Improved chord method for the direct and inverse problems of the distances and azimuths on the reference ellipsoid

Through transformation from geocentric to topocentric space rectangular coordinate system and taking advantage of the plain geometrical relationships from the chord between two points on the ellipsoidal surface, the problems of the distances and azimuths on the reference ellipsoid can be converted to several elementary equations and corresponding corrective terms. Based on this, an improved chord method has been proposed in the article. Numeric experiments have validated that the new algorithm can be effective for arbitrary distances. Moreover, the solution can also be operational without singularity in the polar or equatorial regions, in the situations where the difference in longitude is 180°, and in other special cases. And with suitable corrections, the improved method can be prospectively applied to other problems of distances and azimuths with corresponding precision.