An optimization method for ionospheric parameters in ambiguity resolution of BDS long-range reference station network

doi:10.11947/j.AGCS.2025.20240270

Abstract

Abstract:

The integer ambiguity resolution of the reference station network is the basis of high precision positioning of network RTK. However, with the increase of the range of the reference stations, the spatial residual of atmospheric error makes it difficult to resolution reference station, especially the ionospheric delay error with complex temporal and spatial variation, which seriously affects the resolution performance of the reference station network. The atmospheric parameters are estimated by random walk when the ambiguity resolution of the reference station. Based on the analysis of the ionospheric power spectral density (IPSD) on the ambiguity resolution performance of the reference station, this paper studies the time-varying characteristics of ionospheric observations with different differential intervals. By observing the different trends of noise and ionosphere with differential time intervals, the ionospheric observation noise is weakened to determine the IPSD, and the stochastic model of ionospheric parameters in the ambiguity estimation is optimized, so as to improve the fixed efficiency of the long-distance reference station network, instead of using empirical values or empirical models that do not consider atmospheric variation. The experimental results show that the IPSD estimated in real-time by the 1 s sampling interval data can optimize float solution accuracy of the integer ambiguity of the reference station, and can also reduce the search space of the integer ambiguity. Compared with empirical ionospheric power spectral density, the method proposed in this paper can improve the convergence time by 21% in five reference station networks with a baseline length of more than 100 km, and the success rate of ambiguity resolution is also improved accordingly.

Key words: network RTK, integer ambiguity resolution, stochastic model, ionospheric error, power spectral density

CLC Number:

P228

Jun LI, Huizhong ZHU, Zhiqiang LIU. An optimization method for ionospheric parameters in ambiguity resolution of BDS long-range reference station network[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(2): 221-232.

Figures/Tables 13

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References 31

[1]	李军, 祝会忠, 徐爱功, 等. 电离层时变特性约束的BDS长距离RTK定位算法[J]. 测绘学报, 2023, 52(3): 383-396. DOI:. doi: 10.11947/j.AGCS.2023.20220283
	LI Jun, ZHU Huizhong, XU Aigong, et al. BDS long-range RTK positioning algorithm considering the time-varying properties of ionosphere[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(3): 383-396. DOI:. doi: 10.11947/j.AGCS.2023.20220283
[2]	YUAN Yunbin, MI Xiaolong, ZHANG Baocheng. Initial assessment of single- and dual-frequency BDS-3 RTK positioning[J]. Satellite Navigation, 2020, 1: 31.
[3]	唐卫明, 刘经南, 施闯, 等. 三步法确定网络RTK基准站双差模糊度[J]. 武汉大学学报(信息科学版), 2007, 32(4): 305-308.
	TANG Weiming, LIU Jingnan, SHI Chuang, et al. Three steps method to determine double difference ambiguities resolution of network RTK reference station[J]. Geomatics and Information Science of Wuhan University, 2007, 32(4): 305-308.
[4]	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.
	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.
[5]	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.
[6]	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.
	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.
[7]	高旺, 高成发, 潘树国, 等. 北斗三频宽巷组合网络RTK单历元定位方法[J]. 测绘学报, 2015, 44(6): 641-648. DOI:. doi: 10.11947/.AGCS.2015.20140308
	GAO Wang, GAO Chengfa, PAN Shuguo, et al. Single-epoch positioning method in network RTK with BDS triple-frequency widelane combinations[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(6): 641-648. DOI:. doi: 10.11947/.AGCS.2015.20140308
[8]	ODIJK D, VAN DER MAREL H, SONG I. Precise GPS positioning by applying ionospheric corrections from an active control network[J]. GPS Solutions, 2000, 3(3): 49-57.
[9]	ZHANG Baocheng, HOU Pengyu, ZHA Jiuping, et al. PPP-RTK functional models formulated with undifferenced and uncombined GNSS observations[J]. Satellite Navigation, 2022, 3: 3.
[10]	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.
[11]	TANG Weiming, LIU Wenjian, ZOU Xuan, et al. Improved ambiguity resolution for URTK with dynamic atmosphere constraints[J]. Journal of Geodesy, 2016, 90(12): 1359-1369.
[12]	ZOU Xuan, WANG Yawei, DENG Chenlong, et al. Instantaneous BDS+GPS undifferenced NRTK positioning with dynamic atmospheric constraints[J]. GPS Solutions, 2017, 22(1): 17.
[13]	祝会忠, 雷啸挺, 徐爱功, 等. 顾及GEO卫星约束的长距离BDS三频整周模糊度解算[J]. 测绘学报, 2020, 49(9): 1222-1234. DOI:. doi: 10.11947/j.AGCS.2020.20200263
	ZHU Huizhong, LEI Xiaoting, XU Aigong, et al. The integer ambiguity resolution of BDS triple-frequency between long range stations with GEO satellite constraints[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(9): 1222-1234. DOI:. doi: 10.11947/j.AGCS.2020.20200263
[14]	李博, 程鹏飞, 秘金钟, 等. 一种北斗非差非组合长距离基准站模糊度解算方法[J]. 武汉大学学报(信息科学版), 2023, 48(4): 593-603.
	LI Bo, CHENG Pengfei, BEl Jinzhong, et al. A method for ambiguity resolution of BDS undifferenced and uncombined long-range reference stations[J]. Geomatics and Information Science of Wuhan University, 2023, 48(4): 593-603.
[15]	ZHANG Xiaohong, REN Xiaodong, CHEN Jun, et al. Investigating GNSS PPP-RTK with external ionospheric constraints[J]. Satellite Navigation, 2022, 3: 6.
[16]	SHI Chuang, GU Shengfeng, LOU Yidong, et al. An improved approach to model ionospheric delays for single-frequency precise point positioning[J]. Advances in Space Research, 2012, 49(12): 1698-1708.
[17]	ZHAO Qile, WANG Yintong, GU Shengfeng, et al. Refining ionospheric delay modeling for undifferenced and uncombined GNSS data processing[J]. Journal of Geodesy, 2019, 93(4): 545-560.
[18]	LI Jun, ZHU Huizhong, XU Aigong, et al. Estimating ionospheric power spectral density for long-range RTK positioning using uncombined observations[J]. GPS Solutions, 2023, 27(3): 109.
[19]	LI Jun, ZHU Huizhong, LU Yangyang, et al. Performance analysis of undifferenced NRTK considering time-varying characteristics of atmosphere[J]. Remote Sensing, 2023, 15(19): 4784.
[20]	ALBER C, WARE R, ROCKEN C, et al. Obtaining single path phase delays from GPS double differences[J]. Geophysical Research Letters, 2000, 27(17): 2661-2664.
[21]	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.
[22]	毛健, 崔铁军, 李晓丽, 等. 融合大气数值模式的高精度对流层天顶延迟计算方法[J]. 测绘学报, 2019, 48(7): 862-870. DOI:. doi: 10.11947/j.AGCS.2019.20190003
	MAO Jian, CUI Tiejun, LI Xiaoli, et al. A hight-accuracy method for tropospheric zenith delay error correction by fusing atmospheric numerical models[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(7): 862-870. DOI:. doi: 10.11947/j.AGCS.2019.20190003
[23]	SAASTAMOINEN J. Atmospheric correction for the troposphere and stratosphere in radio ranging satellites[M]//The use of artificial satellites for geodesy. Washington, D. C.: American Geophysical Union, 2013: 247-251.
[24]	LIU Ying, LIU Wanke, ZHANG Xiaohong, et al. An improved GNSS ambiguity best integer equivariant estimation method with Laplacian distribution for urban low-cost RTK positioning[J]. Satellite Navigation, 2024, 5: 12.
[25]	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:. 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:. doi: 10.11947/j.AGCS.2021.20200146
[26]	LI Pan, ZHANG Xiaohong. Integrating GPS and GLONASS to accelerate convergence and initialization times of precise point positioning[J]. GPS Solutions, 2014, 18(3): 461-471.
[27]	葛茂荣, 刘经南. GPS定位中对流层折射估计研究[J]. 测绘学报, 1996, 25(4): 285-291.
	GE Maorong, LIU Jingnan. The estimation methods for tropospheric delays in global positioning system[J]. Acta Geodaetica et Cartographica Sinica, 1996, 25(4): 285-291.
[28]	TEUNISSEN P J G. The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation[J]. Journal of Geodesy, 1995(a), 70(1/2): 65-82.
[29]	TEUNISSEN P J G. Influence of ambiguity precision on the success rate of GNSS integer ambiguity bootstrapping[J]. Journal of Geodesy, 2007, 81(5): 351-358.
[30]	张宝成, 柯成, 查九平, 等. 非差非组合PPP-RTK：模型算法、终端样机与实测结果[J]. 测绘学报, 2022, 51(8): 1725-1735. DOI:. doi: 10.11947/j.AGCS.2022.20210465
	ZHANG Baocheng, KE Cheng, ZHA Jiuping, et al. Undifferenced and uncombined PPP-RTK: algorithmic models, prototype terminals and field-test results[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(8): 1725-1735. DOI:. doi: 10.11947/j.AGCS.2022.20210465
[31]	VERHAGEN S, LI Bofeng, TEUNISSEN P J G. Ps-LAMBDA: ambiguity success rate evaluation software for interferometric applications[J]. Computers & Geosciences, 2013, 54: 361-376.