The "Blob" Filter: Gaussian Mixture Nonlinear Filtering with Re-Sampling for Mixand Narrowing

A new Gaussian mixture filter has been developed, one that uses a re-sampling step in order to limit the covariances of its individual Gaussian components. The new filter has been designed to produce accurate solutions of difficult nonlinear/nonBayesian estimation problems. It uses static multiple-model filter calculations and Extended Kalman Filter (EKF) approximations for each Gaussian mixand in order to perform dynamic propagation and measurement update. The re-sampling step uses a newly designed algorithm that employs linear matrix inequalities in order to bound each mixand's covariance. Resampling occurs between the dynamic propagation and the measurement update in order to ensure bounded covariance in both of these operations. The resulting filter has been tested on a difficult 7-state nonlinear filtering problem. It achieves significantly better accuracy than a simple EKF, an Unscented Kalman Filter, a Moving-Horizon Estimator/BackwardsSmoothing EKF, and a regularized Particle Filter. Keywords—Kalman Filter; Bayesian Filter; Gaussian Mixture Filter.