A Particle Filtering Approach for Joint Detection/Estimation of Multipath Effects on GPS Measurements

Abstract

Multipath propagation causes major impairments to global positioning system (GPS) based navigation. Multipath results in biased GPS measurements, hence inaccurate position estimates. In this paper, multipath effects are considered as abrupt changes affecting the navigation system. A multiple model formulation is proposed whereby the changes are represented by a discrete valued process. The detection of the errors induced by multipath is handled by a Rao-Blackwellized particle filter (RBPF).The RBPF estimates the indicator process jointly with the navigation states and multipath biases. The interest of this approach is its ability to integrate a priori constraints about the propagation environment. The detection is improved by using information from near future GPS measurements at the particle filter (PF) sampling step. A computationally modest delayed sampling is developed, which is based on a minimal duration assumption for multipath effects. Finally, the standard PF resampling stage is modified to include an hypothesis test based decision step.

Joint Particle Filter and UKF Position Tracking in Severe Non-Line-of-Sight Situations

“…Suppose that, at time , the approximation of the posterior distribution is (22) Since the number of possible offspring per particle amounts to , this approximation can be updated in an exhaustive manner as follows: (23) where and stands for the th possible value of the situation vector. In this case, the importance weights are directly proportional to the posterior distribution of the particles (24) As a result, they can be factorized as follows: (25) In this equation, the likelihood is obtained from the UKF associated to particle . This approach has the advantage of not discarding any information.…”

“…This is the classical UKF whose algorithm is summarized in Table III, where , in (III.1), is the sigma set associated with for situation . The probability needed to evaluate (25), is obtained in (III.2). Finally, the posterior distribution of the kinetic states can be approximated by a mixture of Gaussian distribution according to Bayes' rule (27) 3) Resampling: Once the UKFs have been run, it is possible to update the weights according to (25).…”

“…The probability needed to evaluate (25), is obtained in (III.2). Finally, the posterior distribution of the kinetic states can be approximated by a mixture of Gaussian distribution according to Bayes' rule (27) 3) Resampling: Once the UKFs have been run, it is possible to update the weights according to (25). In order to reduce the number of particles from to , a straightforward solution would consist of preserving only the particles with the most significant weight.…”

“…On the other hand, considering the bias as a random walk [22] makes it possible to track non-static MTs. Following this strategy, [23] estimates which measures are in NLOS prior to estimate the bias and [24], [25] uses a PF to track which measures incur a bias change. The LOS-NLOS situation can also be tracked by being modeled as a Markov process as in [21], [26].…”

Joint Particle Filter and UKF Position Tracking Under Strong NLOS Situation

“…The particle degeneracy is avoided using a novel particle- [10] is associated to each particle following the LOS or NLOS hypothesis in a RaoBackwellization framework as in [11]. The UKF is chosen because of its better behavior compared to the classical Extended Kalman Filter, while maintaining the computational cost [7].…”