L1范数探测粗差失效的观测量识别方法

doi:10.11947/j.AGCS.2019.20180395

测绘学报 ›› 2019, Vol. 48 ›› Issue (11): 1430-1438.doi: 10.11947/j.AGCS.2019.20180395

L₁范数探测粗差失效的观测量识别方法

闫广峰^1,2,3, 岑敏仪^1,2,3

1. 西南交通大学地球科学与环境工程学院, 四川成都 611756;
2. 高速铁路运营安全空间信息技术国家地方联合工程实验室, 四川成都 610031;
3. 高速铁路线路工程教育部重点实验室, 四川成都 610031

收稿日期:2018-08-22 修回日期:2019-06-12 出版日期:2019-11-20 发布日期:2019-11-19
通讯作者: 岑敏仪 E-mail:swcmy@home.swjtu.edu.cn
作者简介:闫广峰(1989-),男,博士生,研究方向为现代测量数据处理及应用。E-mail:gf_y1989@163.com

The identification method of gross error detection failpoint in L₁-norm estimation

YAN Guangfeng^1,2,3, CEN Minyi^1,2,3

1. Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China;
2. State-province Joint Engineering Laboratory of Spatial Information Technology of High-Speed Railway Safety, Chengdu 610031, China;
3. Key Laboratory of High-speed Railway Engineering, Ministry of Education, Chengdu 610031, China

Received:2018-08-22 Revised:2019-06-12 Online:2019-11-20 Published:2019-11-19

摘要/Abstract

摘要： 粗差发生时，L₁范数估计求得的条件方程闭合差较最小二乘估计（LS）的残差更能集中反映粗差，从而有助于粗差的发现与定位。然而，存在一类观测值，虽然其具有粗差发现和定位能力，但在采用L₁范数估计解决粗差探测问题时，无论含有多大量级粗差都不能准确定位，为叙述方便，称其为L₁抗差性失效点（robustness failpoint in L₁-norm estimation，RFP-L₁）。显然，只有判定测量系统不存在RFP-L₁，或存在时能够准确判断其是否含有粗差，才能保证基于L₁的粗差探测结果的准确、可靠，此过程中，RFP-L₁的识别是问题解决的基础。本文由条件方程，推导出观测值粗差对条件方程闭合差绝对值和的影响系数计算式，得到了最小影响系数大小与观测值是否为RFP-L₁的判别关系，并探讨了存在RFP-L₁的测量系统设计矩阵数值特点，提出了判断RFP-L₁观测值的方法。仿真试验表明，最小影响系数反映了观测值粗差对L₁范数估计目标函数的影响大小，非RFP-L₁和RFP-L₁的最小影响系数具有分别等于1和小于1的规律性，同时得出，若观测方程中系数矩阵只有±1和0，对应的观测量均不属于RFP-L₁。

关键词: L₁范数估计, 粗差探测, 条件方程, 影响系数

Abstract: The gross errors reflected in the corresponding closure errors of conditional equations obtained by L₁-norm estimation are more significant than those in LS residuals, and thereby, the former estimation is helpful for the gross error detection and location. Unfortunately, there is a kind of observations which have the ability to detect and locate gross errors, no matter how large the gross error is, but it cannot be accurately located in L₁-norm estimation. For convenience of discussion, such observation is called as Robustness Failpoint in L₁-norm estimation, RFP-L₁ for short. Obviously, only to meet such a premise, the results of gross error detection based on L₁-norm estimation can be accurate and reliable, i.e., it is ensured that there is no RFP-L₁ in the surveying system, or whether the RFP-L₁ contains gross error can be judged accurately. And in this process, the accurate identification of RFP-L₁ is the basis for solving the problem. From conditional equation, the calculation formula of influence coefficient which reflect the extent of the influence of gross error on corresponding closure errors of conditional equations is derived, and the distinguish relation of judging whether an observation is RFP-L₁ or not according to the value of least influence coefficient is formulated. Furthermore, the numerical characteristic of design matrix that might contain RFP-L₁ is explored. And at the end, a method of identifying RFP-L₁ is put forward. The simulation results show that the least influence coefficient reflects the influence of gross errors on the objective function of L₁-norm estimation, and the least influence coefficient of normal observation and RFP-L₁ have a significant regularity equal to one and less than one respectively. In addition, it can be concluded that there is no RFP-L₁ in the surveying system with design matrix containing only±1 and 0.

Key words: L₁-norm estimation, gross errors detection, conditional equation, influence coefficient

中图分类号:

P207

闫广峰, 岑敏仪. L₁范数探测粗差失效的观测量识别方法[J]. 测绘学报, 2019, 48(11): 1430-1438.

YAN Guangfeng, CEN Minyi. The identification method of gross error detection failpoint in L₁-norm estimation[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(11): 1430-1438.

参考文献 25

[1]	BAARDA W. A testing procedure for use in geodetic networks[M]. Delft:Netherlands Geodetic Commission, 1968:27-55.
[2]	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 evaluation of multidimensional gross errors[J]. Journal of Wuhan Technical University of Surveying and Mapping, 1996, 21(4):323-329.
[3]	欧吉坤. 粗差的拟准检定法(QUAD法)[J]. 测绘学报, 1999, 28(1):15-20. DOI:10.3321/j.issn:1001-1595.1999.01.004. OU Jikun. Quasi-accurate detection of gross errors (QUAD)[J]. Acta Geodaetica et Cartographica Sinica, 1999, 28(1):15-20. DOI:10.3321/j.issn:1001-1595.1999.01.004.
[4]	李德仁. 利用选择权迭代法进行粗差定位[J]. 武汉测绘科技大学学报, 1984, 9(1):46-68. LI Deren. Gross error location by means of the iteration method with variable weights[J]. Geomatics and Information Science of Wuhan University, 1984, 9(1):46-68.
[5]	RANGELOVA E, FOTOPOULOS G, SIDERIS M G. On the use of iterative re-weighting least-squares and outlier detection for empirically modelling rates of vertical displacement[J]. Journal of Geodesy, 2009, 83(6):523-535.
[6]	YANG Y, SONG L, XU T. Robust estimator for correlated observations based on bifactor equivalent weights[J]. Journal of Geodesy, 2002, 76(6-7):353-358.
[7]	杨元喜. 抗差估计理论及其应用[M]. 北京:解放军出版社, 1993. YANG Yuanxi. Robust estimation theory and its applications[M]. Beijing:PLA Press, 1993.
[8]	BASELGA S. Global optimization solution of robust estimation[J]. Journal of Surveying Engineering, 2007, 133(3):123-128.
[9]	GAO Yang, KRAKIWSKY E J, CZOMPO J. Robust testing procedure for detection of multiple blunders[J]. Journal of Surveying Engineering, 1992, 118(1):11-23.
[10]	岑敏仪. 平差前粗差的发现和定位及其若干规律[D]. 成都:西南交通大学, 1999. CEN Minyi. Gross errors detection and location before adjustment of observed values as well as some theorems for judging gross errors[D]. Chengdu:Southwest Jiaotong University, 1999.
[11]	彭军还, 陶本藻, 黄珹, 等. Lq估计的渐近方差-协方差矩阵及其特点[J]. 测绘学报, 2004, 33(4):293-298. PENG Junhuan, TAO Benzao, HUANG Cheng, et al. The asymptotic variance-covariance matrix in Lq-norm estimate and its characteristic[J]. Acta Geodaetica et Cartographica Sinica, 2004, 33(4):293-298.
[12]	彭军还. L1范数估计的巴尔达型检验及其可靠性[J]. 测绘学报, 2005, 34(3):208-212. DOI:10.3321/j.issn:1001-1595.2005.03.004. PENG Junhuan. Baarda test and its reliability in L1-norm estimation[J]. Acta Geodaetica et Cartographica Sinica, 2005, 34(3):208-212. DOI:10.3321/j.issn:1001-1595.2005.03.004.
[13]	郑肇葆. 线性规划在摄影测量粗差检测中应用的尝试[J]. 测绘学报, 1985, 14(4):241-252. ZHENG Zhaobao. Application of linear programming in the detection of blunders in photogrammetry[J]. Acta Geodaetica et Cartographica Sinica, 1985, 14(4):241-252.
[14]	MARSHALL J, BETHEL J. Basic concepts of L1 norm minimization for surveying applications[J]. Journal of Surveying Engineering, 1996, 122(4):168-179.
[15]	AMIRI-SIMKOOEI A. Formulation of L1 norm minimization in Gauss-Markov models[J]. Journal of Surveying Engineering, 2003, 129(1):37-43.
[16]	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.
[17]	YETKIN M, INAL C. L1 norm minimization in GPS networks[J]. Survey Review, 2011, 43(323):523-532.
[18]	ROUSSEUW P J, LEROY A M. Robust regression and outlier detection[M]. New York:Wiley, 1987.
[19]	CEN M, LI Z, DING Xiaoli, et al. Gross error diagnostics before least squares adjustment of observations[J]. Journal of Geodesy, 2003, 77(9):503-513.
[20]	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. DOI:10.3321/j.issn:1001-1595.2003.02.008. 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 Cartographica Sinica, 2003, 32(2):134-138. DOI:10.3321/j.issn:1001-1595.2003.02.008.
[21]	郑肇葆. 数学规划在测绘学中应用[M]. 北京:测绘出版社, 2003. ZHENG Zhaobao. Application of mathematical programming in surveying and mapping[M]. Beijing:Surveying and Mapping Press, 2003.
[22]	束金龙, 闻人凯. 线性规划理论与模型应用[M]. 北京:科学出版社, 2003. SHU Jinlong, WEN Renkai. Linear programming theory and model applications[M]. Beijing:Science Press, 2003.
[23]	LUENBERGER D G, YE Yinyu. Linear and nonlinear programming[M]. Berlin:Springer, 2008.
[24]	范东明. 任意平面网坐标自动解算的非线性最小二乘平差算法[D]. 成都:西南交大通大学, 2000. FAN Dongming. The algorithm of nonlinear least squares adjustment of any plane networks with coordinates computed automatically[D]. Chengdu:Southwest Jiaotong University, 2000.
[25]	黄维彬. 近代平差理论及其应用[M]. 北京:解放军出版社, 1992. HUANG Weibin. Modern adjustment theory and its application[M]. Beijing:PLA Press, 1992.

L₁范数探测粗差失效的观测量识别方法

The identification method of gross error detection failpoint in L₁-norm estimation

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献 25

相关文章 9

编辑推荐

Metrics

本文评价

[1]	颜金彪, 吴波, 彭馨. 顾及Gestalt邻近与简化原则的平面点集形状重建[J]. 测绘学报, 2020, 49(11): 1485-1496.
[2]	张亚彬, 王利, 范丽红, 曲轩宇. 组合粗差探测的MHSS ARAIM算法[J]. 测绘学报, 2019, 48(1): 9-17.
[3]	张志衡, 彭认灿, 黄文骞, 董箭, 刘国辉. 考虑自然邻点影响域的多波束测深数据趋势面滤波改进算法[J]. 测绘学报, 2018, 47(1): 35-47.
[4]	郑凯, 刘站科, 肖学年, 张小红. 航空重力GPS测速多粗差探测方法[J]. 测绘学报, 2016, 45(6): 663-669.
[5]	仝海波张国柱. 改进M估计的抗多个粗差定位解算方法[J]. 测绘学报, 2014, 43(4): 366-371.
[6]	孙文王庆宾朱志大. 联合多代卫星测高数据构建中国近海及邻域海平面异常序列[J]. , 2013, 42(4): 0-0.
[7]	孙海燕,黄华兵,王喜娜. 多维平差问题粗差的局部分析法[J]. 测绘学报, 2012, 41(1): 54-0.
[8]	李博峰. 基于等效残差积探测粗差的方差-协方差分量估计[J]. 测绘学报, 2011, 40(1): 10-14.
[9]	徐天河,贺凯飞. 移动开窗检验法及其在GOCE数据粗差探测中的应用[J]. 测绘学报, 2009, 38(5): 0-414.