The Antiparticle Filter - An Adaptive Nonlinear Estimator

We introduce the antiparticle filter, AF, a new type of recursive Bayesian estimator that is unlike either the extended Kalman Filter, EKF, unscented Kalman Filter, UKF or the particle filter PF. We show that for a classic problem of robot localization the AF can substantially outperform these other filters in some situations. The AF estimates the posterior distribution as an auxiliary variable Gaussian which gives an analytic formula using no random samples. It adaptively changes the complexity of the posterior distribution as the uncertainty changes. It is equivalent to the EKF when the uncertainty is low while being able to represent non-Gaussian distributions as the uncertainty increases. The computation time can be much faster than a particle filter for the same accuracy. We have simulated comparisons of two types of AF to the EKF, the iterative EKF, the UKF, an iterative UKF, and the PF demonstrating that AF can reduce the error to a consistent accurate value.