平面控制网的复数域最小二乘法估计研究
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摘要
首先依照复数概念与其几何意义对边角控制网、附合导线、坐标转换等测量平差问题进行研究,概括出二维平面上复函型误差方程一般式.然后依据复数域最小二乘法原理,对复函型误差方程进行平差分析.分析过程中克服复数代数化处理的繁琐性弊端,运用矩阵不等式,向量运算等数学工具,得到复数域经典平差模型,拓充经典平差理论.最后通过算例比较,验证复数域经典平差模型的正确性,并分析其应用的合理性.
Firstly, on the basis of study on triangulateration control network adjustment,connecting traverse adjustment,forward intersection and so on,which are based on complex concept and geometry in the paper,general formula of complex error equation of plane survey is proposed.Then adjustment analysis is tried to do according to the least squares theory.It overcomes complicated computation and lengthiness formulas of traditional algebraization.The matrix inequalities and vector operation are used in order to build the complex least squares adjustment model and perfect the surveying adjustment system.Lastly,a comparison of two ways of the example indicates the correctness and effective of this method.
Firstly, on the basis of study on triangulateration control network adjustment,connecting traverse adjustment,forward intersection and so on,which are based on complex concept and geometry in the paper,general formula of complex error equation of plane survey is proposed.Then adjustment analysis is tried to do according to the least squares theory.It overcomes complicated computation and lengthiness formulas of traditional algebraization.The matrix inequalities and vector operation are used in order to build the complex least squares adjustment model and perfect the surveying adjustment system.Lastly,a comparison of two ways of the example indicates the correctness and effective of this method.
引文
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[2]付海强,朱建军,汪长城,等.极化干涉SAR植被高反演复数最小二乘平差法[J].测绘学报,2014,43(10):1061-1607.FU H Q,ZHU J J,WANG C C,et al.Polarimetric SARinterferometry vegetation height inversion method of complex least squares adjustment[J].Acta Geodaetica et Cartographica Sinica,2014,43(10):1061-1607.(Ch).
[3]朱建军,解清华,左廷英,等.复数域最小二乘平差及其在PoIInSAR植被高反演中的应用[J].测绘学报,2014,43(1):45-51.ZHU J J,XIE Q H,ZUO T Y,et al.Criterion of complex least squares adjustment and its application in tree height inversion with PoIInSAR data[J].Acta Geodaetica et Cartographica Sinica,2014,43(1):45-51.(Ch).
[4]林磊.复数的矩阵表示[J].数学教学,2009,6(38):28-32.LIN L.The array expressions of complex number[J].Mathematics Teaching.2009,6(38):28-32.(Ch).
[5]催博文,陈剑,陈心昭,等.复参数最小二乘估计方法[J].安徽大学学报(自然科学版),2005,29(3):5-10.CUI B W,CHEN J,CHEN X Z,et al.Least square method for complex estimation[J].Journal of Anhui University(Natural Science Edition),2005,29(3):5-10.(Ch).
[6]董勇,李梦霞.复数域内最小二乘法估计公式的证明[J].长江大学学报(自然科学版),2007,4(2):129-130.DONG Y,LI M X.The prove to the formula of complex least squares[J].Journal of Yangtze University(Natural Science Edition),2007,4(2):129-130.(Ch).
[7]测量平差教研室.误差理论与测量平差[M].武汉:武汉大学出版社,2007.Surveying Adjustment Teaching and Research Section.Error Theory and Surveying Adjustment[M].Wuhan:Wuhan University Press,2007.(Ch).
[8]张勤,张菊清,岳东杰,等.近代测量数据处理与应用[M].北京:测绘出版社,2011.ZHANG Q,ZHANG J Q,YUE D J,et al.Modern Surveying Data Processing and Application[M].Beijing:Surveying and Mapping Press,2011.(Ch).
[9]西安交通大学高等数学教研室.工程数学复变函数[M].4版.北京:高等教育出版社,2011.Teaching and Research Section of Advanced Mathematics of Xi'an Jiaotong University.Complex Variables Functions of Engineering Mathematics[M].4th Ed.Beijing:Higher Education Press,2011.(Ch).
[10]路见可,钟寿国,刘士强.复变函数[M].武汉:武汉大学出版社,2007.LU J K,ZHONG S G,LIU S Q.Complex Variables Functions[M].Wuhan:Wuhan University Press,2007.(Ch).
[11]纪友清,曹阳,候秉喆,等.复变函数[M].北京:科学出版社,2015.JI Y Q,CAO Y,HOU B Z,et al.Complex Variables Functions[M].Beijing:Science Press,2015.(Ch).
[12]程云鹏.矩阵论[M].2版.西安:西北工业大学出版社,2004.CHENG Y P.Matrix Theory[M].2nd Ed.Xi'an:Northwestern Polytechnical University Press,2004.(Ch).