An Improved Method of Polar Ellipsoid Transverse Mercator Projection Based on Double Projection

Due to the problems that there are deviances when sphere transverse Mercator projection and navigation equipment based on ellipsoid are used together and that traditional ellipsoid transverse Mercator projections which are based on longitude difference to zone the regions are not applicable to polar regions, an improved method of transverse Mercator projection based on double projection has been studied on the basis of analyzing the existence of the problems which are calculation singular and overflow when double projection is used. Firstly, equivalent transformation functions and meridian length ratio formula have been used to deduce coordinate transformations of ellipsoid projection on a sphere, radius of the sphere, and the length ratio formula. Then the sphere transverse Mercator projection formula has been generated by using the piecewise function; the complete coordinate transformation formula and the length ratio formula are all derived from the previous stages. Finally, the meridian convergent angle formula is deduced. From theoretical analysis and simulations, the improved method can solve the problems of calculation singular and overflow. The length deformation when the areas are near the poles is relatively small and it is in accordance with the earth model adopted by the navigation equipment, which can remove the deviances caused by the different earth models and improve the precision of navigation plotting.