Robust GNSS/5G Positioning in LOS/NLOS Environments: A Stein Variational Inference Framework for Particle Filter

High-accuracy positioning in fifth generation (5G) industrial networks is severely challenged by nonline-of-sight (NLOS) propagation, which induces particle degeneracy in conventional particle filters. This letter proposes a robust Stein variational particle filter (RSVPF) that addresses this limitation. By reformulating the problem as a variational inference task, the RSVPF deterministically transports particles to approximate the optimal proposal distribution via a Stein variational gradient flow. The method operates on a hybrid state-space, jointly estimating kinematic state and sight conditions, and is complemented by a projection onto a physically feasible subspace. The proposed framework is shown to mitigate particle impoverishment, enhance robustness against NLOS bias, and provide accurate, stable posterior estimation for integrated global navigation satellite system (GNSS)/5G positioning.