Satellite Selection Method for Multi-Constellation GNSS Using Convex Geometry

This paper proposes a methodology in the context of convex geometry theory aiming to reduce the number of satellites among all visible satellites used for the position computation by a navigation receiver. This reduction is based on the approximate equivalence between geometric dilution of precision minimization and maximization of the size of the polytope (polyhedron in 3-D or polygon in 2-D) expanded by the user-to-satellite unit vector endpoints. The polytope is contained in the convex hull of all vector´s endpoints for the set of satellites in view. An optimal solution for convex hull computation with lower bound computational burden is proposed for both static and time-varying scenarios.