Inverse geodetic problem for long distance based on improved Vincenty’s formula

Abstract Solutions of geodetic problem is an important technical problem in geodesy. Based on the comprehensive analysis of the characteristics of Bessel’s formula and Vincenty’s formula, an improved algorithm is proposed. Firstly, arctangent formula is replaced by arccosine formula to calculate spherical surface angular distance. Secondly, Bessel’s formula is used to replace Vincenty’s formula in the singular region. Finally, the test formulas of geodetic line and azimuth are given. According to the test formula, four points are selected for the test, which are located in the equator, low latitude, middle latitude and high latitude. The geodesic length range of the test is 1000–18000 km and the azimuth range is 0 ∘ 0{\hspace{0.1667em}^{\circ }}– 360 ∘ 360{\hspace{0.1667em}^{\circ }}. The experimental results show that the improved algorithm can solve the problem of singularity and quadrant judgment well. The solution precision of geodetic line is better than 1 mm, and the precision of azimuth is less than 0.0001 second.