Online Particle Smoothing with Application to Map-matching

We introduce a novel method for online smoothing in state-space models that utilises a fixed-lag approximation to overcome the well known issue of path degeneracy. Unlike classical fixed-lag techniques that only approximate certain marginals, we introduce an online resampling algorithm, called particle stitching, that converts these marginal samples into a full posterior approximation. We demonstrate the utility of our method in the context of map-matching, the task of inferring a vehicle's trajectory given a road network and noisy GPS observations. We develop a new state-space model for the difficult task of map-matching on dense, urban road networks.