Adjustment Criterion and Algorithm in Adjustment Model with Uncertain

doi:10.11947/j.AGCS.2015.20130213

Abstract

Abstract: Uncertainty often exists in the process of obtaining measurement data, which affects the reliability of parameter estimation. This paper establishes a new adjustment model in which uncertainty is incorporated into the function model as a parameter. A new adjustment criterion and its iterative algorithm are given based on uncertainty propagation law in the residual error, in which the maximum possible uncertainty is minimized. This paper also analyzes, with examples, the different adjustment criteria and features of optimal solutions about the least-squares adjustment, the uncertainty adjustment and total least-squares adjustment. Existing error theory is extended with new observational data processing method about uncertainty.

Key words: uncertain, adjustment criterion, residual error, total least-squares adjustment, adjustment model

CLC Number:

P207

SONG Yingchun, XIE Xuemei, CHEN Xiaoling. Adjustment Criterion and Algorithm in Adjustment Model with Uncertain[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(2): 135-141.

References

[1] YANG Yuanxi. Some Notes on Uncertainty, Uncertainty Measure and Accuracy in Satellite Navigation[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(5): 646-650.(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.)
[2] TAO Benzao. Basic Theory of Uncertainty of Quality Control in GIS[J]. Journal of Institute of Surveying and Mapping, 2000, 17(4): 235-238. (陶本藻. GIS质量控制中不确定度理论[J]. 测绘学院学报, 2000, 17(4): 235-238.)
[3] XU Zifu, LIU Dong, RUAN Anlu. Review on Uncertainty Measure, Accuracy and Precision[J]. Measuring Technology, 2007, 27(2): 37-39.(许自富, 刘东, 阮安路.不确定度、准确度、精度辨析[J].计量技术, 2007, 27(2): 37-39.)
[4] Bureau International des Poids et Mesures. JCGM 104:2009.Guide to the Expression of Uncertainty in Measurement[S]. Switzerland:[s.n.], 1993.
[5] Bureau International des Poids et Mesures. JCGM 100:2008.Guide to the Expression of Uncertainty in Measurement[S].Switzerland:[s.n.], 1995.
[6] 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. (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.)
[7] 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. (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.)
[8] 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. (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.)
[9] JIA Shuaidong, ZHANG Lihua, SONG Guoda, et al. A Method for Constructing an Adaptive Grid Digital Depth Model Based on Mean Vertical Uncertaintyof Area[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(3): 454-460. (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.)
[10] CHEN Wei. Least Uncertainty Estimation Theory With Applications[D]. Wuhan:Wuhan Univercity, 2005. (陈伟. 最小不确定度估计理论及其应用[D]. 武汉:武汉大学, 2005.)
[11] 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. (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.)
[12] WANG Xinzhou. Maximum Possibility Estimation Restricted by Least Uncertainty[J]. Engineering of Surveying and Mapping, 2003(1):5-8. (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(1):5-8.)
[13] TAO Benzao. Estimation of Accuracy and Uncertainty and Its Application[J].Site Investigation Science and Technology,2003,5: 24-27. (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.)
[14] YANG Yuanxi. Discussion on “A New Measure of Positional Error”[J]. Acta Geodaetica et Cartographica Sinica, 2009,38(3):280-282. (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.)
[15] SCHAFFRIN B, FELUS Y A.A Window on the Future of Geodesy[M].Berlin:Springer, 2005:417-421.
[16] SCHAFFRIN B, WIESER A. On Weighted Total Least-Squares Adjustment for Linear Regression[J]. Journal of Geodesy. 2008, 82(7): 415-421.
[17] 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. (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.)
[18] 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. (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.)
[19] GHAOUI L E, 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]. 1998, 11(4): 235-252.