Intersection of hyperbolae on the earth
Abstract
Several methods are discussed of solving for the point of intersection of a pair of hyperbolic lines of position as generated by commonly used radionavigation systems e.g. Decca, Loran-C, Omega, Syledis, Raydist or HiFix.
Both the plane and the spherical problem are treated by the well-known iterative technique and by a direct trigonometrical solution. Numerous analogies are apparent between the plane and the spherical solutions.
For the direct method on the ellipsoid, a new and easier solution is presented. Notably, geodetic positions on the ellipsoid are calculated accurately for very long lines by spherical trigonometric formulae.
Numerical examples to test the algorithms and a set of Fortran routines are included. The results are verified by Vincenty’s geodetic inverse formula