基于四元数的线阵CCD影像定位技术研究
|
摘要
航天线阵CCD(Chorse Coupled Device)影像在遥感影像定位中具有广泛的应用,其摄影高度大,视场角小,光束窄,以致传统的线性化共线条件方程定向参数之间具有较强的相关性,很难得到稳定的高精度解。本文以四元数为工具,研究了四元数在摄影测量定位中的应用,对基于四元数的线阵CCD影像定位技术所涉及的病态问题求解、四元数描述外方位元素、四元数光束法平差等关键问题进行了深入研究,主要内容包括:
1、研究了基于四元数的空间后方交会和绝对定向直接解法,提出了对偶四元数进行绝对定向的直接解法,把对偶四元数应用于描述绝对定向中的旋转和平移参数,成功进行绝对定向解算并进行对比实验论证。
2、针对线阵CCD影像外方位元素求解中出现的病态问题,从理论上分析了其产生的原因,提出了一种解决病态问题的改进有偏估计新方法,用于求解线阵CCD影像的外方位元素。
3、将四元数理论引入到线阵CCD影像定位中,用四元数描述其摄影姿态并构建旋转矩阵,借鉴EFP思想,提出了基于四元数的外方位元素改进EFP(Equivalent Frame Photo)模型,由此进行外定向并进行实验论证。
4、将一幅线阵CCD影像首尾扫描行的外方位角元素用四元数描述,利用四元数球面线性插值(Spherical Linear Interpolation,SLERP)内插得到任意一扫描行姿态,提出了外方位元素的SLERP模型,推导出了相应的误差方程,并进行外定向计算,有效避免了欧拉角模型涉及的大量三角函数计算及不稳定因素,为线阵CCD影像外定向提供了一个新的技术途径。
5、考虑到控制点数据可能存在粗差的情况,引入粗差探测,结合基于四元数的外方位元素改进EFP模型和SLERP模型进行外定向,并利用严密的空间前方交会进行定位实验,结果论证了算法的正确性及优越性。
6、研究了基于四元数的线阵CCD影像光束法平差,该方法对平差初始值要求不高,只需取零初始值即可。实验结果表明平面的平差精度较高,高程精度稍差一些。
Line-array CCD Images are widely used in positioning of remote sensing imagery. However, the orientation parameters of traditional linearization collinear equation are highly correlated because of such factors as big flying height, small angle of coverage, narrow light beam and so on, and thus, are fairly difficult to gain steady and precise solutions. This dissertation makes a comprehensive study on the subjects related to photogrammetric positioning of the line-array CCD images based on quaternion, which includes the solution of ill-posed problem, describing exterior orientation elements by quaternion, bundle block adjustment based on quaternion, etc. The followings are what we have done in this dissertation:
1. Making a comprehensive study on the subjects related to photogrammetric positioning and close-form solution of absolute oritentaion based on quaternion, putting forward a new close-form solution method based on dual quaternion. Dual quaternion is introduced into absolute orientation to describe rotation parameters and translation parameters, and experiments were done in all these methods.
2. Analyzing the reasons theoretically to ill-posed problems which are appeared in the process of solving exterior orientation elements, and putting forward an improved bias-estimation method to compute the exterior orientation elements of line-array CCD images in the aspect of computation methods.
3. Using quaternion to describe the attitude elements of line-array CCD images in the aspect of model selection, putting forward an improved EFP model of exterior orientation elements based on the idea of Equivalent Frame Photo, and doing some exterior orientation experiments through the improved EFP model.
4. Gaining the quaternion attitude elements of any scan line through the method of Spherical Linear Interpolation of quaternion, when quaternion is used to describe the exterior orientation elements of the first and the last scan line of a line-array CCD image, putting forward a SLERP model for exterior orientation elements, and then doing some exterior orientation experiments by SLERP model. It successfully avoids a great deal of computation of trigonometric functions and the potential unstable factors, provides a new technique for exterior orientation of line-array CCD image.
5. Considering that there are some coordinate blunders in Ground Control Points (GCPs), a blunder detection method is used in the process of exterior orientation by the combination of quaternion improved EFP model and quaternion SLERP model, doing some positioning experiments by space intersection, and the experimental results verified the reliability and stability of these methods.
6. The quaternion-based bundle block adjustment of line-array CCD images is studied in this dissertation. Favorable initial values of computation parameters in bundle block adjustment are not required by this method, and the initial values can be assumed to zero. Experimental results indicate that the plane precision is very high, while the height precision is less admirable.
1、研究了基于四元数的空间后方交会和绝对定向直接解法,提出了对偶四元数进行绝对定向的直接解法,把对偶四元数应用于描述绝对定向中的旋转和平移参数,成功进行绝对定向解算并进行对比实验论证。
2、针对线阵CCD影像外方位元素求解中出现的病态问题,从理论上分析了其产生的原因,提出了一种解决病态问题的改进有偏估计新方法,用于求解线阵CCD影像的外方位元素。
3、将四元数理论引入到线阵CCD影像定位中,用四元数描述其摄影姿态并构建旋转矩阵,借鉴EFP思想,提出了基于四元数的外方位元素改进EFP(Equivalent Frame Photo)模型,由此进行外定向并进行实验论证。
4、将一幅线阵CCD影像首尾扫描行的外方位角元素用四元数描述,利用四元数球面线性插值(Spherical Linear Interpolation,SLERP)内插得到任意一扫描行姿态,提出了外方位元素的SLERP模型,推导出了相应的误差方程,并进行外定向计算,有效避免了欧拉角模型涉及的大量三角函数计算及不稳定因素,为线阵CCD影像外定向提供了一个新的技术途径。
5、考虑到控制点数据可能存在粗差的情况,引入粗差探测,结合基于四元数的外方位元素改进EFP模型和SLERP模型进行外定向,并利用严密的空间前方交会进行定位实验,结果论证了算法的正确性及优越性。
6、研究了基于四元数的线阵CCD影像光束法平差,该方法对平差初始值要求不高,只需取零初始值即可。实验结果表明平面的平差精度较高,高程精度稍差一些。
Line-array CCD Images are widely used in positioning of remote sensing imagery. However, the orientation parameters of traditional linearization collinear equation are highly correlated because of such factors as big flying height, small angle of coverage, narrow light beam and so on, and thus, are fairly difficult to gain steady and precise solutions. This dissertation makes a comprehensive study on the subjects related to photogrammetric positioning of the line-array CCD images based on quaternion, which includes the solution of ill-posed problem, describing exterior orientation elements by quaternion, bundle block adjustment based on quaternion, etc. The followings are what we have done in this dissertation:
1. Making a comprehensive study on the subjects related to photogrammetric positioning and close-form solution of absolute oritentaion based on quaternion, putting forward a new close-form solution method based on dual quaternion. Dual quaternion is introduced into absolute orientation to describe rotation parameters and translation parameters, and experiments were done in all these methods.
2. Analyzing the reasons theoretically to ill-posed problems which are appeared in the process of solving exterior orientation elements, and putting forward an improved bias-estimation method to compute the exterior orientation elements of line-array CCD images in the aspect of computation methods.
3. Using quaternion to describe the attitude elements of line-array CCD images in the aspect of model selection, putting forward an improved EFP model of exterior orientation elements based on the idea of Equivalent Frame Photo, and doing some exterior orientation experiments through the improved EFP model.
4. Gaining the quaternion attitude elements of any scan line through the method of Spherical Linear Interpolation of quaternion, when quaternion is used to describe the exterior orientation elements of the first and the last scan line of a line-array CCD image, putting forward a SLERP model for exterior orientation elements, and then doing some exterior orientation experiments by SLERP model. It successfully avoids a great deal of computation of trigonometric functions and the potential unstable factors, provides a new technique for exterior orientation of line-array CCD image.
5. Considering that there are some coordinate blunders in Ground Control Points (GCPs), a blunder detection method is used in the process of exterior orientation by the combination of quaternion improved EFP model and quaternion SLERP model, doing some positioning experiments by space intersection, and the experimental results verified the reliability and stability of these methods.
6. The quaternion-based bundle block adjustment of line-array CCD images is studied in this dissertation. Favorable initial values of computation parameters in bundle block adjustment are not required by this method, and the initial values can be assumed to zero. Experimental results indicate that the plane precision is very high, while the height precision is less admirable.
引文
[1]David G E.Mapping with a strip camera[J].PERS,1961:638-652.
[2]Eugnee Derenyi,Konecny G.Oeientation of Continuous Strip Imagery[J].PE,1966,32(3):773-779.
[3]Colvoresses,an Automated Mapping Satelite System(Mapsat)[J].PE&RS,1982,48(10):1585-1591.
[4]李德仁,程家喻.SPOT影像的光束法平差[J].测绘学报,1988,17(3):162-170.
[5]R.G.Ley.Some Aspects of Heighting Extraction from SPOT Imagery[J].Photogrammetric Record,1988,12(72):823-832.
[6]AL-ROUSAN N,CHENG P.Automated DEM Extraction and Orthoimage Generation from SPOT Level 1B Imagery[J].1997,63(8):965-974.
[7]ORUN A.B.,NATARAJAN K.,A Modified Bundle Adjustment Software for SPOT Imagery and Photography:Tradeoff[J].Photogrammetric Engineering & Remote Sensing,1994,60(12):1431-1437.
[8]N.G.Kardoulas,A.C.Bird,A.I.Lawan.Geometric Correction of SPOT and Landsat Imagery:A Comparison of Map-and GPS-Derived Control Points[J].PE&RS,1996,62(10):1173-1177.
[9]P.V.Radhadevi,R.Ramachandran.A.S.R.K.V.Murali Mohan.Restitution of IRS-1C PAN Data Using An Orbit Attitude Model and Minimum Control[J].ISPRS Journal of Photogrammetry & Remote Sensing,1998,53(2):262-271.
[10]Clive Fraser,Juliang Shao.Exterior Orientation Determination of MOMS-02 Three-Line Imagry:Experiences with Australian Testfield Data[A].IAPRS,Vienna,1996,31(B3):207-214.
[11]W.Komus,M.Lehner,H.Ebner,et al.Photogrammetric point determination and DEM generation using MOMS-2P/PRIRODA three-line imagery[A].In:ISPRS Commission IV "GIS Between Visions and Applications",Stuttgart,Germany,1998.
[12]姜挺,龚志辉,江刚武等.基于三线阵航天遥感影像的DEM自动生成[J].测绘学院学报,2004,21(3):178-183.
[13]黄玉琪.数字摄影测量若干关键技术的研究与实践[D].郑州:信息工程大学博士学位论文.2000.
[14]张艳.线阵列推扫式影像的数字摄影测量处理[D].郑州:信息工程大学硕士学位论文.2003.
[15]郭海涛.基于卫星遥感影像的单片测图与修测技术的研究[D].郑州:信息工程大学硕士学位论文.2002.
[16]张鹏强.线阵CCD遥感卫星影像目标精确定位技术研究与实践[D].郑州:信息工程大学硕士学位论文.2003.
[17]Okamoto Atsushi,et al.Geometric characteristics of alternative triangulation models for satellite image [J],ASPRS 1999 Annual Conference Proceedings,Orego,USA,1999.
[18]Susumu Hattori,et al.Orientation of high-resolution satellite image based on affine model[J].International Archives of Photogrammetry and Remote Sensing.Amsterdam,2000,XIX(B3):359-366.
[19]Tetsu Ono.Digital mapping using high resolution satellite imagery based on 2D Affine Projection Model [J].International Archives of Photogrammetry and Remote Sensing.Amsterdam,2000,XIX(B3):672-677.
[20]Tao C Vincent,Yong Hu.Image rectification using a generic sensor model-rational function model[J].International Archives of Photogrammetry and Remote Sensing.Amsterdam,2000,XIX(B4):874-881.
[21]Tao C Vincent,Yong Hu.A Comprehensive Study of the Rational Function Model for Photogrammetry Processing[J].Photogrammetric Engineering and Remote Senering.2001.67(12):1347-1357.
[22]Xinghe Yang.Piece-wise linear rational function approximation in digital photogrammetry.ASPRS 2001Annual Conference Proceeding.St.Louis,USA,2001.
[23]Ian Dowman,John T Dolloff.An evaluation of rational funcation for photogrammetric restitution[J].International Archives of Photogrammetry and Remote Sensing.Amsterdam,2000,XIX(B3):254-266.
[24]Yong Hu,Tao C Vincent.Updating solutions of rational funcational model using additional control points for enhanced photogrammtric processing[J].Proceeding of ISPRS Working Group I/2,I/5 and I/7 on "High Resolution Mapping from Space 2001".Hanover,Germany,2001.
[25]Thierry T and C Philip.2000.Demystification ofIKONOS[J].Earth Observation Magazine(EOM).(7).
[26]张剑清,张祖勋.高分辨率遥感影像基于仿射变换的严格几何模型[J],武汉大学学报·信息科学版,2002.6,27(6):555-559.
[27]张永生,巩丹超等.高分辨率遥感卫星应用——成像模型、处理算法及应用技术[M],北京:科学出版社,2004.
[28]巩丹超.高分辨率卫星遥感立体影像处理模型与算法[D].郑州:信息工程大学博士学位论文.2000.
[29]刘军.高分辨率卫星CCD立体影像定位技术研究[D].郑州:信息工程大学硕士学位论文.2003.
[30]Udo Tempelmann,Bruce Chaplin,et al.Photogrammetric Software For The LH Systems ADS40 Airborne Digital Sensor[A].IAPRS,ⅩⅩⅩⅢ(B2),Amsterdam,2000.
[31]Changno Lee,HENRY J,et al.Rigorous Mathematical,Modeling of Airborne Pushbroom Imaging Systems[J].PE&RS,2000,66(4):385-392.
[32]Daniela Poli.General Model for Airborne and Spacebome Line Array Sensors[A].In:Pecora 15/Land Satellite Information Ⅳ/ISPRS Commission I/FIEOS 2002 Conference Proceedings.Denver,USA,2002.
[33]Alanip,Naser EL-Sheimy,et al.System Performance Analysis of INS/DGPS Intergrated System for Mobile Mapping Systems[A].The 4~(th) International Symposiumon Mobile Mapping Technology,2004.
[34]Falin Wu,Kefei Zhang,James Macnae.An Investigation of Precise Point Positioning Application for Airborne Geophysical Survey[A].In:IGNSS Symposium 2006,Australia.
[35]李德仁,赵双明,陆宇红等.机载三线阵传感器影像区域网联合平差[J],测绘学报,2007.8,36(3):245-250.
[36]赵双明,李德仁.ADS40机载数字传感器平差数学模型及其实验[J],测绘学报,2006.11,35(4):342-346.
[37]刘军.GPS/IMU辅助机载线阵CCD影像定位技术研究[D].郑州:信息工程大学博士学位论文.2007.
[38]刘俊峰.三维转动的四元数表达[J].大学物理,2003,23(4):39-43.
[39]HAMILTON W R.Elements of Quaternions[M].London:Longmans Green and Co.,1899.
[40]Fuzhen Zhang.Quaternions and Matrices of Quatemions[J].LINEAR ALGEBRA AND ITS APPLICATIONS 1997,252:21-57.
[41]黄钢.一种用于陀螺对准估计的非线性观测器[J],导航与控制译文集,2004,2:55-58.
[42]张士邈,刘放,秦永元.捷联惯导姿态算法若干问题的研究[J].中国惯性技术学报,2002,10(2):1-6.
[43]肖亚伦.航天器飞行动力学原理[M],北京:宇航出版社,1995.
[44]周江华,苗育红,李宏等.四元数在刚体姿态仿真中的应用研究[J].飞行力学,2000,18(4):28-32.
[45]陈万春,肖亚伦,赵丽红等.四元数的核心矩阵及其在航天器姿态控制中的应用[J].航空学报,2009.9,21(5):389-392.
[46]张燕.利用四元数实现三维地球场景的漫游[J],计算机工程与应用,2004,33:59-61.
[47]詹海生,李广鑫,王鸿利.3D游戏与计算机图形学中的数学方法[M],北京:清华大学出版社,2004.
[48]Berthold K.P.Horn.closed-form solution of absolute orientation using unit quatenions[J],Optical Society of America,1987,4(4):629-642.
[49]Dr.Ljudmila meister,Quatemions and their application in Photogrammetry and Navigation[D],Tu Bergakademie Freiberg,Freiberg Germany,1997.
[50]江刚武,姜挺,王勇,龚辉.基于单位四元数的无初值依赖空间后方交会[J],测绘学报,2007.5,36(2):169-175.
[51]王勇,姜挺,江刚武等.基于单位四元数描述的单像空间后方交会[J],测绘科学技术学报,2007,24(2):133-135.
[52]屈昊.基于对偶四元数的三维物体匹配方法的研究[D],哈尔滨工程大学,2004.
[53]江延川.解析摄影测量学[M].北京:解放军出版社,1991:232-246.
[54]E.H.Thompson.On exact linear solution of the problem of absolute orientation[J],Photogrammetria 1959,15:163-179.
[55]G.H.Schut.On exact linear equations for the computation of the rotational elements of absolute orientation[J],Photogrammetria,1960,16:34-37.
[56]H.L.Oswal,S.Balasubramanian.An exact solution of absolute orientation[J],Photogramm.1968,Eng.34:1079-1083.
[57]Berthold K.P.Horn.Closed-form solution of absolute orientation using orthonormal matrices[J].Journal of the optical society of America,Series A.1988.5(7):1127-1135.
[58]胡永胜,李海鸿.绝对定向的一种线性解法[J],武测科技,1990,3:16-21.
[59]龚辉,江刚武,姜挺.基于单位四元数的绝对定向直接解法[J].测绘通报,2007.9,9:10-13.
[60]江刚武,王净,张锐.基于单位四元数的绝对定向直接解法[J].测绘科学技术学报,2007.6,24(3):193-199.
[61]James Samuel Goddard.POSE AND MOTION ESTIMATION FROM VISION USING DUAL QUATERNION-BASED EXTENDED KALMAN FILTERING[D],The University of Tennessee,Knoxville,1997.
[62]武雪冬,王耀南.基于八元数的立体摄像机外部参数定标方法[J],湖南理工学院学报(自然科学版),2003.9,16(3):25-29.
[63]李炽岚.深海采矿补偿平台并联机构单位对偶四元数位置分析[J],能源技术与管理,2006,6:61-63.
[64]张劲夫,蔡泰信.对偶四元数及其在刚体定位中的应用[J],黄淮学刊,1993.12,9(4):27-30.
[65]朱述龙,朱宝山,王红卫.遥感图像处理与应用[M].北京:科学出版社,2006.
[66]钱曾波,刘静宇,肖国超.航天摄影测量tM].北京:解放军出版社.1990.
[67]朱华统,黄继文.椭球大地计算[M].北京:八一出版社.2001.
[68]康宁.基于GPU的全球地形实时绘制技术,郑州:信息工程大学硕士学位论文.2007.
[69]郭海涛,张保明,归庆明.广义岭估计在解算单线阵CCD卫星影像外方位元素中的应用[J].武汉大学学报信息科学版,2003.8,28(4):444-447.
[70]王涛,张艳,徐青,谭兵,邢帅.线阵推扫式影像外定向的一种新算法[J].测绘学报,2005,34(1):35-39.
[71]燕琴,张祖勋,张剑清.异轨遥感CCD影像外方位元素的解求[J].武汉测绘科技大学学报·信息科学版,2001,26(3):270-274.
[72]Yasser El-Mandili,Kurt Novak.Precision Rectification of SPOT Imagery Using the Direct Linear Transform Model[J].PE&RS,1996,62(1):67-72.
[73]王振杰.测量中不适定问题的正则化解法[M],北京:科学出版社,2006.
[74]隋立芬,宋力杰.误差理论与测量平差基础[M].郑州:信息工程大学测绘学院出版社,2003.
[75]郭建锋.测量平差系统病态性的诊断与处理[D].郑州:信息工程大学硕士学位论文,2002.
[76]陈希孺,王松桂.近代回归分析[M].合肥:安徽教育出版社.1987.
[77]Tikhonov A N,Arsenin V Y.Solution of Ill-Posed Problems[M].New York:Wiley.1977.
[78]刘继军.不适定问题的正则化方法及应用[M],北京:科学出版社,2005.
[79]王振杰,欧吉坤,柳林涛.一种解算病态问题的方法——两步解法[J].武汉大学学报·信息科学版,2005.9,30(9):821-824.
[80]肖庭延,于慎根,王彦飞.反问题的数值解法[M],北京:科学出版社,2003.
[81]王振杰,欧吉坤.用L-曲线法确定岭估计中的岭参数[J].武汉大学学报·信息科学版,2004.3,29(3):235-238.
[82]Hansen P C,O' Leary D P.The use of the l-curve in the regularization of discrete Ill-posed problem[J].SIAM J.Sci.Comput,1993,14(6):1487-1503.
[83]王勇.基于四元数描述的摄影测量定位理论研究[D].郑州:信息工程大学硕士学位论文,2007.
[84]王任享.三线阵CCD影像卫星摄影测量原理[M].北京:测绘出版社.2006.
[85]宋伟东,王伟玺,胡行华.利用Metadata数据文件精确获取SPOT-5外方位元素[J],测绘通报,2003,12:29-31.
[86]燕琴,张继贤.SPOT5 Dimap文件解析及其在影像纠正中的应用[J],遥感信息,2005.5:12-15.
[87]虞铭财,杨勋年,汪国昭.高阶连续的单位四元数插值曲线[J].计算机辅助设计与图形学学报,2005.3,17(3):437-441.
[88]徐青,吴寿虎,朱述龙,邱振戈.近代摄影测量[M].北京:解放军出版社.2000.
[89]李德仁.利用选择权迭代法进行粗差定位[J].武汉测绘学院学报,1984,9(1):48-66.
[90]张祖勋,张剑清.数字摄影测量学[M].武汉:武汉测绘科技大学出版社.1990:220-224.
[91]杜治全,郑顺义.光束法平差的一种快速算法[J].地理空间信息,2007.2,5(1):78-80.
[92]袁修孝,季顺平.谢酬.基于已知定向参数影像的光束法区域网平差[J].武汉大学学报·信息科学版,2005.11,30(11):955-959.
[93]张森林.三行线阵列扫描数据的平差方案及精度分析[J].武汉测绘科技大学学报,1988,13(4):60-69.
[2]Eugnee Derenyi,Konecny G.Oeientation of Continuous Strip Imagery[J].PE,1966,32(3):773-779.
[3]Colvoresses,an Automated Mapping Satelite System(Mapsat)[J].PE&RS,1982,48(10):1585-1591.
[4]李德仁,程家喻.SPOT影像的光束法平差[J].测绘学报,1988,17(3):162-170.
[5]R.G.Ley.Some Aspects of Heighting Extraction from SPOT Imagery[J].Photogrammetric Record,1988,12(72):823-832.
[6]AL-ROUSAN N,CHENG P.Automated DEM Extraction and Orthoimage Generation from SPOT Level 1B Imagery[J].1997,63(8):965-974.
[7]ORUN A.B.,NATARAJAN K.,A Modified Bundle Adjustment Software for SPOT Imagery and Photography:Tradeoff[J].Photogrammetric Engineering & Remote Sensing,1994,60(12):1431-1437.
[8]N.G.Kardoulas,A.C.Bird,A.I.Lawan.Geometric Correction of SPOT and Landsat Imagery:A Comparison of Map-and GPS-Derived Control Points[J].PE&RS,1996,62(10):1173-1177.
[9]P.V.Radhadevi,R.Ramachandran.A.S.R.K.V.Murali Mohan.Restitution of IRS-1C PAN Data Using An Orbit Attitude Model and Minimum Control[J].ISPRS Journal of Photogrammetry & Remote Sensing,1998,53(2):262-271.
[10]Clive Fraser,Juliang Shao.Exterior Orientation Determination of MOMS-02 Three-Line Imagry:Experiences with Australian Testfield Data[A].IAPRS,Vienna,1996,31(B3):207-214.
[11]W.Komus,M.Lehner,H.Ebner,et al.Photogrammetric point determination and DEM generation using MOMS-2P/PRIRODA three-line imagery[A].In:ISPRS Commission IV "GIS Between Visions and Applications",Stuttgart,Germany,1998.
[12]姜挺,龚志辉,江刚武等.基于三线阵航天遥感影像的DEM自动生成[J].测绘学院学报,2004,21(3):178-183.
[13]黄玉琪.数字摄影测量若干关键技术的研究与实践[D].郑州:信息工程大学博士学位论文.2000.
[14]张艳.线阵列推扫式影像的数字摄影测量处理[D].郑州:信息工程大学硕士学位论文.2003.
[15]郭海涛.基于卫星遥感影像的单片测图与修测技术的研究[D].郑州:信息工程大学硕士学位论文.2002.
[16]张鹏强.线阵CCD遥感卫星影像目标精确定位技术研究与实践[D].郑州:信息工程大学硕士学位论文.2003.
[17]Okamoto Atsushi,et al.Geometric characteristics of alternative triangulation models for satellite image [J],ASPRS 1999 Annual Conference Proceedings,Orego,USA,1999.
[18]Susumu Hattori,et al.Orientation of high-resolution satellite image based on affine model[J].International Archives of Photogrammetry and Remote Sensing.Amsterdam,2000,XIX(B3):359-366.
[19]Tetsu Ono.Digital mapping using high resolution satellite imagery based on 2D Affine Projection Model [J].International Archives of Photogrammetry and Remote Sensing.Amsterdam,2000,XIX(B3):672-677.
[20]Tao C Vincent,Yong Hu.Image rectification using a generic sensor model-rational function model[J].International Archives of Photogrammetry and Remote Sensing.Amsterdam,2000,XIX(B4):874-881.
[21]Tao C Vincent,Yong Hu.A Comprehensive Study of the Rational Function Model for Photogrammetry Processing[J].Photogrammetric Engineering and Remote Senering.2001.67(12):1347-1357.
[22]Xinghe Yang.Piece-wise linear rational function approximation in digital photogrammetry.ASPRS 2001Annual Conference Proceeding.St.Louis,USA,2001.
[23]Ian Dowman,John T Dolloff.An evaluation of rational funcation for photogrammetric restitution[J].International Archives of Photogrammetry and Remote Sensing.Amsterdam,2000,XIX(B3):254-266.
[24]Yong Hu,Tao C Vincent.Updating solutions of rational funcational model using additional control points for enhanced photogrammtric processing[J].Proceeding of ISPRS Working Group I/2,I/5 and I/7 on "High Resolution Mapping from Space 2001".Hanover,Germany,2001.
[25]Thierry T and C Philip.2000.Demystification ofIKONOS[J].Earth Observation Magazine(EOM).(7).
[26]张剑清,张祖勋.高分辨率遥感影像基于仿射变换的严格几何模型[J],武汉大学学报·信息科学版,2002.6,27(6):555-559.
[27]张永生,巩丹超等.高分辨率遥感卫星应用——成像模型、处理算法及应用技术[M],北京:科学出版社,2004.
[28]巩丹超.高分辨率卫星遥感立体影像处理模型与算法[D].郑州:信息工程大学博士学位论文.2000.
[29]刘军.高分辨率卫星CCD立体影像定位技术研究[D].郑州:信息工程大学硕士学位论文.2003.
[30]Udo Tempelmann,Bruce Chaplin,et al.Photogrammetric Software For The LH Systems ADS40 Airborne Digital Sensor[A].IAPRS,ⅩⅩⅩⅢ(B2),Amsterdam,2000.
[31]Changno Lee,HENRY J,et al.Rigorous Mathematical,Modeling of Airborne Pushbroom Imaging Systems[J].PE&RS,2000,66(4):385-392.
[32]Daniela Poli.General Model for Airborne and Spacebome Line Array Sensors[A].In:Pecora 15/Land Satellite Information Ⅳ/ISPRS Commission I/FIEOS 2002 Conference Proceedings.Denver,USA,2002.
[33]Alanip,Naser EL-Sheimy,et al.System Performance Analysis of INS/DGPS Intergrated System for Mobile Mapping Systems[A].The 4~(th) International Symposiumon Mobile Mapping Technology,2004.
[34]Falin Wu,Kefei Zhang,James Macnae.An Investigation of Precise Point Positioning Application for Airborne Geophysical Survey[A].In:IGNSS Symposium 2006,Australia.
[35]李德仁,赵双明,陆宇红等.机载三线阵传感器影像区域网联合平差[J],测绘学报,2007.8,36(3):245-250.
[36]赵双明,李德仁.ADS40机载数字传感器平差数学模型及其实验[J],测绘学报,2006.11,35(4):342-346.
[37]刘军.GPS/IMU辅助机载线阵CCD影像定位技术研究[D].郑州:信息工程大学博士学位论文.2007.
[38]刘俊峰.三维转动的四元数表达[J].大学物理,2003,23(4):39-43.
[39]HAMILTON W R.Elements of Quaternions[M].London:Longmans Green and Co.,1899.
[40]Fuzhen Zhang.Quaternions and Matrices of Quatemions[J].LINEAR ALGEBRA AND ITS APPLICATIONS 1997,252:21-57.
[41]黄钢.一种用于陀螺对准估计的非线性观测器[J],导航与控制译文集,2004,2:55-58.
[42]张士邈,刘放,秦永元.捷联惯导姿态算法若干问题的研究[J].中国惯性技术学报,2002,10(2):1-6.
[43]肖亚伦.航天器飞行动力学原理[M],北京:宇航出版社,1995.
[44]周江华,苗育红,李宏等.四元数在刚体姿态仿真中的应用研究[J].飞行力学,2000,18(4):28-32.
[45]陈万春,肖亚伦,赵丽红等.四元数的核心矩阵及其在航天器姿态控制中的应用[J].航空学报,2009.9,21(5):389-392.
[46]张燕.利用四元数实现三维地球场景的漫游[J],计算机工程与应用,2004,33:59-61.
[47]詹海生,李广鑫,王鸿利.3D游戏与计算机图形学中的数学方法[M],北京:清华大学出版社,2004.
[48]Berthold K.P.Horn.closed-form solution of absolute orientation using unit quatenions[J],Optical Society of America,1987,4(4):629-642.
[49]Dr.Ljudmila meister,Quatemions and their application in Photogrammetry and Navigation[D],Tu Bergakademie Freiberg,Freiberg Germany,1997.
[50]江刚武,姜挺,王勇,龚辉.基于单位四元数的无初值依赖空间后方交会[J],测绘学报,2007.5,36(2):169-175.
[51]王勇,姜挺,江刚武等.基于单位四元数描述的单像空间后方交会[J],测绘科学技术学报,2007,24(2):133-135.
[52]屈昊.基于对偶四元数的三维物体匹配方法的研究[D],哈尔滨工程大学,2004.
[53]江延川.解析摄影测量学[M].北京:解放军出版社,1991:232-246.
[54]E.H.Thompson.On exact linear solution of the problem of absolute orientation[J],Photogrammetria 1959,15:163-179.
[55]G.H.Schut.On exact linear equations for the computation of the rotational elements of absolute orientation[J],Photogrammetria,1960,16:34-37.
[56]H.L.Oswal,S.Balasubramanian.An exact solution of absolute orientation[J],Photogramm.1968,Eng.34:1079-1083.
[57]Berthold K.P.Horn.Closed-form solution of absolute orientation using orthonormal matrices[J].Journal of the optical society of America,Series A.1988.5(7):1127-1135.
[58]胡永胜,李海鸿.绝对定向的一种线性解法[J],武测科技,1990,3:16-21.
[59]龚辉,江刚武,姜挺.基于单位四元数的绝对定向直接解法[J].测绘通报,2007.9,9:10-13.
[60]江刚武,王净,张锐.基于单位四元数的绝对定向直接解法[J].测绘科学技术学报,2007.6,24(3):193-199.
[61]James Samuel Goddard.POSE AND MOTION ESTIMATION FROM VISION USING DUAL QUATERNION-BASED EXTENDED KALMAN FILTERING[D],The University of Tennessee,Knoxville,1997.
[62]武雪冬,王耀南.基于八元数的立体摄像机外部参数定标方法[J],湖南理工学院学报(自然科学版),2003.9,16(3):25-29.
[63]李炽岚.深海采矿补偿平台并联机构单位对偶四元数位置分析[J],能源技术与管理,2006,6:61-63.
[64]张劲夫,蔡泰信.对偶四元数及其在刚体定位中的应用[J],黄淮学刊,1993.12,9(4):27-30.
[65]朱述龙,朱宝山,王红卫.遥感图像处理与应用[M].北京:科学出版社,2006.
[66]钱曾波,刘静宇,肖国超.航天摄影测量tM].北京:解放军出版社.1990.
[67]朱华统,黄继文.椭球大地计算[M].北京:八一出版社.2001.
[68]康宁.基于GPU的全球地形实时绘制技术,郑州:信息工程大学硕士学位论文.2007.
[69]郭海涛,张保明,归庆明.广义岭估计在解算单线阵CCD卫星影像外方位元素中的应用[J].武汉大学学报信息科学版,2003.8,28(4):444-447.
[70]王涛,张艳,徐青,谭兵,邢帅.线阵推扫式影像外定向的一种新算法[J].测绘学报,2005,34(1):35-39.
[71]燕琴,张祖勋,张剑清.异轨遥感CCD影像外方位元素的解求[J].武汉测绘科技大学学报·信息科学版,2001,26(3):270-274.
[72]Yasser El-Mandili,Kurt Novak.Precision Rectification of SPOT Imagery Using the Direct Linear Transform Model[J].PE&RS,1996,62(1):67-72.
[73]王振杰.测量中不适定问题的正则化解法[M],北京:科学出版社,2006.
[74]隋立芬,宋力杰.误差理论与测量平差基础[M].郑州:信息工程大学测绘学院出版社,2003.
[75]郭建锋.测量平差系统病态性的诊断与处理[D].郑州:信息工程大学硕士学位论文,2002.
[76]陈希孺,王松桂.近代回归分析[M].合肥:安徽教育出版社.1987.
[77]Tikhonov A N,Arsenin V Y.Solution of Ill-Posed Problems[M].New York:Wiley.1977.
[78]刘继军.不适定问题的正则化方法及应用[M],北京:科学出版社,2005.
[79]王振杰,欧吉坤,柳林涛.一种解算病态问题的方法——两步解法[J].武汉大学学报·信息科学版,2005.9,30(9):821-824.
[80]肖庭延,于慎根,王彦飞.反问题的数值解法[M],北京:科学出版社,2003.
[81]王振杰,欧吉坤.用L-曲线法确定岭估计中的岭参数[J].武汉大学学报·信息科学版,2004.3,29(3):235-238.
[82]Hansen P C,O' Leary D P.The use of the l-curve in the regularization of discrete Ill-posed problem[J].SIAM J.Sci.Comput,1993,14(6):1487-1503.
[83]王勇.基于四元数描述的摄影测量定位理论研究[D].郑州:信息工程大学硕士学位论文,2007.
[84]王任享.三线阵CCD影像卫星摄影测量原理[M].北京:测绘出版社.2006.
[85]宋伟东,王伟玺,胡行华.利用Metadata数据文件精确获取SPOT-5外方位元素[J],测绘通报,2003,12:29-31.
[86]燕琴,张继贤.SPOT5 Dimap文件解析及其在影像纠正中的应用[J],遥感信息,2005.5:12-15.
[87]虞铭财,杨勋年,汪国昭.高阶连续的单位四元数插值曲线[J].计算机辅助设计与图形学学报,2005.3,17(3):437-441.
[88]徐青,吴寿虎,朱述龙,邱振戈.近代摄影测量[M].北京:解放军出版社.2000.
[89]李德仁.利用选择权迭代法进行粗差定位[J].武汉测绘学院学报,1984,9(1):48-66.
[90]张祖勋,张剑清.数字摄影测量学[M].武汉:武汉测绘科技大学出版社.1990:220-224.
[91]杜治全,郑顺义.光束法平差的一种快速算法[J].地理空间信息,2007.2,5(1):78-80.
[92]袁修孝,季顺平.谢酬.基于已知定向参数影像的光束法区域网平差[J].武汉大学学报·信息科学版,2005.11,30(11):955-959.
[93]张森林.三行线阵列扫描数据的平差方案及精度分析[J].武汉测绘科技大学学报,1988,13(4):60-69.