Research On Application Of Oblique Ellipsoid Gauss Projection Method In High Speed Railway

With the process of social development,high-speed railway need to further enhance the safety,comfort and smoothness.Due to the vast size of China,high-speed railways span across the east,west,north and south,with large measurement areas and long lines,and the lines have features such as large turns and large height differences when passing through areas with complex terrain.In order to control the projection length deformation of the large height difference line not exceeding 10mm/km:Firstly,this paper discusses the research background,research objectives,and the current status of domestic and international research on methods to control projection length deformation.The real number representation of Gaussian projection and Gaussian projection positive solution as well as the non-iterative complex variable function representation are described.The main factors of Gaussian projection length deformation and the basis of line segmentation are studied.The important methods to control the projection length deformation,ellipsoidal expansion method,ellipsoidal translation method,and ellipsoidal deformation method are briefly described.Secondly,based on the principle of Gaussian projection theory of oblique axis ellipsoidal deformation method: the least squares principle is used to convert the base ellipsoid to the oblique axis reference ellipsoid to reduce the Gaussian projection deformation correction;the ellipsoidal transformation method is used to convert to the oblique axis deformation ellipsoid to reduce the elevation normalization correction.The conversion of the base ellipsoid E0 to the oblique axis ellipsoid E1 in right-angle spatial coordinates and geodesic coordinates is described.Then the geodesic coordinates of the oblique axis ellipsoid E1 are converted to the geodesic coordinates of the oblique axis transform ellipsoid E2 by three ellipsoidal transformation methods.The Gaussian projection of the obliquely transformed ellipsoid is further studied.Thirdly,a high-precision engineering control network is studied in depth for the high-speed railway long-line project with large height difference,in order to articulate the Gaussian plane coordinates before and after the ellipsoidal transformation of the oblique axis under the requirement of projection length deformation.The eccentric derivatives of the complex variable z composed of Gaussian plane horizontal and vertical coordinates with respect to the parameters long radius a,eccentricity e,geodesic latitude B,and longitude l are solved by using the non-iterative complex variable function of the positive solution of Gaussian projection,and the formula of Gaussian plane coordinate displacement is derived according to the change amount of geodesic coordinates of ellipsoidal transformation,and the Gaussian plane coordinate transformation model before and after ellipsoidal transformation is constructed.The factors and magnitudes of the expansion ellipsoid,translation ellipsoid,and deformation ellipsoid affecting the Gaussian plane coordinate change quantities dx,dy are also analyzed by using the Gaussian plane coordinate differentiation formula.Finally,the validation and accuracy comparison analysis of the ellipsoidal Gaussian projection method of oblique axis transformation and the Gaussian plane coordinate conversion model before and after ellipsoidal transformation are carried out by the actual engineering data,which verifies the correctness of the theoretical model and the superiority of Gaussian plane coordinate conversion.