Satellite Positioning with Large Constellations

Modern global navigation satellite system receivers can access signals from several satellite constellations (including GPS, GLONASS, Galileo, BeiDou). Once these constellations are all fully operational, a typical receiver can expect to have on the order of 40-50 satellites in view. Motivated by that observation, this paper presents an asymptotic analysis of positioning algorithms in the large-constellation regime. We determine the exact asymptotic behavior for both pseudo-range and carrier-phase positioning. One interesting insight from our analysis is that the standard carrier-phase positioning approach based on resolving the carrier-phase integer ambiguities fails for large satellite constellations. Instead, we adopt a Bayesian approach, in which the ambiguities are treated as noise terms and not explicitly estimated.