Joint 9D Receiver Localization and Ephemeris Correction with LEO and $5$G Base Stations

Abstract

This paper leverages Fisher information to examine the interaction between low-Earth orbit (LEO) satellites and 5G base stations (BSs) in enabling 9D receiver localization and refining LEO ephemeris. First, we propose a channel model that incorporates all relevant links: LEO-receiver, LEO-BS, and BS-receiver.Then, we utilize the Fisher information matrix (FIM) to quantify the information available about the channel parameters in these links. By transforming these FIMs, we derive the FIM for 9D receiver localization parameters-comprising 3D position, 3D orientation, and 3D velocity-along with LEO position and velocity offsets. We present closed-form expressions for the FIM entries corresponding to these localization parameters. Our identifiability analysis based on the FIM reveals that: i) With a single LEO, three BSs, and three time slots are required to estimate the 9D localization parameters and correct the LEO position and velocity. ii) With two LEOs, the same configuration (three BSs and three time slots) suffices for both tasks. iii) With three LEOs, three BSs and four time slots are needed to achieve the same goal. A key insight from the Cramer-Rao lower bound (CRLB) analysis is that, under the configuration of one LEO, three BSs, and three time slots, the estimated errors for receiver positioning, velocity, and orientation, as well as LEO position and velocity offsets, are 0.1 cm, 1 mm/s, 0.001 rad, 0.01 m, and 1 m/s, respectively. The receiver localization parameters are estimated after 1 s while the LEO offset parameters are estimated after 20 s. Additionally, our CRLB analysis indicates that operating frequency has minimal impact on receiver orientation estimation accuracy, and the number of receive antennas has a negligible effect on LEO velocity estimation accuracy.