多像空间前方交会的抗差总体最小二乘估计
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摘要
为充分利用现有观测数据来确定地面点位置,根据立体像对的前方交会原理,通过建立目标点到多条同名射线距离的加权平方和作为目标函数,对其求一阶和二阶导数,得到多像空间前方交会的抗差总体最小二乘估计。相对于立体像对,多张像片的空间前方交会方法可利用更多的观测信息并引入了稳健估计理论,具有更高的交会精度及稳健性能。最后,通过算例验证了该方法的正确性与稳健性,可一定程度上丰富摄影测量空间前方交会理论。
In order to take full advantage of available observation resources,based on theory of space intersection with stereo images,by conducting weighted quadratic sum of spatial distance from the target point to multiple space lines as the objective function and carrying out its first as well as second derivatives,robust total least squares estimation of space intersection appropriate for multi-images was realized.Compared to stereopair,more observed information and theories of robust estimation were considered in the process of space intersection with multi-images,bringing about higher intersection accuracy and robustness.Finally,correctness and robustness of the method was verified though example analysis,which can enrich the space intersection theory in photogrammetry to some degree.
In order to take full advantage of available observation resources,based on theory of space intersection with stereo images,by conducting weighted quadratic sum of spatial distance from the target point to multiple space lines as the objective function and carrying out its first as well as second derivatives,robust total least squares estimation of space intersection appropriate for multi-images was realized.Compared to stereopair,more observed information and theories of robust estimation were considered in the process of space intersection with multi-images,bringing about higher intersection accuracy and robustness.Finally,correctness and robustness of the method was verified though example analysis,which can enrich the space intersection theory in photogrammetry to some degree.
引文
[1]冯其强,李广云,李宗春.数字工业摄影测量技术及应用[M].北京:测绘出版社,2013.FENG Qiqiang,LI Guangyun,LI Zongchun.Digital Industrial Photogrammetry Technology and Applications[M].Beijing:Surveying and Mapping Press,2013.
[2]张剑清,潘励,王树根.摄影测量学[M].武汉:武汉大学出版社,2009.ZHANG Jianqing,PAN Li,WANG Shugen.Photogrammetry[M].Wuhan:Wuhan University Press,2009.
[3]王佩军,徐亚明.摄影测量学[M].武汉:武汉大学出版社,2005.WANG Peijun,XU Yaming.Photogrammetry[M].Wuhan:Wuhan University Press,2005.
[4]郑顺义,郭宝云,李彩林.基于模型和广义点摄影测量的圆柱体自动三维重建与检测[J].测绘学报,2011,40(4):477-482.ZHENG Shunyi,GUO Baoyun,LI Cailin.3DReconstruction and Inspection of Cylinder Based on Geometric Model and Generalized Point Photogrammetry[J].Acta Geodaetica et Cartographica Sinica,2011,40(4):477-482.
[5]张春森,张卫龙,郭丙轩,等.倾斜影像的三维纹理快速重建[J].测绘学报,2015,44(7):782-790.DOI:10.11947/j.AGCS.2015.20140341.ZHANG Chunsen,ZHANG Weilong,GUO Bingxuan,et al.Rapidly 3D Texture Reconstruction Based on Oblique Photography[J].Acta Geodaetica et Cartographica Sinica,2015,44(7):782-790.DOI:10.11947/j.AGCS.2015.20140341.
[6]盛庆红,肖晖.卫星遥感与摄影测量[M].北京:科学出版社,2015.SHENG Qinghong,XIAO Hui.Satellite Remote Sensing and Photogrammetry[M].Beijing:Science Press,2015.
[7]曾凡洋,钟若飞,宋杨,等.车载全景影像核线匹配和空间前方交会[J].遥感学报,2014,18(6):1230-1236.ZENG Fanyang,ZHONG Ruofei,SONG Yang,et al.Vehicle Panoramic Image Matching Based on Epipolar Geometry and Space Forward Intersection[J].Journal of Remote Sensing,2014,18(6):1230-1236.
[8]张祖勋,郭大海,柯涛,等.抗震救灾中航空摄影测量的应急响应[J].遥感学报,2008,12(6):852-857.ZHANG Zuxun,GUO Dahai,KE Tao,et al.The Use of Aerial Photogrammetry in the Fast Response for China Earthquake Rescue[J].Journal of Remote Sensing,2008,12(6):852-857.
[9]王任享,胡莘,王新义,等.“天绘一号”卫星工程建设与应用[J].遥感学报,2012,16(S):2-5.WANG Renxiang,HU Xin,WANG Xinyi,et al.The Construction and Application of Mapping Satellite-1Engineering[J].Journal of Remote Sensing,2012,16(S):2-5.
[10]王任享,胡莘,王建荣.天绘一号无地面控制点摄影测量[J].测绘学报,2013,42(1):1-5.WANG Renxiang,HU Xin,WANG Jianrong.Photogrammetry of Mapping Satellite-1without Ground Control Points[J].Acta Geodaetica et Cartographica Sinica,2013,42(1):1-5.
[11]冯其强,黄桂平,李广云.基于多片前方交会的工业摄影测量自动匹配[J].中国图像图形学报,2009,14(6):1194-1198.FENG Qiqiang,HUANG Guiping,LI Guangyun.Automatching of Artificial Target Points in Industrial Photogrammetry Based on Space Intersection[J].Journal of Image and Graphics,2009,14(6):1194-1198.
[12]张晓东,杨元喜,胡庆武,等.可量测序列影像的加权整体最小二乘导航[J].应用科学学报,2013,31(2):147-153.ZHANG Xiaodong,YANG Yuanxi,HU Qingwu,et al.Weighted Global Least Square Navigation Based on Measurable Image Sequence[J].Journal of Applied Sciences-Electronics and Information Engineering,2013,31(2):147-153.
[13]龚循强,李志林.稳健加权总体最小二乘法[J].测绘学报,2014,43(9):888-894,901.DOI:10.13485/j.cnki.11-2089.2014.0140.GONG Xunqiang,LI Zhilin.A Robust Weighted Total Least Squares Method[J].Acta Geodaetica et Cartographica Sinica,2014,43(9):888-894,901.DOI:10.13485/j.cnki.11-2089.2014.0140.
[14]王彬,李建成,高井祥,等.抗差加权整体最小二乘模型的牛顿-高斯算法[J].测绘学报,2015,44(6):602-608.DOI:10.11947/j.AGCS.2015.20130704.WANG Bin,LI Jiancheng,GAO Jingxiang,et al.NewtonGauss Algorithm of Robust Weighted Total Least Squares Model[J].Acta Geodaetica et Cartographica Sinica,2015,44(6):602-608.DOI:10.11947/j.AGCS.2015.20130704.
[15]GOLUB G H,VAN LOAN C F.An Analysis of the Total Least Squares Problem[J].SIAM Journal on Numerical Analysis,1980,17(6):883-893.
[16]VAN HUFFEL S,VANDEWALLE J.The Total Least Squares Problem:Computational Aspects and Analysis[M].Philadelphia:SIAM,1991.
[17]MARKOVSKY I,VAN HUFFEL S.Overview of Total Least-squares Methods[J].Signal Processing,2007,87(10):2283-2302.
[18]张贤达.矩阵分析与应用[M].2版.北京:清华大学出版社,2013.ZHANG Xianda.Matrix Analysis and Applications[M].Beijing:Tsinghua University Press,2013.
[19]胡川,陈义,朱卫东,等.整体最小二乘和最小二乘拟合空间直线的比较[J].大地测量与地球动力学,2015,35(4):689-692,701.HU Chuan,CHEN Yi,ZHU Weidong,et al.Comparisons of Total Least Squares and Least Squares for Fitting Spatial Lines[J].Journal of Geodesy and Geodynamics,2015,35(4):689-692,701.
[20]DING Ye,ZHU Limin,DING Han.Semidefinite Programming for Chebyshev Fitting of Spatial Straight Line with Applications to Cutter Location Planning and Tolerance Evaluation[J].Precision Engineering,2007,31(4):364-368.
[21]潘国荣,唐杭.特征分解与选权迭代在空间直线拟合中的应用[J].东南大学学报(自然科学版),2013,43(S2):250-255.PAN Guorong,TANG Hang.Application of Eigen Decomposition and Selecting Weight Iteration in Spatial Line Fitting[J].Journal of Southeast University(Natural Science Edition),2013,43(S2):250-255.
[22]姚宜斌,刘经南,施闯.相关稳健估计及其在测量数据处理中的应用[J].测绘信息与工程,2001(3):5-8.YAO Yibin,LIU Jingnan,SHI Chuang.Dependent Robust Estimation and Its Applications in Survey Data Processing[J].Journal of Geomatics,2001,2001(3):5-8.
[23]杨元喜,宋力杰,徐天河.大地测量相关观测抗差估计理论[J].测绘学报,2002,31(2):95-99.YANG Yuanxi,SONG Lijie,XU Tianhe.Robust Parameter Estimation for Geodetic Correlated Observations[J].Acta Geodaetica et Cartographica Sinica,2002,31(2):95-99.
[24]李德仁,袁修孝.误差处理与可靠性理论[M].武汉:武汉大学出版社,2012.LI Deren,YUAN Xiuxiao.Error Processing and Reliability Theory[M].Wuhan:Wuhan University Press,2012.
[25]王新洲,陶本藻,邱卫宁,等.高等测量平差[M].北京:测绘出版社,2013.WANG Xinzhou,TAO Benzao,QIU Weining,et al.Advanced Surveying Adjustment[M].Beijing:Surveying and Mapping Press,2013.
[26]费业泰.误差理论与数据处理[M].北京:机械工业出版社,2015.FEI Yetai.Errors Theory and Data Processing[M].Beijing:China Machine Press,2015.
[27]周江文.经典误差理论与抗差估计[J].测绘学报,1989,18(2):115-120.ZHOU Jiangwen.Classical Theory of Errors and Robust Estimation[J].Acta Geodaetica et Cartographica Sinica,1989,18(2):115-120.
[28]袁修孝,曹金山.高分辨率卫星遥感精确对地目标定位理论与方法[M].北京:科学出版社,2012.YUAN Xiuxiao,CAO Jinshan.Theories and Methods of Precise Object Positioning for High Resolution Satellite Imagery[M].Beijing:Science Press,2012.
[2]张剑清,潘励,王树根.摄影测量学[M].武汉:武汉大学出版社,2009.ZHANG Jianqing,PAN Li,WANG Shugen.Photogrammetry[M].Wuhan:Wuhan University Press,2009.
[3]王佩军,徐亚明.摄影测量学[M].武汉:武汉大学出版社,2005.WANG Peijun,XU Yaming.Photogrammetry[M].Wuhan:Wuhan University Press,2005.
[4]郑顺义,郭宝云,李彩林.基于模型和广义点摄影测量的圆柱体自动三维重建与检测[J].测绘学报,2011,40(4):477-482.ZHENG Shunyi,GUO Baoyun,LI Cailin.3DReconstruction and Inspection of Cylinder Based on Geometric Model and Generalized Point Photogrammetry[J].Acta Geodaetica et Cartographica Sinica,2011,40(4):477-482.
[5]张春森,张卫龙,郭丙轩,等.倾斜影像的三维纹理快速重建[J].测绘学报,2015,44(7):782-790.DOI:10.11947/j.AGCS.2015.20140341.ZHANG Chunsen,ZHANG Weilong,GUO Bingxuan,et al.Rapidly 3D Texture Reconstruction Based on Oblique Photography[J].Acta Geodaetica et Cartographica Sinica,2015,44(7):782-790.DOI:10.11947/j.AGCS.2015.20140341.
[6]盛庆红,肖晖.卫星遥感与摄影测量[M].北京:科学出版社,2015.SHENG Qinghong,XIAO Hui.Satellite Remote Sensing and Photogrammetry[M].Beijing:Science Press,2015.
[7]曾凡洋,钟若飞,宋杨,等.车载全景影像核线匹配和空间前方交会[J].遥感学报,2014,18(6):1230-1236.ZENG Fanyang,ZHONG Ruofei,SONG Yang,et al.Vehicle Panoramic Image Matching Based on Epipolar Geometry and Space Forward Intersection[J].Journal of Remote Sensing,2014,18(6):1230-1236.
[8]张祖勋,郭大海,柯涛,等.抗震救灾中航空摄影测量的应急响应[J].遥感学报,2008,12(6):852-857.ZHANG Zuxun,GUO Dahai,KE Tao,et al.The Use of Aerial Photogrammetry in the Fast Response for China Earthquake Rescue[J].Journal of Remote Sensing,2008,12(6):852-857.
[9]王任享,胡莘,王新义,等.“天绘一号”卫星工程建设与应用[J].遥感学报,2012,16(S):2-5.WANG Renxiang,HU Xin,WANG Xinyi,et al.The Construction and Application of Mapping Satellite-1Engineering[J].Journal of Remote Sensing,2012,16(S):2-5.
[10]王任享,胡莘,王建荣.天绘一号无地面控制点摄影测量[J].测绘学报,2013,42(1):1-5.WANG Renxiang,HU Xin,WANG Jianrong.Photogrammetry of Mapping Satellite-1without Ground Control Points[J].Acta Geodaetica et Cartographica Sinica,2013,42(1):1-5.
[11]冯其强,黄桂平,李广云.基于多片前方交会的工业摄影测量自动匹配[J].中国图像图形学报,2009,14(6):1194-1198.FENG Qiqiang,HUANG Guiping,LI Guangyun.Automatching of Artificial Target Points in Industrial Photogrammetry Based on Space Intersection[J].Journal of Image and Graphics,2009,14(6):1194-1198.
[12]张晓东,杨元喜,胡庆武,等.可量测序列影像的加权整体最小二乘导航[J].应用科学学报,2013,31(2):147-153.ZHANG Xiaodong,YANG Yuanxi,HU Qingwu,et al.Weighted Global Least Square Navigation Based on Measurable Image Sequence[J].Journal of Applied Sciences-Electronics and Information Engineering,2013,31(2):147-153.
[13]龚循强,李志林.稳健加权总体最小二乘法[J].测绘学报,2014,43(9):888-894,901.DOI:10.13485/j.cnki.11-2089.2014.0140.GONG Xunqiang,LI Zhilin.A Robust Weighted Total Least Squares Method[J].Acta Geodaetica et Cartographica Sinica,2014,43(9):888-894,901.DOI:10.13485/j.cnki.11-2089.2014.0140.
[14]王彬,李建成,高井祥,等.抗差加权整体最小二乘模型的牛顿-高斯算法[J].测绘学报,2015,44(6):602-608.DOI:10.11947/j.AGCS.2015.20130704.WANG Bin,LI Jiancheng,GAO Jingxiang,et al.NewtonGauss Algorithm of Robust Weighted Total Least Squares Model[J].Acta Geodaetica et Cartographica Sinica,2015,44(6):602-608.DOI:10.11947/j.AGCS.2015.20130704.
[15]GOLUB G H,VAN LOAN C F.An Analysis of the Total Least Squares Problem[J].SIAM Journal on Numerical Analysis,1980,17(6):883-893.
[16]VAN HUFFEL S,VANDEWALLE J.The Total Least Squares Problem:Computational Aspects and Analysis[M].Philadelphia:SIAM,1991.
[17]MARKOVSKY I,VAN HUFFEL S.Overview of Total Least-squares Methods[J].Signal Processing,2007,87(10):2283-2302.
[18]张贤达.矩阵分析与应用[M].2版.北京:清华大学出版社,2013.ZHANG Xianda.Matrix Analysis and Applications[M].Beijing:Tsinghua University Press,2013.
[19]胡川,陈义,朱卫东,等.整体最小二乘和最小二乘拟合空间直线的比较[J].大地测量与地球动力学,2015,35(4):689-692,701.HU Chuan,CHEN Yi,ZHU Weidong,et al.Comparisons of Total Least Squares and Least Squares for Fitting Spatial Lines[J].Journal of Geodesy and Geodynamics,2015,35(4):689-692,701.
[20]DING Ye,ZHU Limin,DING Han.Semidefinite Programming for Chebyshev Fitting of Spatial Straight Line with Applications to Cutter Location Planning and Tolerance Evaluation[J].Precision Engineering,2007,31(4):364-368.
[21]潘国荣,唐杭.特征分解与选权迭代在空间直线拟合中的应用[J].东南大学学报(自然科学版),2013,43(S2):250-255.PAN Guorong,TANG Hang.Application of Eigen Decomposition and Selecting Weight Iteration in Spatial Line Fitting[J].Journal of Southeast University(Natural Science Edition),2013,43(S2):250-255.
[22]姚宜斌,刘经南,施闯.相关稳健估计及其在测量数据处理中的应用[J].测绘信息与工程,2001(3):5-8.YAO Yibin,LIU Jingnan,SHI Chuang.Dependent Robust Estimation and Its Applications in Survey Data Processing[J].Journal of Geomatics,2001,2001(3):5-8.
[23]杨元喜,宋力杰,徐天河.大地测量相关观测抗差估计理论[J].测绘学报,2002,31(2):95-99.YANG Yuanxi,SONG Lijie,XU Tianhe.Robust Parameter Estimation for Geodetic Correlated Observations[J].Acta Geodaetica et Cartographica Sinica,2002,31(2):95-99.
[24]李德仁,袁修孝.误差处理与可靠性理论[M].武汉:武汉大学出版社,2012.LI Deren,YUAN Xiuxiao.Error Processing and Reliability Theory[M].Wuhan:Wuhan University Press,2012.
[25]王新洲,陶本藻,邱卫宁,等.高等测量平差[M].北京:测绘出版社,2013.WANG Xinzhou,TAO Benzao,QIU Weining,et al.Advanced Surveying Adjustment[M].Beijing:Surveying and Mapping Press,2013.
[26]费业泰.误差理论与数据处理[M].北京:机械工业出版社,2015.FEI Yetai.Errors Theory and Data Processing[M].Beijing:China Machine Press,2015.
[27]周江文.经典误差理论与抗差估计[J].测绘学报,1989,18(2):115-120.ZHOU Jiangwen.Classical Theory of Errors and Robust Estimation[J].Acta Geodaetica et Cartographica Sinica,1989,18(2):115-120.
[28]袁修孝,曹金山.高分辨率卫星遥感精确对地目标定位理论与方法[M].北京:科学出版社,2012.YUAN Xiuxiao,CAO Jinshan.Theories and Methods of Precise Object Positioning for High Resolution Satellite Imagery[M].Beijing:Science Press,2012.