An Information-Theoretic Examination of Next Generation Location Systems: The Role of LEOs, RISs and the Near Field

Abstract

Navigation is integral to modern infrastructure, with GPS serving as the foundation for applications in transportation, banking, and communications. Despite its widespread success, GPS is vulnerable to failures due to its low received signal power, susceptibility to jamming, and reduced accuracy in dense urban environments and deep fades. A failure of GPS could have severe consequences, making it crucial to explore alternative or supplementary navigation technologies. This work investigates the potential of three approaches—low Earth orbit (LEO) satellites, reconfigurable intelligent surfaces (RISs), and near-field propagation—to enhance localization accuracy and resilience. LEO satellites, originally designed for communication, have recently seen widespread deployment through constellations such as Starlink, OneWeb, and Kuiper. Their growing presence presents an opportunity to explore their feasibility for 9D localization, which includes 3D position, velocity, and orientation estimation. However, using LEO satellites for localization introduces significant challenges, including ionospheric delays, high Doppler shifts, limited synchronization due to the absence of atomic clocks, and uncertainty in satellite ephemeris data. To address these challenges, we leverage estimation theory and the Fisher Information Matrix (FIM) to establish theoretical bounds on localization performance. Our analysis shows that localization is possible using signals from multiple LEO satellites observed across several time slots, even in the presence of time and frequency offsets. We derive closed-form expressions for the FIM and identify conditions under which localization is feasible, highlighting the required number of satellites, base stations, and transmission slots. RISs provide another avenue for enhancing localization by dynamically shaping wireless propagation channels through software-controlled meta-material surfaces. We analyze the localization potential of RISs under both near-field and far-field conditions, focusing on angle of incidence, reflection, and orientation estimation. Our FIM-based study reveals that in far-field scenarios, angle estimation is only feasible with multiple RIS phase profiles, whereas in near-field, a single phase profile suffices. This distinction has implications for RIS-aided positioning, indicating that a single RIS reflection may not provide sufficient information for localizing a user in the far-field unless additional mechanisms, such as multiple reflections or phase variations, are employed. We further investigate near-field propagation, assessing the available localization information when a source transmits to a destination node. Our Fisher information analysis reveals that in the near-field regime, 3D orientation and position can be jointly estimated, whereas in the far-field, only 2D orientation and position can be determined. Additionally, we explore the impact of propagation model mismatches on direction-of-arrival (DOA) estimation using the MUSIC algorithm. Our simulations quantify the performance degradation when incorrect assumptions are made about the propagation environment, showing that estimation accuracy suffers significantly when near-field effects are ignored. Notably, in near-field scenarios, using a far-field-based beamforming model leads to an underestimation of DOA estimation errors, while in the far-field, MUSIC remains effective with appropriate beamforming design. Overall, our findings indicate that LEO satellites, RISs, and near-field propagation hold significant potential for overcoming the limitations of GPS and enabling precise localization for next-generation applications. By leveraging these technologies, it may be possible to achieve robust navigation in environments where GPS performance is compromised, paving the way for resilient and high-accuracy positioning solutions.