Satellite Selection Method for Multi-Constellation GNSS Using Convex Geometry

Abstract

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.