部分待估参数具有先验随机性的WTLS平差
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摘要
部分待估参数具有先验随机信息,且误差方程系数矩阵含有观测误差,是一类新的平差问题。本文构造了部分待估参数含有先验随机信息的加权整体最小二乘平差函数模型,推导该模型参数估计与精度评定公式,给出计算步骤,适用于一般情形。实例对比分析证明,该算法正确可靠,迭代收敛速度较优。
A total least square with partial random parameter adjustment problem occurs if some of the estimated parameters in an adjustment problem have priori random information and the error equation coefficient matrix contains observation errors.This paper proposes a function model of total least squares adjustment with additional partial random parameters.The model has general adaptability.The algorithms formula of parameter estimation and accuracy evaluation are derived,and the steps of computation are presented,which can process the data that only partial(from 0 to all)parameter has random prior information.The feasibility,reliability and correctness of the algorithms are demonstrated by several examples and comparative analysis.The proposed algorithms have advantages in iterative convergence times.
A total least square with partial random parameter adjustment problem occurs if some of the estimated parameters in an adjustment problem have priori random information and the error equation coefficient matrix contains observation errors.This paper proposes a function model of total least squares adjustment with additional partial random parameters.The model has general adaptability.The algorithms formula of parameter estimation and accuracy evaluation are derived,and the steps of computation are presented,which can process the data that only partial(from 0 to all)parameter has random prior information.The feasibility,reliability and correctness of the algorithms are demonstrated by several examples and comparative analysis.The proposed algorithms have advantages in iterative convergence times.
引文
[1]Schaffrin B,Wieser A.On Weighted Total Least-Squares Adjustment for Linear Regression[J].Journal of Geodesy,2008,82(7):415-421
[2]Jazaeri S,Amiri-Simkooei A R,Sharifi M A.Iterative Algorithm for Weighted Total Least Squares Adjustment[J].Survey Review,2014,46(334):19-27
[3]Zhang S L,Tong X H,Zhang K L.A Solution to EIV Model with Inequality Constraints and Its Geodetic Applications[J].Journal of Geodesy,2013,87(1):23-28
[4]Shen Y Z,LI B F,Chen Y.An Iterative Solution of Weighted Total Least-Squares Adjustment[J].Journal of Geodesy,2011,85(4):229-238
[5]Schaffrin B.Total Least-Squares Collocation:The TotalLeast Squares Approach to EIV-Models with Prior Information[C].The 18th Int Workshop on Matrices and Statistics,Smolenice Castle,Slovakia,2009
[6]Snow K.Topics in Total Least-Squares Adjustment within the Errors-in-Variables Model:Singular Cofactor Matrices and Prior Information[D].Ohio:The Ohio State University,2012
[7]Snow K,Schaffrin B.Weighted Total Least-Squares Collocation with Geodetic Applications[C].The 2012 SIAM Conference on Applied Linear Algebra,Valencia,2012
[8]Snow K,Schaffrin B.Total Least-Squares Adjustment with Prior Information vs.the Penalized Least-Squares Approach to EIV-Models[C].The 59th ISI World Statistics Congress,Hong Kong,2013
[9]Fang X.Weighted Total Least Squares:Necessary and Sufficient Conditions,Fixed and Random Parameters[J].Journal of Geodesy,2013,87(8):733-749
[10]王乐洋,陈汉清,温扬茂.地壳形变分析的总体最小二乘配置方法[J].大地测量与地球动力学,2017,37(2):163-168(Wang Leyang,Chen Hanqing,Wen Yangmao.Analysis of Crust Deformation Based on Total Least Squares Collocation[J].Journal of Geodesy and Geodynamics,2017,37(2):163-168)
[11]Golub G H,Loan C F V.An Analysis of the Total Least Squares Problem[J].SIAM J Numer,Anal,1980,17(6):883-893
[12]Huffel S V,Vandewalle J.The Total Least Squares Problem:Computational Aspects and Analysis[M].Philadelphia:SIAM,1991
[13]Amiri-Simkooei A R,Zangeneh-Nejad F,Asgari J.On the Covariance Matrix of Weighted Total Least-Squares Estimates[J].Journal of Surveying Engineering,2016,142(3)
[14]Wang L Y,Zhao Y W.Unscented Transformation with Scaled Symmetric Sampling Strategy for Precision Estimation of Total Least Squares[J].Studia Geophysica et Geodaetica,2017,61(3):385-411
[15]Neri F,Saitta G,Chiofalo S.An Accurate and Straightforward Approach to Line Regression Analysis of Error-Affected Experimental Data[J].J Phys Ser E:Sci Instr,1989,22(4):215-217
[16]Gander W,Golub G H,Strebel R.Least-Squares Fitting of Circles and Ellipses[J].Bit Numerical Mathematics,1994,34(4):558-578
[17]Schaffrin B,Snow K.Total Least-Squares Regularization of Tykhonov Type and an Ancient Racetrack in Corinth[J].Linear Algebra&Its Applications,2010,432(8):2 061-2 076
[2]Jazaeri S,Amiri-Simkooei A R,Sharifi M A.Iterative Algorithm for Weighted Total Least Squares Adjustment[J].Survey Review,2014,46(334):19-27
[3]Zhang S L,Tong X H,Zhang K L.A Solution to EIV Model with Inequality Constraints and Its Geodetic Applications[J].Journal of Geodesy,2013,87(1):23-28
[4]Shen Y Z,LI B F,Chen Y.An Iterative Solution of Weighted Total Least-Squares Adjustment[J].Journal of Geodesy,2011,85(4):229-238
[5]Schaffrin B.Total Least-Squares Collocation:The TotalLeast Squares Approach to EIV-Models with Prior Information[C].The 18th Int Workshop on Matrices and Statistics,Smolenice Castle,Slovakia,2009
[6]Snow K.Topics in Total Least-Squares Adjustment within the Errors-in-Variables Model:Singular Cofactor Matrices and Prior Information[D].Ohio:The Ohio State University,2012
[7]Snow K,Schaffrin B.Weighted Total Least-Squares Collocation with Geodetic Applications[C].The 2012 SIAM Conference on Applied Linear Algebra,Valencia,2012
[8]Snow K,Schaffrin B.Total Least-Squares Adjustment with Prior Information vs.the Penalized Least-Squares Approach to EIV-Models[C].The 59th ISI World Statistics Congress,Hong Kong,2013
[9]Fang X.Weighted Total Least Squares:Necessary and Sufficient Conditions,Fixed and Random Parameters[J].Journal of Geodesy,2013,87(8):733-749
[10]王乐洋,陈汉清,温扬茂.地壳形变分析的总体最小二乘配置方法[J].大地测量与地球动力学,2017,37(2):163-168(Wang Leyang,Chen Hanqing,Wen Yangmao.Analysis of Crust Deformation Based on Total Least Squares Collocation[J].Journal of Geodesy and Geodynamics,2017,37(2):163-168)
[11]Golub G H,Loan C F V.An Analysis of the Total Least Squares Problem[J].SIAM J Numer,Anal,1980,17(6):883-893
[12]Huffel S V,Vandewalle J.The Total Least Squares Problem:Computational Aspects and Analysis[M].Philadelphia:SIAM,1991
[13]Amiri-Simkooei A R,Zangeneh-Nejad F,Asgari J.On the Covariance Matrix of Weighted Total Least-Squares Estimates[J].Journal of Surveying Engineering,2016,142(3)
[14]Wang L Y,Zhao Y W.Unscented Transformation with Scaled Symmetric Sampling Strategy for Precision Estimation of Total Least Squares[J].Studia Geophysica et Geodaetica,2017,61(3):385-411
[15]Neri F,Saitta G,Chiofalo S.An Accurate and Straightforward Approach to Line Regression Analysis of Error-Affected Experimental Data[J].J Phys Ser E:Sci Instr,1989,22(4):215-217
[16]Gander W,Golub G H,Strebel R.Least-Squares Fitting of Circles and Ellipses[J].Bit Numerical Mathematics,1994,34(4):558-578
[17]Schaffrin B,Snow K.Total Least-Squares Regularization of Tykhonov Type and an Ancient Racetrack in Corinth[J].Linear Algebra&Its Applications,2010,432(8):2 061-2 076