全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...
测绘学报  2015 

复数域总体最小二乘平差

DOI: 10.11947/j.AGCS.2015.20130701, PP. 866-876

Keywords: 复数,总体最小二乘,混合总体最小二乘,最小二乘,平差准则

Full-Text   Cite this paper   Add to My Lib

Abstract:

在复数域最小二乘的基础上提出了复数域总体最小二乘平差方法,推导了复数域总体最小二乘和复数混合总体最小二乘的相关公式。通过算例比较分析了复数观测值的残差的模的平方和最小(平差准则1)下及残差的实部和虚部的平方和分别最小(平差准则2)下的复数最小二乘、复数观测值和系数矩阵的残差的模的平方和最小(平差准则3)下及残差的实部和虚部的平方和分别最小(平差准则4)下的复数总体最小二乘方法的优劣。试验结果表明平差准则1下复数最小二乘较平差准则2下得到的结果更加合理,平差准则3下复数总体最小二乘较平差准则4下得到的结果更为准确;当顾及系数矩阵误差时,平差准则3下复数总体最小二乘要优于平差准则1下复数最小二乘。

References

[1]  MILLER K S. Complex Linear Least Squares[J]. SIAM Review, 1973, 15(4): 706-726.
[2]  GU Xiangqian, KANG Hongwen, CAO Hongxing. The Least-square Method in Complex Number Domain[J]. Progress in Natural Science, 2006, 16(1): 49-54. (谷湘潜, 康红文, 曹洪兴. 复数域内的最小二乘法[J]. 自然科学进展, 2006, 16(1): 49-54.)
[3]  CUI Bowen, CHEN Jian, CHEN Xinzhao, et al. U-D Factorization Based Least Squares Methods for Complex Estimation[C]//CHENG Daizhan, WANG Xingyu. Proceedings of the 23rd Chinese Control Conference. Shanghai: East China University of Science and Technology Press, 2004: 264-267. (崔博文, 陈剑, 陈心昭, 等. 基于U-D分解的复参数最小二乘估计方法[C]//程代展, 王行愚. 第二十三届中国控制会议论文集. 上海: 华东理工大学出版社, 2004: 264-267.)
[4]  CUI Bowen, CHEN Jian, CHEN Xinzhao, et al. Least Square Method for Complex Estimation[J]. Journal of Anhui University:Natural Science Edition, 2005, 29(3): 5-10. (崔博文, 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.)
[5]  DONG Yong, LI Mengxia. The Prove to the Formula of Complex Least Squares[J]. Journal of Yangtze University (Natural Science Edition) 2007, 4(2): 129-130. (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.)
[6]  LI Mengxia, CHEN Zhong. The Modification of Least Square Method (LSM) in the Complex Field[J]. Journal of Yangtze University:Natural Science Edition, 2008, 5(3): 7-8. (李梦霞, 陈忠. 复数域内最小二乘法的一种改进[J]. 长江大学学报:自然科学版, 2008, 5(3): 7-8.)
[7]  GU Xiangqian. A Spectrum Model Basing on the Principle of Atmospheric Self-memorial[J]. Chinese Science Bulletin, 1998, 43(9): 909-917. (谷湘潜. 一个基于大气自忆原理的谱模式[J]. 科学通报, 1998, 43(9): 909-917.)
[8]  GU Xiangqian, KANG Hongwen, JIANG Jianmin. Monthly Temperature Forecasts by Using a Complex Autoregressive Model[J]. Journal of Applied Meteorological Science, 2007, 18(4): 435-440. (谷湘潜, 康红文, 江剑民. 用复数自回归模式预报月平均气温[J]. 应用气象学报, 2007, 18(4): 435-440.)
[9]  GRIGOLI F, CESCA S, DAHM T, et al. A Complex Linear Least-squares Method to Derive Relative and Absolute Orientations of Seismic Sensors[J]. Geophysical Journal International, 2012, 188(3): 1243-1254.
[10]  CUI Bowen. Real-time Fault Detection Technique for Inverter Based on Complex Parameter Estimation[J]. Chinese Journal of Scientific Instrument, 2006, 27(6): 393-395. (崔博文. 基于复参数估计的逆变器故障实时检测[J]. 仪器仪表学报, 2006, 27(6): 393-395.)
[11]  ZHU Jianjun, XIE Qinghua, ZUO Tingying, et al. Criterion of Complex Least Squares Adjustment and Its Application in Tree Height Inversion with PolInSAR Data[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(1): 45-51. (朱建军, 解清华, 左廷英, 等. 复数域最小二乘平差及其在 PolInSAR 植被高反演中的应用[J]. 测绘学报, 2014, 43(1): 45-51.)
[12]  GOLUB G H, VAN LOAN C F. An Analysis of the Total Least Squares Problem[J]. SIMA Journal on Numerical Analysis, 1980, 17(6): 883-893.
[13]  SCHAFFRIN B, WIESER A. On Weighted Total Least Squares Adjustment for Linear Regression[J]. Journal of Geodesy, 2008, 82(7): 415-421.
[14]  SHEN Yunzhong, LI Bofeng, CHEN Yi. An Iterative Solution of Weighted Total Least-squares Adjustment[J]. Journal of Geodesy, 2010, 85(4): 229-238.
[15]  WANG Leyang, XU Caijun. Total Least Squares Adjustment with Weighting Scaling Factor[J]. Geomatics and Information Science of Wuhan University, 2011, 36(8): 887-890. (王乐洋, 许才军. 附有相对权比的总体最小二乘平差[J]. 武汉大学学报:信息科学版, 2011, 36(8): 887-890.)
[16]  WANG Leyang. Research on Theory and Application of Total Least Squares in Geodetic Inversion[D]. Wuhan: Wuhan University, 2011. (王乐洋. 基于总体最小二乘的大地测量反演理论及应用研究[D]. 武汉: 武汉大学, 2011.)
[17]  TONG Xiaohua, JIN Yanmin, LI Lingyun. An Improved Weighted Total Least Squares Method with Applications in Linear Fitting and Coordinate Transformation[J]. Journal of Surveying Engineering, 2011, 137(4): 120-128.
[18]  XU Caijun, WANG Leyang, WEN Yangmao, et al. Strain Rates in the Sichuan-Yunnan Region Based upon the Total Least Squares Heterogeneous Strain Model from GPS Data[J]. Terrestrial, Atmospheric and Oceanic Sciences, 2011, 22(2): 133-147.
[19]  GE Xuming, WU Jicang. Generalized Regularization to Ill-posed Total Least Squares Problem[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(3): 372-377. (葛旭明, 伍吉仓. 病态总体最小二乘问题的广义正则化[J]. 测绘学报, 2012, 41(3): 372-377.)
[20]  ZHOU Yongjun, ZHU Jianjun, DENG Caihua. The Consistency between Row-wised Weighted Total Least Squares and Condition Adjustment with Parameters[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(1): 48-53. (周拥军, 朱建军, 邓才华. 附参数的条件平差与按行独立的加权总体最小二乘法估计的一致性研究[J]. 测绘学报, 2012, 41(1): 48-53.)
[21]  WANG Leyang, XU Caijun. Progress in Total Least Squares[J]. Geomatics and Information Science of Wuhan University, 2013, 38(7): 850-856. (王乐洋, 许才军. 总体最小二乘研究进展[J]. 武汉大学学报:信息科学版, 2013, 38(7): 850-856.)
[22]  WANG Leyang, XU Caijun, WEN Yangmao. Fault Parameters of 2008 Qinghai Dacaidan Mw 6.3 Earthquake from STLN Inversion and InSAR Data[J]. Acta Geodaetica et Cartographica Sinica, 2013, 42(2): 168-176. (王乐洋, 许才军, 温扬茂. 利用STLN和InSAR数据反演2008年青海大柴旦Mw 6.3级地震断层参数[J]. 测绘学报, 2013, 42(2): 168-176.)
[23]  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. (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.)
[24]  HU Chuan, CHEN Yi. An Iterative Algorithm for Nonlinear Total Least Squares Adjustment[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(7): 668-674. (胡川, 陈义. 非线性整体最小平差迭代算法[J]. 测绘学报, 2014, 43(7): 668-674.)
[25]  YAO Yibin, KONG Jian. A New Combined LS Method Considering Random Errors of Design Matrix[J]. Geomatics and Information Science of Wuhan University, 2014, 39(9): 1028-1032. (姚宜斌, 孔建. 顾及设计矩阵随机误差的最小二乘组合新解法[J]. 武汉大学学报:信息科学版, 2014, 39(9): 1028-1032.)
[26]  XU Peiliang, LIU Jingnan, ZENG Wenxian, et al. Effects of Errors-in-variables on Weighted Least Squares Estimation[J]. Journal of Geodesy, 2014, 88(7): 705-716.
[27]  The Complex Random Matrix Submit to Normal Distribution[DB/OL]. (2012-05-20)[2013-06-17]. http://www.docin.com/p-668298205.html.
[28]  ZENG Wenxian. Effect of the Random Design Matrix on Adjustment of an EIV Model and Its Reliability Theory[D]. Wuhan: Wuhan University, 2013: 27-55. (曾文宪. 系数矩阵误差对EIV模型平差结果的影响研究[D]. 武汉: 武汉大学, 2013: 27-55.)

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133