Optimised proposals for improved propagation of multi-modal distributions in particle filters

Particle filters are an increasingly popular algorithm for tracking in non-linear and non-Gaussian scenarios. However, in scenarios involving multiple pronounced and persistent modes, particle filters can struggle to maintain accurate estimates of the weights associated with these modes. Indeed, particle filters often lose modes all together. We explain why this phenomenon occurs. We articulate some convergence results for particle filters in a context that aims to be accessible to engineering practitioners. We use this review of convergence results to argue the utility of optimised proposal distributions in multi-modal scenarios. We demonstrate the validity of this argument by applying particle filters to synthetic data where multi-modal structure is designed to exist but this structure is unknown to the particle filter. We find that optimised particle filters outperform naïve particle filter both when the same number of particles is used and when the total computational cost is kept approximately constant: a smaller number of particles with an optimised proposal distribution can out perform a larger number of particles with a naïve proposal distribution. Furthermore, the benefits derived from previous work, which explicitly stratifies the particle filter with the intent of improving performance in multi-modal scenarios, is found to be less than the benefits derived from using optimised proposals. We conclude that multi-modality, perhaps surprisingly, does not motivate a different approach to applications of particle filters to other challenging scenarios.