Gaussian Mixture Nonlinear Filtering With Resampling for Mixand Narrowing

A new Gaussian mixture filter has been developed, one that uses a resampling 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-Gaussian 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 resampling step uses a newly designed algorithm that employs 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 resampling algorithm also attempts to economize on the number of new mixands. The resulting filter has been tested on a difficult seven-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.