Geolocation with Large LEO Constellations: Insights from Fisher Information

TL;DR

This paper explores the potential of using low earth orbit (LEO) satellites for precise 9D localization of terrestrial receivers by analyzing signal processing algorithms, estimation theory, and Fisher Information Matrix, highlighting advantages over GPS.

Contribution

It introduces conditions for 9D localization using signals from multiple LEO satellites and compares the information structure with GPS, advancing satellite-based localization methods.

Findings

Conditions for 9D localization with LEO signals established

Fisher Information Matrix used to analyze localization potential

Comparison with GPS information structure provided

Abstract

Interest in the use of the low earth orbit (LEO) in space - from $160 \text{ km}$ to $2000 \text{ km}$ - has skyrocketed; this is evident by the fact that National Aeronautics and Space Administration (NASA) has partnered with various commercial platforms like Axiom Space, Blue Origin, SpaceX, Sierra Space, Starlab Space, ThinkOrbital, and Vast Space to deploy satellites. %and platforms like Northrop Grumman and Boeing to transport cargo and crew. The most apparent advantage of satellites in LEO over satellites in Geostationary (GEO) and medium earth orbit (MEO) is their closeness to the earth; hence, signals from LEOs encounter lower propagation losses and reduced propagation delay, opening up the possibility of using these LEO satellites for localization. This article reviews the existing signal processing algorithms for localization using LEO satellites, introduces the basics of estimation theory, connects estimation theory to model identifiability with Fisher Information Matrix (FIM), and with the FIM, provides conditions that allow for $9$D localization of a terrestrial receiver using signals from multiple LEOs (unsynchronized in time and frequency) across multiple time slots and multiple receive antennas. We also compare the structure of the information available in LEO satellites with the structure of the information available in the Global Positioning System (GPS).