Analyzing Localizability of LEO/MEO Hybrid Networks: A Stochastic Geometry Approach

TL;DR

This paper introduces a stochastic geometry framework to analyze the localizability of hybrid LEO/MEO satellite networks, providing analytical expressions and modeling techniques for performance evaluation and demonstrating the benefits of hybrid configurations.

Contribution

It pioneers the application of stochastic geometry to hybrid LEO/MEO satellite positioning, proposing new models for MEO constellations and analyzing the impact of configurations on localizability.

Findings

Analytical expressions for K-availability and K-localizability probabilities.

Hybrid LEO/MEO networks improve positioning performance.

Modeling techniques for MEO satellite constellations using stochastic geometry.

Abstract

With the increase in global positioning service demands and the requirement for more precise positioning, assisting existing medium and high orbit satellite-enabled positioning systems with low Earth orbit (LEO) satellites has garnered widespread attention. However, providing low computational complexity performance analysis for hybrid LEO/MEO massive satellite constellations remains a challenge. In this article, we introduce for the first time the application of stochastic geometry (SG) framework in satellite-enabled positioning performance analysis and provide an analytical expression for the K-availiability probability and K-localizability probability under bidirectional beam alignment transmissions. The K-localizability probability, defined as the probability that at least K satellites can participate in the positioning process, serves as a prerequisite for positioning. Since the modeling of MEO satellite constellations within the SG framework has not yet been studied, we integrate the advantages of Cox point processes and binomial point processes, proposing a doubly stochastic binomial point process binomial point process for accurate modeling of MEO satellite constellations. Finally, we investigate the impact of constellation configurations and antenna patterns on the localizability performance of LEO, MEO, and hybrid MEO/LEO constellations. We also demonstrate the network performance gains brought to MEO positioning systems by incorporating assistance from LEO satellites.