Exact and heuristic formulae to compute the geodetic height from the ellipse equation

Abstract

The conversion of the cartesian coordinates of a point to its geodetic equivalent coordinates in reference to the geodetic ellipsoid is one of the main challenges in geodesy. The ellipse equation in the meridian plane significantly influences the value of the geodetic coordinates. This research analyzes this influence and how it can contribute to their solutions. The study investigates the mathematical relation between them and presents an exact formula relating to the geodetic height and the ellipse equation. In addition, a heuristic formula for the relation between the geodetic height and the ellipse equation is proposed, which is independent of the geodetic latitude and has a relative accuracy better than 99.9 %. The calculation is stable, and the cost is low.

Keywords

• Ellipse equation
• Geodetic height
• Heuristic geodetic height