Analysis of parallelizable resampling algorithms for particle filtering

Particle filtering methods are powerful tools for online estimation and tracking in nonlinear and non-Gaussian dynamical systems. They commonly consist of three steps: (1) drawing samples in the state-space of the system, (2) computing proper importance weights of each sample and (3) resampling. Steps 1 and 2 can be carried out concurrently for each sample, but standard resampling techniques require strong interaction. This is an important limitation, because one of the potential advantages of particle filtering is the possibility to perform very fast online signal processing using parallel computing devices. It is only very recently that resampling techniques specifically designed for parallel computation have been proposed, but little is known about the properties of such algorithms and how they compare to standard methods. In this paper, we investigate two classes of such techniques, distributed resampling with non-proportional allocation (DRNA) and local selection (LS). Namely, we analyze the effect of DRNA and LS on the sample variance of the importance weights; the distortion, due to the resampling step, of the discrete probability measure given by the particle filter; and the variance of estimators after resampling. Finally, we carry out computer simulations to support the analytical results and to illustrate the actual performance of DRNA and LS. Two typical problems are considered: vehicle navigation and tracking the dynamic variables of the chaotic Lorenz system driven by white noise.