A new method for height determinations based on solving the geodetic fixed boundary value problem

The simple method for height determination is spirit leveling. The leveled height differences are path-dependent. Ergo height from spirit leveling is not unique. The problem can be solved by converting the path-dependent leveled height differences into unique path-independent height differences (Vanicek and Krakiwsky, 1986). The difference between the potentials of two close equipotential surface can be written as: (1) Practically, instead of potential, it is better to use geopotential numbers: (2) Having derived geopotential numbers, we can compute various height systems such as dynamic height, orthometric height and normal height. According to (1), with gravity measured along the leveling line, the potential difference as a path-independent quantity can be determined. In this method we can only compute geopotential numbers for points where we can establish a leveling path. On the other hand with geoid height at hand and the availability of geodetic height from GPS, we can compute orthometric height. With computation of mean gravity, orthometric height can be converted to geopotential number. But there are still some open problems with computation of geoid and mean gravity. The aim of this paper is the presentation of a new method for computation of geopotentail numbers based on solving the fixed geodetic boundary value problem. With the availability of GPS coordinates for the point on the Earth’s surface, the outer boundary of the Earth can be regarded as a known and fixed boundary. With boundary observations on the Earth’s surface at hand, we deal with a fixed geodetic boundary value problem. The problem is defined as follows