Fundamentals of LEO Based Localization

TL;DR

This paper derives the fundamental limits of LEO-based localization by analyzing signals from multiple LEOs, considering various offsets and mobility factors, to evaluate the conditions for accurate 9D localization.

Contribution

It introduces a comprehensive Fisher Information Matrix framework for LEO-based localization, accounting for practical offsets and mobility, and determines the system requirements for 3D and 9D localization accuracy.

Findings

Derived FIM for channel and location parameters.

Identified conditions for 3D and 9D localization.

Quantified system parameters needed for accurate localization.

Abstract

In this paper, we derive the fundamental limits of low earth orbit (LEO) enabled localization by analyzing the available information in signals from multiple LEOs during different transmission time slots received on a multiple antennas and evaluate the utility of these signals for $9$D localization ($3$D position, $3$D orientation, and $3$D velocity estimation). We start by deriving the Fisher Information Matrix (FIM) for the channel parameters that are present in the signals received from LEOs in the same or multiple constellations during multiple transmission time slots. To accomplish this, we define a system model that captures i) time offset between LEOs caused by having relatively cheap clocks, ii) frequency offset between LEOs, iii) the unknown Doppler rate caused by high mobility LEOs, and iv) multiple transmission time slots from a particular LEO. We transform the FIM for the channel parameters to the FIM for the location parameters and determine the required conditions for localization. To do this, we start with the $3$D localization cases: i) $3$D positioning with known velocity and orientation, ii) $3$D orientation estimation with known position and velocity, and iii) $3$D velocity estimation with known position and orientation. Subsequently, we derive the FIM for the full $9$D localization case ($3$D position, $3$D orientation, and $3$D velocity estimation) in terms of the FIM for the $3$D localization. Using these results, we determine the number of LEOs, the operating frequency, the number of transmission time slots, and the number of receive antennas that allow for different levels of location estimation.