具有不确定性平差算法

王志忠; 陈丹华; 宋迎春

doi:10.11947/j.AGCS.2017.20160522

测绘学报 >

2017 , Vol. 46 >Issue 7: 834 - 840

DOI: https://doi.org/10.11947/j.AGCS.2017.20160522

大地测量学与导航

具有不确定性平差算法

王志忠 ,
陈丹华 ,
宋迎春

展开

1. 中南大学地球信息科学与物理学院, 湖南长沙 410083;
2. 中南大学数学与统计学院, 湖南长沙 410083

王志忠(1963—),男,博士,博士生导师,研究方向为测量数据处理。

收稿日期: 2016-10-12

修回日期: 2017-02-27

网络出版日期: 2017-07-25

基金资助

国家自然科学基金（41574006）

收起

An Algorithm in Adjustment Model with Uncertainty

WANG Zhizhong ,
CHEN Danhua ,
SONG Yingchun

Expand

1. School of Geosciences and Info-physic, Central South University, Changsha 410083, China;
2. School of Mathamatic and Statistics, Central South University, Changsha 410083, China

Received date: 2016-10-12

Revised date: 2017-02-27

Online published: 2017-07-25

Supported by

The National Natural Science Foundation of China (No. 41574006)

Fold

摘要

观测不确定性常常影响参数估计的有效性。将不确定度作为参数融入平差模型，可以有效地降低不确定性的影响。本文提出有界不确定性误差约束下，随机误差与不确定性误差平方和最小的平差准则，并给出了一个不确定性平差模型迭代算法。通过仿真实例，对不确定性最小二乘法与总体最小二乘法进行了比较。结果显示：在一定程度上，不确定性最小二乘方法的估计结果要略优于总体最小二乘方法，且在不确定性较大时，该方法有较好的适用性。

关键词： 平差模型; 平差准则; 不确定性; 总体最小二乘估计; 先验信息

本文引用格式

王志忠 , 陈丹华 , 宋迎春 . 具有不确定性平差算法[J]. 测绘学报, 2017 , 46(7) : 834 -840 . DOI: 10.11947/j.AGCS.2017.20160522

Abstract

The uncertainty of observation often affects the validity of parameter estimation, and the effects of uncertainty can be reduced effectively by incorporating uncertainty into the adjustment model as an observation error parameter. An adjustment criterion is proposed under the bound constrain of uncertainty, in which the sum of squares of random error and uncertainty error should be minimized, and provided an iteration algorithm to solve the adjustment model. With simulation examples, the estimation results of uncertainty least-square method are compared with that of total least-square method. The results show that the estimation results of uncertainty least-square method are better than that of total least-square method to a certain extent and more applicable when uncertainty is greater.

Key words： adjustment model; adjustment criterion; uncertainty; total least-squares estimation; prior information

参考文献

[1] 杨元喜. 卫星导航的不确定性、不确定度与精度若干注记[J]. 测绘学报, 2012, 41(5): 646-650. YANG Yuanxi. Some Notes on Uncertainty, Uncertainty Measure and Accuracy in Satellite Navigation[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(5): 646-650.
[2] BRAVO J M, ALAMO T, REDONDO M J, et al. An Algorithm for Bounded-error Identification of Nonlinear Systems Based on DC Functions[J]. Automatica, 2008, 44(2): 437-444.
[3] Bureau International des Poids et Mesures. JCGM 104: 2009. Guide to the Expression of Uncertainty in Measurement[S]. Berne: Bureau International des Poids et Mesures, 1993.
[4] 邹永刚, 翟京生, 刘雁春, 等. 利用不确定度的海底数字高程模型构建[J]. 武汉大学学报(信息科学版), 2011, 36(8): 964-968. ZOU Yonggang, ZHAI Jingsheng, LIU Yanchun, et al. Seabed DEM Construction Based on Uncertainty[J]. Geomatics and Information Science of Wuhan University, 2011, 36(8): 964-968.
[5] 史玉峰, 史文中, 靳奉祥. GIS中空间数据不确定性的混合熵模型研究[J]. 武汉大学学报(信息科学版), 2006, 31(1): 82-85. SHI Yufeng, SHI Wenzhong, JIN Fengxiang. Hybrid Entropy Model of Spatial Data Uncertainty in GIS[J]. Geomatics and Information Science of Wuhan University, 2006, 31(1): 82-85.
[6] 张正禄, 范国庆, 张松林, 等. 测量的广义可靠性研究[J]. 武汉大学学报(信息科学版), 2012, 37(5): 577-581. ZHANG Zhenglu, FAN Guoqing, ZHANG Songlin, et al. General Reliability of Measurement[J]. Geomatics and Information Science of Wuhan University, 2012, 37(5): 577-581.
[7] 贾帅东, 张立华, 宋国大, 等. 基于区域平均垂直不确定度的自适应网格水深建模方法[J]. 测绘学报, 2012, 41(3): 454-460. JIA Shuaidong, ZHANG Lihua, SONG Guoda, et al. A Method for Constructing an Adaptive Grid Digital Depth Model Based on Mean Vertical Uncertainty of Area[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(3): 454-460.
[8] 陈伟. 最小不确定度估计理论及其应用[D]. 武汉: 武汉大学, 2005. CHEN Wei. Least Uncertainty Estimation Theory with Applications[D]. Wuhan: Wuhan University, 2005.
[9] 陈伟, 王新洲. 最小不确定度估计原理及其病态问题解法研究[J]. 武汉大学学报(信息科学版), 2008, 33(7): 752-754. CHEN Wei, WANG Xinzhou. Least Uncertainty Estimation Theory and Its Applications to Resolving Morbid Problems[J]. Geomatics and Information Science of Wuhan University, 2008, 33(7): 752-754.
[10] 王新洲. 最小不确定度约束下的极大可能性估计[J]. 测绘工程, 2003, 12(1): 5-8. WANG Xinzhou. Maximum Possibility Estimation Restricted by Least Uncertainty[J]. Engineering of Surveying and Mapping, 2003, 12(1): 5-8.
[11] 陶本藻. 精确度和不确定度估计及应用[J]. 勘察科学技术, 2003(5): 24-27. TAO Benzao. Estimation of Accuracy and Uncertainty and Its Application[J]. Site Investigation Science and Technology, 2003(5): 24-27.
[12] 杨元喜. 关于“新的点位误差度量”的讨论[J]. 测绘学报, 2009, 38(3): 280-282. YANG Yuanxi. Discussion on “A New Measure of Positional Error”[J]. Acta Geodaetica et Cartographica Sinica, 2009, 38(3): 280-282.
[13] 宋迎春, 左廷英, 朱建军. 带有线性不等式约束平差模型的算法研究[J]. 测绘学报, 2008, 37(4): 433-437. SONG Yingchun, ZUO Tingying, ZHU Jianjun. Research on Algorithm of Adjustment Model with Linear Inequality Constrained Parameters[J]. Acta Geodaetica et Cartographica Sinica, 2008, 37(4): 433-437.
[14] SANSÒ F. A Window on the Future of Geodesy[M]. Berlin: Springer, 2005: 417-421.
[15] SCHAFFRIN B, WIESER A. On Weighted Total Least-squares Adjustment for Linear Regression[J]. Journal of Geodesy, 2008, 82(7): 415-421.
[16] 邱卫宁, 齐公玉, 田丰瑞. 整体最小二乘求解线性模型的改进算法[J]. 武汉大学学报(信息科学版), 2010, 35(6): 708-710. QIU Weining, QI Gongyu, TIAN Fengrui. An Improved Algorithm of Total Least Squares for Linear Models[J]. Geomatics and Information Science of Wuhan University, 2010, 35(6): 708-710.
[17] 孔建, 姚宜斌, 吴寒. 整体最小二乘的迭代解法[J]. 武汉大学学报(信息科学版), 2010, 35(6): 711-714. KONG Jian, YAO Yibin, WU Han. Iterative Method for Total Least-squares[J]. Geomatics and Information Science of Wuhan University, 2010, 35(6): 711-714.
[18] FANG Xing. Weighted Total Least Squares: Necessary and Sufficient Conditions, Fixed and Random Parameters[J]. Journal of Geodesy, 2013, 87(8): 733-749.
[19] EL GHAOUI L, LEBRET H. Robust Solutions to Least-squares Problems with Uncertain Data[J]. SIAM Journal on Matrix Analysis and Applications, 1997, 18(4): 1035-1064.
[20] CHANDRASEKARAN S, GOLUB G H, GU M, et al. Parameter Estimation in the Presence of Bounded Data Uncertainties[J]. SIAM Journal on Matrix Analysis and Applications, 1998, 19(1): 235-252.
[21] 宋迎春, 金昊, 崔先强. 带有不确定性的观测数据平差解算方法[J]. 武汉大学学报(信息科学版), 2014, 39(7): 788-792. SONG Yingchun, JIN Hao, CUI Xianqiang. Adjustment Algorithm about Observation Data with Uncertain[J]. Geomatics and Information Science of Wuhan University, 2014, 39(7): 788-792.
[22] 宋迎春, 谢雪梅, 陈晓林. 不确定性平差模型的平差准则与解算方法[J]. 测绘学报, 2015, 44(2): 135-141. DOI: 10.11947/j.AGCS.2015.20130213. SONG Yingchun, XIE Xuemei, CHEN Xiaolin. Adjustment Criterion and Algorithm in Adjustment Model with Uncertain[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(2): 135-141. DOI: 10.11947/j.AGCS.2015.20130213.
[23] 王志忠, 朱建军. 污染模型下的最优估计[J]. 测绘学报, 1999, 28(1): 51-56. WANG Zhizhong, ZHU Jianjun. Optimal Estimation under Contaminated Error Model[J]. Acta Geodaetica et Cartographica Sinica, 1999, 28(1): 51-56.
[24] 朱建军. 污染误差模型下的测量数据处理理论[D]. 长沙: 中南工业大学, 1998. ZHU Jianjun. The Theory of Surveying Adjustment under Contaminated Error Model[D]. Changsha: Central South University of Technology, 1998.
[25] 鲁铁定. 总体最小二乘平差理论及其在测绘数据处理中的应用[D]. 武汉: 武汉大学, 2010. LU Tieding. Research on the Total Least Squares and Its Applications in Surveying Data Processing[D]. Wuhan: Wuhan University, 2010.
[26] SCHAFFRIN B, FELUS Y A. On Total Least-squares Adjustment with Constraints[M]//SANSÒ F. A Window on the Future of Geodesy. Berlin: Springer, 2005: 417-421.
[27] SCHAFFRIN B, LEE I P, FELUS YA, et al. Total Least-squares (TLS) for Geodetic Straight-line and Plane Adjustment[J]. Bollettino di Geodesia e Scienze Affini, 2006, 65(3): 141-168.

Options

文章导航

模态框（Modal）标题

摘要

本文引用格式

Abstract

参考文献