# MapReduce Particle Filtering with Exact Resampling and Deterministic Runtime

## TL;DR

This paper presents a scalable MapReduce implementation of particle filtering with an exact, deterministic resampling method that efficiently handles large numbers of particles across distributed systems.

## Contribution

It introduces a novel resampling component for particle filters that is exact, scalable, and suitable for distributed computing environments.

## Key findings

- Resampling component has $O(N)$ spatial complexity and deterministic $O(( ext{log} N)^2)$ time complexity.
- Particle filter with $2^{24}$ particles distributed over 512 cores demonstrates scalability.
- New implementation improves efficiency and accuracy of particle filtering in big data contexts.

## Abstract

Particle filtering is a numerical Bayesian technique that has great potential for solving sequential estimation problems involving non-linear and non-Gaussian models. Since the estimation accuracy achieved by particle filters improves as the number of particles increases, it is natural to consider as many particles as possible. MapReduce is a generic programming model that makes it possible to scale a wide variety of algorithms to Big data. However, despite the application of particle filters across many domains, little attention has been devoted to implementing particle filters using MapReduce. In this paper, we describe an implementation of a particle filter using MapReduce. We focus on a component that what would otherwise be a bottleneck to parallel execution, the resampling component. We devise a new implementation of this component, which requires no approximations, has $O\left(N\right)$ spatial complexity and deterministic $O\left(\left(\log N\right)^2\right)$ time complexity. Results demonstrate the utility of this new component and culminate in consideration of a particle filter with $2^{24}$ particles being distributed across $512$ processor cores.