Resampling and Network Theory

Abstract

Particle filtering provides an approximate representation of a tracked posterior density which converges asymptotically to the true posterior as the number of particles used increases. The greater the number of particles, the higher the computational complexity. This complexity can be implemented by operating the particle filter in parallel architectures. However, the resampling step in the particle filter requires a high level of synchronization and extensive information interchange between the particles, which impedes the use of parallel hardware systems. This paper establishes a new perspective for understanding particle filtering — that particle filtering can be achieved by adopting the principles of information exchange within a network, the nodes of which are now the particles in the particle filter. We propose to connect particles via a minimally connected network and resample each locally. This strategy facilitates full information exchange among the particles, but with each particle communicating with only a small fixed set of other particles, thus leading to minimal communication overhead. The key benefit is that this approach facilitates the use of many particles for accurate posterior approximation and tracking accuracy.