一种获取不确定度的方法在位错模型中的应用
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摘要
针对带不确定性的平差算法(least-square with uncertainty,ULS)中不确定度的选择问题,提出类L曲线法,并在位错模型中进行实验,解算位错参数。通过与LS和TLS的解算结果进行比较发现,ULS的解具有更高的精度,最高优于LS和TLS近60%。
This paper proposes a similar L-shaped curve method processing uncertainty selection problem of ULS,and then experiments on the dislocation model and calculating dislocation parameters.Finally,comparison of the result of ULS with those of LS and TLS,shows that ULS has higher precision,increased by nearly 60% over LS and TLS.
This paper proposes a similar L-shaped curve method processing uncertainty selection problem of ULS,and then experiments on the dislocation model and calculating dislocation parameters.Finally,comparison of the result of ULS with those of LS and TLS,shows that ULS has higher precision,increased by nearly 60% over LS and TLS.
引文
[1]谢建,朱建军.等式约束病态模型的正则化解及其统计性质[J].武汉大学学报:信息科学版,2013,38(12):1 440-1 444(Xie Jian,Zhu Jianjun.A Regularized Solution and Statistical Properties of Ill-Posed Problem with Equality Constraints[J].Geomatics and Information Science of Wuhan University,2013,38(12):1 440-1 444)
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[14]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(Song Yingchun,Xie Xuemei,Chen Xiaolin.Adjustment Criterion and Algorithm in Adjustment Model with Uncertainty[J].Acta Geodaetica et Cartogra phica Sinica,2015,44(2):135-141)
[15]邹渤,宋迎春,唐争气,等.沉降观测AR模型的不确定性平差算法[J].大地测量与地球动力学,2016,36(8):686-688(Zou Bo,Song Yingchun,Tang Zhengqi,et al.Adjustment Algorithm on AR Model with Uncertain in Settlement Observation[J].Journal of Geodesy and Geodynamics,2016,36(8):686-688)
[16]Okada Y.Surface Deformation Due to Shear and Tensile Faults in a Half-Space[J].Bulletin of the Seismological Society of America,1985,92(2):1 018-1 040
[2]谢建,朱建军.等式约束对病态问题的影响及约束正则化方法[J].武汉大学学报:信息科学版,2015,40(10):1 344-1 348(Xie Jian,Zhu Jianjun.Influence of Equality Constraints on Ill-Conditioned Problems and Constrained Regularization Method[J].Geomatics and Information Science of Wuhan University,2015,40(10):1 344-1 348)
[3]王乐洋,于冬冬.病态总体最小二乘问题的虚拟观测解法[J].测绘学报,2014,43(6):575-581(Wang Leyang,Yu Dongdong.Virtual Observation Method to Ill-Posed Total Least Squares Problem[J].Acta Geodaetica et Cartographica Sinica,2014,43(6):575-581)
[4]王乐洋,郑玄威,申兴林,等.坐标转换Partial-EIV总体最小二乘方法[J].测绘工程,2015,24(12):12-16(Wang Leyang,Zheng Xuanwei,Shen Xinglin,et al.Partial-EIV Total Least Squares Method for Coordinate Transformation[J].Engineering of Surveying and Mapping,2015,24(12):12-16)
[5]杨娟,陶叶青.GPS高程异常拟合的稳健总体最小二乘算法[J].大地测量与地球动力学,2014,34(5):130-133(Yang Juan,Tao Yeqing.A Solution of GPS Elevation Anomaly Fitting Based on Robust Total Least Squares[J].Journal of Geodesy and Geodynamics,2014,34(5):130-133)
[6]Markovsky I,Huffel S.Overview of Total Least-Squares Methods[J].Signal Processing,2007,87(10):2 283-2 302
[7]Schaffrin B,Wieser A.On Weighted Total Least-Squares Adjustment for Linear Regression[J].Journal of Geodesy,2008,82(7):415-421
[8]陈玮娴,陈义,袁庆,等.加权总体最小二乘在三维激光标靶拟合中的应用[J].大地测量与地球动力学,2010,30(5):90-96(Chen Weixian,Chen Yi,Yuan Qing,et al.Application of Weighted Total Least Squares to Target Fitting of Three-Dimensional Laser Scanning[J].Journal of Geodesy and Geodynamics,2010,30(5):90-96)
[9]王乐洋.地壳应变参数反演的总体最小二乘方法[J].大地测量与地球动力学,2013,33(3):106-110(Wang Leyang.Inversion of Crustal Strain Parameters Based on Total Least Squares[J].Journal of Geodesy and Geodynamics,2013,33(3):106-110)
[10]Beck A,Ben-Tal A.On the Solution of the Tikhonov Regularization of the Total Least Squares Problem[J].SIAM Journal on Optimization,2006,17(1):98-118
[11]余岸竹,姜挺,郭文月,等.总体最小二乘用于线阵卫星遥感影像光束法平差解算[J].测绘学报,2016,45(4):442-449(Yu Anzhu,Jiang Ting,Guo Wenyue,et al.Bundle Adjustment for Satellite Linear Array Images Based on Total Least Squares[J].Acta Geodaetica et Cartographica Sinica,2016,45(4):442-449)
[12]陈义,陆珏.以三维坐标转换为例解算稳健总体最小二乘方法[J].测绘学报,2012,41(5):715-722(Chen Yi,Lu Jue.Performing 3DSimilarity Transformation by Robust Total Least Squares[J].Acta Geodaetica et Cartographica Sinica,2012,41(5):715-722)
[13]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 Uncertainty[J].Geomatics and Information Science of Wuhan University,2014,39(7):788-792)
[14]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(Song Yingchun,Xie Xuemei,Chen Xiaolin.Adjustment Criterion and Algorithm in Adjustment Model with Uncertainty[J].Acta Geodaetica et Cartogra phica Sinica,2015,44(2):135-141)
[15]邹渤,宋迎春,唐争气,等.沉降观测AR模型的不确定性平差算法[J].大地测量与地球动力学,2016,36(8):686-688(Zou Bo,Song Yingchun,Tang Zhengqi,et al.Adjustment Algorithm on AR Model with Uncertain in Settlement Observation[J].Journal of Geodesy and Geodynamics,2016,36(8):686-688)
[16]Okada Y.Surface Deformation Due to Shear and Tensile Faults in a Half-Space[J].Bulletin of the Seismological Society of America,1985,92(2):1 018-1 040