Temporal Parallelization of Bayesian Filters and Smoothers

05/30/2019

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by   Simo Särkkä, et al.

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This paper presents algorithms for the temporal parallelization of Bayesian filters and smoothers. We define the elements and the operators to pose these problems as the solutions to all-prefix-sums operations for which efficient parallel scan-algorithms are available. We present the temporal parallelization of the general Bayesian filtering and smoothing equations, and the specific linear/Gaussian models, and discrete hidden Markov models. The advantage of the proposed algorithms is that they reduce the linear complexity of standard filtering and smoothing algorithms with respect to time to logarithmic.