽层析算法[J]. 测绘学报, 2018, 47(9):1179-1187. DOI:10.11947/j.AGCS.2018.20170412. ZHAO Qingzhi, YAO Yibin, YAO Wanqiang, et al. A method to improve the utilization rate of satellite rays for three-dimensional water vapor tomography using the ECMWF data[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(9):1179-1187. DOI:10.11947/j.AGCS.2018.20170412.
[23] YAO Yibin, ZHAO Qingzhi, ZHANG Bin. A method to improve the utilization of GNSS observation for water vapor tomography[J]. Annales Geophysicae, 2016, 34(1):143-152.