Deterministic resampling: Unbiased sampling to avoid sample impoverishment in particle filters

A novel resampling algorithm (called Deterministic Resampling) is proposed, which avoids uncensored discarding of low weighted particles thereby avoiding sample impoverishment. The diversity of particles is maintained by deterministically sampling support particles to improve the residual resampling. A proof is given that our approach can be strictly unbiased and maintains the original state density distribution. Additionally, it is practically simple to implement in low dimensional state space applications. The core idea behind our approach is that it is important to (re)sample based on both the weight of particles and their state values, especially when the sample size is small. Our approach, verified by simulations, indicates that estimation accuracy is better than traditional methods with an affordable computation burden.