New Branching Filters With Explicit Negative Dependence

Particle filters are used to solve nonlinear filtering problems. We focus on the sampling step of a particle filter and present new algorithms that introduce explicit negative dependence between the number of particles reassigned at each location, with the goal of improving the performance of the filtering algorithm. We review partial and complete sampling in the context of both interacting and branching filters, that is, when the number of particles stays constant through all steps and when it does not. In particular, we use the quick simulation field algorithm to reproduce the variance structure induced by the minimal variance filter and create a new filtering algorithm. A numerical example is used to assess the performance of the new algorithms.