Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with rand...Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.展开更多
三维基准转换广泛应用于大地测量、摄影测量、点云配准等领域,求解大角度、任意比例尺的三维基准转换参数的研究有很多。然而,当观测值中含有粗差时,得到的转换参数估值会受到不利影响甚至被严重扭曲。为处理含有粗差的大角度三维基准...三维基准转换广泛应用于大地测量、摄影测量、点云配准等领域,求解大角度、任意比例尺的三维基准转换参数的研究有很多。然而,当观测值中含有粗差时,得到的转换参数估值会受到不利影响甚至被严重扭曲。为处理含有粗差的大角度三维基准转换问题,本文首先将大角度三维基准转换问题抽象为具有等式约束的最小二乘问题(Constrained least squares, CLS),推导参数在正交约束条件下的最小二乘解。然后,将灵敏度分析方法应用到CLS问题中,研究残差加权平方和对观测值扰动的局部敏感性,并基于这些敏感度指标构造局部检验统计量,进而推导出一个适用于CLS问题的粗差探测算法。最后,为核实该算法的有效性进行了仿真与实测数据实验。实验结果表明:本文提出的基于灵敏度检验统计量的数据探测算法可以降低粗差的负面影响,得到可靠的参数估值,从而有效解决大角度三维基准转换中的粗差处理问题。展开更多
To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model(MAM error model),we use an impr...To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model(MAM error model),we use an improved artificial bee colony algorithm without derivative and the bootstrap method to estimate the parameters and evaluate the accuracy of MAM error model.The improved artificial bee colony algorithm can update individuals in multiple dimensions and improve the cooperation ability between individuals by constructing a new search equation based on the idea of quasi-affine transformation.The experimental results show that based on the weighted least squares criterion,the algorithm can get the results consistent with the weighted least squares method without multiple formula derivation.The parameter estimation and accuracy evaluation method based on the bootstrap method can get better parameter estimation and more reasonable accuracy information than existing methods,which provides a new idea for the theory of parameter estimation and accuracy evaluation of the MAM error model.展开更多
基金the financial support of the National Natural Science Foundation of China(Grant No.42074016,42104025,42274057and 41704007)Hunan Provincial Natural Science Foundation of China(Grant No.2021JJ30244)Scientific Research Fund of Hunan Provincial Education Department(Grant No.22B0496)。
文摘Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.
文摘三维基准转换广泛应用于大地测量、摄影测量、点云配准等领域,求解大角度、任意比例尺的三维基准转换参数的研究有很多。然而,当观测值中含有粗差时,得到的转换参数估值会受到不利影响甚至被严重扭曲。为处理含有粗差的大角度三维基准转换问题,本文首先将大角度三维基准转换问题抽象为具有等式约束的最小二乘问题(Constrained least squares, CLS),推导参数在正交约束条件下的最小二乘解。然后,将灵敏度分析方法应用到CLS问题中,研究残差加权平方和对观测值扰动的局部敏感性,并基于这些敏感度指标构造局部检验统计量,进而推导出一个适用于CLS问题的粗差探测算法。最后,为核实该算法的有效性进行了仿真与实测数据实验。实验结果表明:本文提出的基于灵敏度检验统计量的数据探测算法可以降低粗差的负面影响,得到可靠的参数估值,从而有效解决大角度三维基准转换中的粗差处理问题。
基金supported by the National Natural Science Foundation of China(No.42174011 and No.41874001).
文摘To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model(MAM error model),we use an improved artificial bee colony algorithm without derivative and the bootstrap method to estimate the parameters and evaluate the accuracy of MAM error model.The improved artificial bee colony algorithm can update individuals in multiple dimensions and improve the cooperation ability between individuals by constructing a new search equation based on the idea of quasi-affine transformation.The experimental results show that based on the weighted least squares criterion,the algorithm can get the results consistent with the weighted least squares method without multiple formula derivation.The parameter estimation and accuracy evaluation method based on the bootstrap method can get better parameter estimation and more reasonable accuracy information than existing methods,which provides a new idea for the theory of parameter estimation and accuracy evaluation of the MAM error model.
