On the performance of parallelisation schemes for particle filtering

Abstract

Considerable effort has been recently devoted to the design of schemes for the parallel implementation of sequential Monte Carlo (SMC) methods for dynamical systems, also widely known as particle filters (PFs). In this paper, we present a brief survey of recent techniques, with an emphasis on the availability of analytical results regarding their performance. Most parallelisation methods can be interpreted as running an ensemble of lower-cost PFs, and the differences between schemes depend on the degree of interaction among the members of the ensemble. We also provide some insights on the use of the simplest scheme for the parallelisation of SMC methods, which consists in splitting the computational budget into M non-interacting PFs with N particles each and then obtaining the desired estimators by averaging over the M independent outcomes of the filters. This approach minimises the parallelisation overhead yet still displays desirable theoretical properties. We analyse the mean square error (MSE) of estimators of moments of the optimal filtering distribution and show the effect of the parallelisation scheme on the approximation error rates. Following these results, we propose a time-error index to compare schemes with different degrees of parallelisation. Finally, we provide two numerical examples involving stochastic versions of the Lorenz 63 and Lorenz 96 systems. In both cases, we show that the ensemble of non-interacting PFs can attain the approximation accuracy of a centralised PF (with the same total number of particles) in just a fraction of its running time using a standard multicore computer.

Bayesian fusion: scalable unification of distributed statistical analyses

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Particle Filter Tracking of Complex Stochastic Systems Applied to In Silico Wavefront Propagation

“…We implemented two algorithms, the Auxiliary Particle Filtering (APF) and the Independent APF (IAPF), using a pool of multi-core CPUs for the implementation of the parallel filters. The details for the algorithms are described in [6]. To characterize the tracking states, let us denote…”

MultiPDF particle filtering in state estimation of nonlinear objects

“…Parallel forms of different types of resampling known from the literature are shown, as well as the time bene-fits resulting from them. The need and applicability of the parallelization of PF calculations were also highlighted in the surveys [29,30], in which several proposals were also presented, like non-interacting particle filters (not using communication between sub-filters) or particle islands (using the sequential Monte Carlo SMC method). Additionally, the total particles' population is divided here into sub-populations (named "islands").…”