When linearizing three-dimensional(3 D)coordinate similarity transformation model with large rotations,we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions.To alleviate the...When linearizing three-dimensional(3 D)coordinate similarity transformation model with large rotations,we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions.To alleviate the problem,a series of conversions are contributed to the 3 D coordinate similarity transformation model in this paper.We deduced a complete solution for the 3 D coordinate similarity transformation at any rotation with the nonlinear adjustment methodology,which involves the errors of the common and the non-common points.Furthermore,as the large condition number of the normal matrix resulted in an intractable form,we introduced the bary-centralization technique and a surrogate process for deterministic element of the normal matrix,and proved its benefit for alleviating the condition number.The experimental results show that our approach can obtain the smaller condition number to stabilize the convergence of the interested parameters.Especially,our approach can be implemented for considering the errors of the common and the non-common points,thus the accuracy of the transformed coordinates improves.展开更多
In this paper, a transformation model named SARC(static-filter adjustment with restricted condition) is presented, which is more practical and more rigorous in theory and fitting any angle of rotation parameter. The t...In this paper, a transformation model named SARC(static-filter adjustment with restricted condition) is presented, which is more practical and more rigorous in theory and fitting any angle of rotation parameter. The transformation procedure is divided into 4 steps: ① the original and object coordinates can be regarded as observations with errors; ② rigorous formula is firstly deduced in order to compute the first approximation of the transformation parameters by use of four common points and the transformation equation is linearized; ③ calculate the most probable values and variances of the seven transformation parameters by SARC model; ④ to demonstrate validity of SARC , an example is given.展开更多
This paper deals with transformation procedures for observed GPS data from the world geodetic system WGS84 into the national geodetic grid datum SUTCN （system of united trigonometric cadaster network） and Baa（the B...This paper deals with transformation procedures for observed GPS data from the world geodetic system WGS84 into the national geodetic grid datum SUTCN （system of united trigonometric cadaster network） and Baa（the Baltic Sea after adjustment）.Transformation from WGS84 into SUTCN is performed most frequently by means of the 7element Helmert transformation with three identical points.Geodetic network was adjusted by two ways.展开更多
基金supported by the National Natural Science Foundation of China,Nos.41874001 and 41664001Support Program for Outstanding Youth Talents in Jiangxi Province,No.20162BCB23050National Key Research and Development Program,No.2016YFB0501405。
文摘When linearizing three-dimensional(3 D)coordinate similarity transformation model with large rotations,we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions.To alleviate the problem,a series of conversions are contributed to the 3 D coordinate similarity transformation model in this paper.We deduced a complete solution for the 3 D coordinate similarity transformation at any rotation with the nonlinear adjustment methodology,which involves the errors of the common and the non-common points.Furthermore,as the large condition number of the normal matrix resulted in an intractable form,we introduced the bary-centralization technique and a surrogate process for deterministic element of the normal matrix,and proved its benefit for alleviating the condition number.The experimental results show that our approach can obtain the smaller condition number to stabilize the convergence of the interested parameters.Especially,our approach can be implemented for considering the errors of the common and the non-common points,thus the accuracy of the transformed coordinates improves.
文摘In this paper, a transformation model named SARC(static-filter adjustment with restricted condition) is presented, which is more practical and more rigorous in theory and fitting any angle of rotation parameter. The transformation procedure is divided into 4 steps: ① the original and object coordinates can be regarded as observations with errors; ② rigorous formula is firstly deduced in order to compute the first approximation of the transformation parameters by use of four common points and the transformation equation is linearized; ③ calculate the most probable values and variances of the seven transformation parameters by SARC model; ④ to demonstrate validity of SARC , an example is given.
文摘This paper deals with transformation procedures for observed GPS data from the world geodetic system WGS84 into the national geodetic grid datum SUTCN （system of united trigonometric cadaster network） and Baa（the Baltic Sea after adjustment）.Transformation from WGS84 into SUTCN is performed most frequently by means of the 7element Helmert transformation with three identical points.Geodetic network was adjusted by two ways.
