Multidimensional Gross Error Separability Analysis in CPⅢ Network Considering Observation Space Information
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摘要:
高铁轨道控制网（CPⅢ网）是一个自由测站、自动观测的边角同测后方交会测量网，其观测值间的粗差可区分性除了与控制网设计空间有关外，还会受到全站仪自动观测等观测空间因素的影响. 为此，在由粗差判断方程得到CPⅢ网多维观测值粗差可区分能力的设计空间相关关系基础上，考虑CPⅢ网数据采集中全站仪自动观测特点，引入观测值时序相关性，将观测值间的可靠性关系由传统只考虑设计空间影响扩展到综合评价设计空间和观测空间影响，挖掘得到符合CPⅢ网测量实际的多维粗差可区分能力的规律；然后，采用蒙特卡罗方法验证顾及观测空间信息的CPⅢ网多维粗差可区分能力的正确性. 研究结果表明：CPⅢ网观测值可靠性会受到观测空间的影响，在粗差探测实践中应予以考虑；CPⅢ网中每个测量边观测值均有粗差发现与定位能力；观测同一个目标点的3个测量边中最多可发现并定位1个测量边中的2个粗差；当测站点无错误时，1个测站观测
n 个目标点的n 个测量边中，最多可以发现并定位⌊n /2⌋个测量边中的2⌊n /2⌋个粗差.Abstract:The CPⅢ network of high-speed railways is a resection surveying network with free station observation and automatic observation, enabling simultaneous edge and angle measurements. The separability of gross errors between observations is not only related to the design space of the control network but also affected by observation space factors such as automatic observation of the total station. Therefore, the gross error judgment equation (GEJE) was used to obtain the design space correlation of the separability of multidimensional gross errors of observations in the CPⅢ network. By considering the characteristics of automatic observation of total station during data acquisition in the CPⅢ network, the temporal correlation of observations was introduced. The reliability relationship between observations was extended from the traditional consideration of design space effects to the comprehensive evaluation of both design space and observation space effects. The law of multidimensional gross error separability in accordance with the actual measurement of the CPⅢ network was obtained. Then, the Monte Carlo method was used to demonstrate the correctness of the separability of multidimensional gross errors in the CPⅢ network considering the observation space information. The results show that the reliability of CPⅢ observations will be affected by the observation space, which should be considered in the practice of gross error detection. The observations of each edge in the CPⅢ network have gross error detectability and identifiability. At most two gross errors in one edge can be detected and located in the three edges of the same target. If there is no error in the observation station, at most 2⌊
n /2⌋ gross errors in ⌊n /2⌋ edges can be detected and located amongn edges of one observation station observingn targets. -
图 4 单测站污染率与成功率关系
Figure 4. Relationship between contamination rate and success rate in one observation station
图 5 单测站污染率与平均正确率关系
Figure 5. Relationship between contamination rate and average accuracy in one observation station
表 1 CPⅢ网粗差检验结果
Table 1. Gross error test results of CPⅢ network
参数 观测值总数/个 粗差观测值数/个 粗差测量边数/个 粗差测站数/个 污染率/% 相关粗差比例/% 取值 70918 2724 557 5 3.8 40.9 
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表 2 方案1实验结果
Table 2. Experimental results of scheme 1
粗差大小 实验数/次 发现粗差/次 正确定位/次 成功率/% 2σ～4σ 803 462 462 57.5 4σ～6σ 452 327 327 72.3 6σ～8σ 480 385 385 80.2 8σ～10σ 486 410 410 84.4 10σ～12σ 364 325 325 89.3 12σ～14σ 630 605 605 96.0 14σ～16σ 606 600 600 99.0 16σ～18σ 499 492 492 98.6 18σ～20σ 680 677 677 99.6
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表 3 方案2实验结果
Table 3. Experimental results of scheme 2
粗差测量
边/个实验
数/次发现粗
差/次正确
定位/次错误
定位/次成功
率/%1 494 491 491 0 99.4 2 506 499 162 344 32.0
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[1] CEN M, LI Z, DING X, et al. Gross error diagnostics before least squares adjustment of observations[J]. Journal of Geodesy, 2003, 77(9): 503-513. doi: 10.1007/s00190-003-0343-4 [2] HEKIMOGLU S, ERENOGLU R C, SANLI D U, et al. Detecting configuration weaknesses in geodetic networks[J]. Survey Review, 2011, 43(323): 713-730. doi: 10.1179/003962611X13117748892632 [3] 李广云,范百兴. 精密工程测量技术及其发展[J]. 测绘学报,2017,46(10): 1742-1751.LI Guangyun, FAN Baixing. The development of precise engineering surveying technology[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(10): 1742-1751. [4] 闫广峰,高山,章健华. CPⅢ区段搭接严密平差法研究[J]. 铁道学报,2014,36(7): 101-105.YAN Guangfeng, GAO Shan, ZHANG Jianhua. Research on rigorous adjustment lapping between adjacent of CPⅢ plane network[J]. Journal of the China Railway Society, 2014, 36(7): 101-105. [5] LI B F. Surveying network design and adjustment for ballastless track HSR: case study with the first HSR in China[J]. Journal of Surveying Engineering, 2016, 142(3): 04015015.1-04015015.11. [6] YAN G F, CEN M Y, LI Y. Gross error detectability and identifiability analysis in track control network for high-speed railway based on GEJE[J]. Journal of Surveying Engineering, 2020, 146(1): 04019020.1-04019020.9. [7] 闫广峰. 高速铁路轨道控制网测量数据质量控制研究[D]. 成都: 西南交通大学,2020. [8] 岑敏仪,顾利亚,李志林,等. 基于判断矩阵的观测量粗差发现和定位相关性分析[J]. 测绘学报,2005,34(1): 24-29.CEN Minyi, GU Liya, LI Zhilin, et al. Judgement matrix based correlation analysis of detectable and locatable gross errors in observations[J]. Acta Geodaetica et Cartographic Sinica, 2005, 34(1): 24-29. [9] 李德仁. 高斯-马尔可夫模型含两个备选假设时的区分可能性和可靠性理论[J]. 测绘学报,1985,14(2): 92-110.LI Deren. Trennbarkeit und zuverlassigkeit bei zwei verschiedenen alternativhypothesen im Gaus-Markoff-modell[J]. Acta Geodaetica et Cartographic Sinica, 1985, 14(2): 92-110. [10] YANG L, WANG J L, KNIGHT N L, et al. Outlier separability analysis with a multiple alternative hypotheses test[J]. Journal of Geodesy, 2013, 87(6): 591-604. doi: 10.1007/s00190-013-0629-0 [11] 卓健成. 工程控制测量建网理论[M]. 成都: 西南交通大学出版社,1996. [12] KHODABANDEH A, AMIRI-SIMKOOEI A R. Recursive algorithm for L1 norm estimation in linear models[J]. Journal of Surveying Engineering, 2011, 137(1): 1-8. doi: 10.1061/(ASCE)SU.1943-5428.0000031 [13] 郑肇葆. 数学规划在测绘学中应用[M]. 2版. 北京: 测绘出版社,2003. [14] 於宗俦,李明峰. 多维粗差的同时定位与定值[J]. 武汉测绘科技大学学报,1996,21(4): 323-329.YU Zongchou, LI Mingfeng. Simultaneous location and fixed value of multidimensional gross errors[J]. Geomatics and Information Science of Wuhan University, 1996, 21(4): 323-329. [15] 欧吉坤. 粗差的拟准检定法(QUAD法)[J]. 测绘学报,1999,28(1): 15-20.OU Jikun. Quasi-quasi-verification method of gross error (QUAD method)[J]. Acta Geodaetica et Cartographica Sinica, 1999, 28(1): 15-20. [16] GUI Q, GONG Y, LI G, et al. A Bayesian approach to the detection of gross errors based on posterior probability[J]. Journal of Geodesy, 2007, 81(10): 651-659. doi: 10.1007/s00190-006-0132-y [17] YANG Y, SONG L, XU T. Robust estimator for correlated observations based on bifactor equivalent weights[J]. Journal of Geodesy, 2002, 76(6): 353-358. [18] AMIRI-SIMKOOEI A. Formulation of L1 norm minimization in Gauss-Markov models[J]. Journal of Surveying Engineering, 2003, 129(1): 37-43. doi: 10.1061/(ASCE)0733-9453(2003)129:1(37) [19] 岑敏仪,卓健成,李志林,等. 判断观测值粗差能否发现和定位的一种验前方法[J]. 测绘学报,2003,32(2): 134-138.CEN Minyi, ZHUO Jiancheng, LI Zhilin, et al. A method of judging whether gross errors detectable and locatable in observations before least squares adjustment[J]. Acta Geodaetica et Cartographic Sinica, 2003, 32(2): 134-138. [20] 顾利亚,岑敏仪,李志林. 粗差发现和定位能力与相关系数的关系[J]. 武汉大学学报(信息科学版),2005,30(7): 621-624.GU Liya, CEN Minyi, LI Zhilin. Relationship between the ability of gross error detectable and identifiable and the correlation coefficient[J]. Geomatics and Information Science of Wuhan University, 2005, 30(7): 621-624. -
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