Conversion of Earth-centered Earth-fixed coordinates to geodetic coordinates

The transformations between Earth-centered Earth-fixed (ECEF) coordinates and geodetic coordinates are required in many applications, for example, in NAVSTAR/GPS navigation and geodesy. The transformation from ECEF coordinates to geodetic coordinates is usually carried out by approximation methods in practice, and the exact transformation methods are not used frequently. In this paper, several exact transformation formulas from ECEF coordinates to geodetic coordinates are reviewed and compared with the approximation methods in complexity and in sensitivity to computer round-off error. The relationship among some exact transformation solutions and the approaches are pointed out