Satellite Positioning with Large Constellations

TL;DR

This paper analyzes the asymptotic behavior of satellite positioning algorithms with large constellations, revealing limitations of traditional methods and proposing a Bayesian approach for improved accuracy in systems with 40-50 satellites.

Contribution

It provides an asymptotic analysis of positioning algorithms in large satellite constellations and introduces a Bayesian method that treats ambiguities as noise, overcoming limitations of standard techniques.

Findings

Standard carrier-phase positioning fails with large constellations.

Bayesian approach effectively handles ambiguities as noise.

Asymptotic behavior characterized for pseudo-range and carrier-phase methods.

Abstract

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.