Resampling-free fast particle filtering with application to tracking rhythmic biomedical signals

The particle filter is known to be a powerful tool for the estimation of time varying latent states guided by nonlinear dynamics and sensor measurements.Particle filter’s traditional resampling step is essential because it avoids degeneracy of particles by stochastically eliminating the small weight particles that do not contribute to the posterior probability density function and replacing them by copies of those having large weights. Nevertheless, resampling is computationally costly since it requires extensive and sequential communication among the particles. This work proposes a novel method of particle filtering that eliminates the need for resampling and prevents degeneracy by substituting low-weight particles with a simple cutoff decision strategy based on the cumulative sum of weights. The proposed scheme limits replacement over only a few important particles and hence substantially accelerates the filtering process. We show the merits of the proposed method via simulations using a nonlinear example and also apply the method for tracking harmonics of real biomedical signals.