Soft systematic resampling for accurate posterior approximation and increased information retention in particle filtering

The resampling step in the particle filter results in the loss of information contained in the lower weight particles. While the stochastic resamplers cause further loss by reweighing all particles to the same number, the deterministic resamplers impede the accumulation of information contained in the weights that are increasing over time. The soft resampler overcomes this information loss problem by redistributing the discarded weight among the lower weights. However, the technique does not accurately approximate the posterior because it always discards the lower weight particles located near tails of the cumulative distribution of the posterior density. In this paper, we rectify this problem by proposing a method to stochastically resample these discarded particles.