Particle Flow Filters: Biases and Bias Avoidance

Particle flow filters are appealing due to their potential resistance to particle collapse. However, common implementations exhibit undesirable biases or particle divergence. This paper shows that the explicit and incompressible flows, unlike the Gromov flow, are inherently biased. Another issue is errors in the numerical integration of the flow. The benefits of implicit stochastic-integration methods are demonstrated and a new adaptive step-size selection heuristic is presented.