Measurement Selection for LEO Mega-Constellation Integrated Communication and Navigation: A Theoretical Analysis

Abstract

The rapid deployment of low earth orbit (LEO) mega-constellations is driving the convergence of communication and navigation in future wireless networks. To effectively use these satellites for positioning, the selection of an appropriate measurement method is a key design challenge governed by the achievable positioning accuracy. However, existing positioning performance analysis methods based on the Cramér-Rao lower bound (CRLB) rely on numerical simulations of multi-epoch instantaneous satellite geometries, resulting in high computational complexity. This paper proposes an asymptotic positioning performance analysis method. It provides closed-form solutions for the asymptotic three-dimensional positioning CRLB of time of arrival, time difference of arrival, and frequency offset of arrival measurement methods under the condition of inter-constellation clock asynchrony. Furthermore, considering satellite availability constraints, a framework is proposed to calculate the practical asymptotic CRLB by integrating the joint probability density function of the satellites’ azimuth and elevation relative to the receiver. Monte Carlo simulations verify that this method can accurately characterize the positioning performance of the three measurement methods. Additionally, the proposed method utilizes only a single global inversion, which significantly reduces the computational overhead and provides fast, reliable guidance for selecting the optimal measurement technique for LEO mega-constellation navigation systems.