This paper addresses the problem of indoor positioning, where complex propagation characteristics call for advanced Bayesian filters for accurate position tracking. We propose to employ the Stein Particle Filter (SPF) to approximate the posterior distribution with a set of particles, using the Stein Variational Gradient Descent (SVGD) method. A novel SPF tracking method, referred to as Annealed Stein Particle Filter (A-SPF), is designed by exploiting the annealed scheduling of SVGD. Compared to SPF, the A-SPF captures multi-modal distributions that easily arise in indoor localization problems from multipath without requiring higher number of particles. Experimentation activities are carried out in two indoor scenarios, an office and a machinery area, where Ultra Wide-Band (UWB) technology is used to collect raw data. Results show the improved positioning performance of the proposed A-SPF compared to conventional solutions based on extended Kalman filter and particle filter, as well as with standard SPF.