Particle Smoothing for Conditionally Linear Gaussian Models as Message Passing Over Factor Graphs

In this paper, the fixed-lag smoothing problem for conditionally linear Gaussian state-space models is investigated from a factor graph perspective. More specifically, after formulating Bayesian smoothing for an arbitrary state-space model as a forward–backward message passing over a factor graph, we focus on the above-mentioned class ofmodels and derive two novel particle smoothers for it. Both the proposed techniques are based on the well-known two-filter smoothing approach and employ marginalized particle filtering in their forward pass. However, on the one hand, the first smoothing technique can only be employed to improve the accuracy of state estimates with respect to that achieved by forward filtering. On the other hand, the second method, that belongs to the class of Rao–Blackwellized particle smoothers, also provides a pointmass approximation of the so-called joint smoothing distribution. Finally, our smoothing algorithms are compared, in terms of estimation accuracy and computational requirements, with a Rao–Blackwellized particle smoother recently proposed by Lindsten et al. (“Rao–Blackwellized particle smoothers for conditionally linear Gaussian models,” IEEE J. Sel. Topics Signal Process., vol. 10, no. 2, pp. 353–365, 2016).