Research On Improvement Method Of Algorithm For Coordinate Transformation

The application of different coordinate system coordinates in various fields is limited in the practical surveying and mapping application by the problem of multiple coordinate system surveying and mapping results in the same area,which is not conducive to the development of the real economy.Using similarity transformation to establish one-to-one correspondence among different coordinate systems,that is,achieving coordinate transformation among different coordinate systems,is one of the approaches to solve the problem.Therefore,it is of great theoretical significance and application value to study the solving method of coordinate transformation model.Of which,the plane and three-dimensional coordinate transformation model are the most widely used coordinate transformation model.4-parameter planar coordinate transformation and 7-parameter three-dimensional space coordinate transformation model have been systematically outlined in the paper.Moreover,existing methods of coordinate transformation model have been narrated and analyzed with deficiencies presented.Research conducted in this paper mainly focuses on:(1)Methods of weighted total least squares,mixed total least squares,total least squares and least squares are introduced.Advantages and disadvantages of these four methods in the plane coordinate transformation and three-dimensional space coordinate transformation are analyzed through simulated examples.According to experimental results,it shows that parameter estimation that is closer to the true value can be obtained with considerations of random errors containing in the coefficient matrix and the observation vector as well as the highest computing accuracy of computing different elements of the weighted total least square method in plane coordinate transformation and three-dimensional space coordinate transformation.(2)The traditional method of least squares collocation is introduced together with analyzing the essential thoughts and deficiencies of the least squares collocation method in plane and three-dimensional coordinate transformation.Considering that random errors in the observation vector are the essence of the least squares collocation processing the plane and three-dimensional space coordinate transformation,a better calculation accuracy can be obtained while regarding the random errors in the common point as signals.In essence,errors in the observation vector and coordinate of common point belonging to the same type of error,should be handled in a similar way.In response to this situation,a weighted total least squares collocation is proposed to deal with the problem of the plane and three-dimensional space coordinate transformation.With this method,random errors of the common point(coefficient matrix)and the observation vector can be considered at the same time while regarding the model errors as signals.Simulation experiments show that the weighted total least squares collocation method can obtain more accurate parameter estimation and estimated value than the least squares collocation method.The precision in the plane and three-dimensional examples is increased by 36.2% and 10.1% respectively.(3)The traditional datum transformation model and seamless datum transformation model are introduced with differences analyzed.The application of seamless datum transformation is applied to the solution of 4-parameter planar coordinate transformation model parameters.Also,advantages and disadvantages of these two methods in the plane coordinate transformation and three-dimensional space coordinate transformation are analyzed through simulated examples.Experimental results show that the seamless datum transformation model that can take into account the random errors of the common point and the non-common point at the same time can obtain more accurate parameter estimation and predicted effect,compared with the traditional one.