LEO- and RIS-Empowered User Tracking: A Riemannian Manifold Approach

Low Earth orbit (LEO) satellites and reconfigurable intelligent surfaces (RISs) have recently drawn significant attention as two transformative technologies, and the synergy between them emerges as a promising paradigm for providing cross-environment communication and positioning services. This paper investigates an integrated terrestrial and non-terrestrial wireless network that leverages LEO satellites and RISs to achieve simultaneous tracking of the three-dimensional (3D) position, 3D velocity, and 3D orientation of user equipment (UE). To address inherent challenges including nonlinear observation function, constrained UE state, and unknown observation statistics, we develop a Riemannian manifold-based unscented Kalman filter (UKF) method. This method propagates statistics over nonlinear functions using generated sigma points and maintains state constraints through projection onto the defined manifold space. Additionally, by employing Fisher information matrices (FIMs) of the sigma points, a belief assignment principle is proposed to approximate the unknown observation covariance matrix, thereby ensuring accurate measurement updates in the UKF procedure. Numerical results demonstrate a substantial enhancement in tracking accuracy facilitated by RIS integration, despite urban signal reception challenges from LEO satellites. In addition, extensive simulations underscore the superior performance of the proposed tracking method and FIM-based belief assignment over the adopted benchmarks. Furthermore, the robustness of the proposed UKF is verified across various uncertainty levels.

I. Introduction

In the realm of modern wireless systems, the importance of advanced user tracking mechanisms is increasingly prominent. Current tracking methodologies encompass a wide range, including global navigation satellite systems (GNSS) [1], radio frequency identification (RFID) [2], advanced computer vision techniques [3], inertial navigation systems (INS) [4], acoustic sensors [5], laser [6], radar [7], and wireless sensor networks [8]. Among these technologies, using wireless radio signals stands out as a particularly innovative and effective solution [9]. The integration of tracking with wireless communication systems not only addresses the localization needs but also enhances the efficiency and reliability of communication networks [10]. Compared with other techniques, the high flexibility, expansive global reach, and inherent connectivity infrastructure of wireless communication systems make them well-suited for integration at different levels. In particular, the transition from the fifth generation (5G) to the sixth generation (6G) heralds an era characterized by ultra-fast speeds, minimal latency, and exceptional reliability in wireless networks [11], [12]. This evolution significantly enhances the integration and adaptability of tracking systems across diverse domains, ranging from indoor scenarios to outdoor environments, and from ground-level applications to space-based contexts [13], [14].