The historical development of geodetic coordinate system in Korea is introduced.

A new form of geodetic coordinate system with length quantity as coordinate parameters was presented for the first time in a former paper of the authors,and this paper shows that those two forms of geodetic coordinate system are regular coordinate system,then the fundamental and method of transformation between the two geodetic coordinate systems are proposed.

A new form of geodetic coordinate system based on geodesic coordinate instead of geodetic longitude and latitude is proposed.

With the extensive application of GPS technique,the transformation model between two geodetic coordinate systems,geodetic coordinates formulae by differential method,which is carried out by the seven-parameter similarity transformation model and some well-known formulae such as Bursa-Wolf and Molodensky-Badekas models etc.

In order to satisfy the requirement for the route location of the Shanghai-Hangzhou magnetic suspension project, a new form of geodetic coordinate system was proposed.

Based on the theories of Differential Geometry and Geodesy,algorithms and formulas for direct and inverse solution of geodetic problem in the new form of geodetic coordinate system on the ellipsoidal surface are deduced in this paper.