Feedback particle filter: Application and evaluation

Recent research has provided several new methods for avoiding degeneracy in particle filters. These methods implement Bayes' rule using a continuous transition between prior and posterior. The feedback particle filter (FPF) is one of them. The FPF uses feedback gains to adjust each particle according to the measurement, which is in contrast to conventional particle filters based on importance sampling. The gains are found as solutions to partial differential equations. This paper contains an evaluation of the FPF on two highly nonlinear estimation problems. The FPF is compared with conventional particle filters and the unscented Kalman filter. Sensitivity to the choice of gains is discussed and illustrated. We demonstrate that with a sensible approximation of the exact gain function, the FPF can decrease tracking errors with more than one magnitude while significantly improving the quality of the particle distribution.