Implementation of the Daum-Huang exact-flow particle filter

Several versions of the Daum-Huang (DH) filter have been introduced recently to address the task of discrete-time nonlinear filtering. The filters propagate a particle set over time to track the system state, but, in contrast to conventional particle filters, there is no proposal density or importance sampling involved. Particles are smoothly migrated using a particle flow derived from a log-homotopy relating the prior and the posterior. Impressive performance has been demonstrated for a wide range of systems, but the implemented algorithms rely on an extended/unscented Kalman filter (EKF/UKF) that is executed in parallel. We illustrate through simulation that the performance of the exact flow DH filter can be compromised when the UKF and EKF fail. By introducing simple but important modifications to the exact flow DH filter implementation, the performance can be improved dramatically.