  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
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.
