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/non-Bayesian 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/Backwards-Smoothing EKF, and a regularized Particle Filter.