Rao-Blackwellized Gaussian Sum Particle Filtering for Multipath Assisted Positioning

Abstract

In multipath assisted positioning, multipath components arriving at a receiver are regarded as being transmitted by a virtual transmitter in a line-of-sight condition. As the locations and clock offsets of the virtual and physical transmitters are in general unknown, simultaneous localization and mapping (SLAM) schemes can be applied to simultaneously localize a user and estimate the states of physical and virtual transmitters as landmarks. Hence, multipath assisted positioning enables localizing a user with only one physical transmitter depending on the scenario. In this paper, we present and derive a novel filtering approach for our multipath assisted positioning algorithm called Channel-SLAM. Making use of Rao-Blackwellization, the location of a user is tracked by a particle filter, and each landmark is represented by a sum of Gaussian probability density functions, whose parameters are estimated by unscented Kalman filters. Since data association, that is, finding correspondences among landmarks, is essential for robust longterm SLAM, we also derive a data association scheme. We evaluate our filtering approach for multipath assisted positioning by simulations in an urban scenario and by outdoor measurements.

Gaussian Mixture Model Learning for Multipath Assisted Positioning

“…We first sample position components from a GMM while ignoring the b v, t axis, and its correlations with position components to achieve this goal. Then we assign a b v, t value according to b v, t = b v, t + x Rx,t , x Tx, t − x Rx,t , x Tx, t + v, (12) where the apostrophe marks value obtained from a corresponding GMM component, and v is a zero-mean normally distributed additional value.…”

“…Due to the system's nonlinearity, the SLAM methods for multipath assisted positioning use, in most cases, sampling particles to approximate the true posterior Probability Density Function (PDF). The two main techniques practically used are Rao-Blackwellized Particle Filter (RBPF) [11], [12], and Nonparametric Belief Propagation (NBP) [13]. The disadvantage of particle-based approaches for parameter estimation is a significant computational complexity, which can be easily forbidding the algorithm to work in a real-time scenario.…”

ROV State Estimation Using Mixture of Gaussian Based on Expectation-Maximization Cubature Particle Filter

“…Mixture of Gaussian (MOG) can be seen as a combination of k single Gaussian models; MOG is widely utilized to mimic non-Gaussian density because it enhances the real-time state estimation performance while maintaining the estimation performance [21]. Kotecha and Djuric [22] extended MOG and PF to dynamic space models with non-Gaussian noise; Ulmschneider et al [23] used MOG in multi-path-assisted positioning to improve the positioning accuracy. A recursive estimator for non-Gaussian problems was derived in [24]; any probability density can be approximated by a mixture model of finite Gaussian functions [25].…”