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

M.L. Psiaki

Abstract:	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. Re-sampling 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.
Published in:	Proceedings of IEEE/ION PLANS 2014 May 5 - 8, 2014 Hyatt Regency Hotel Monterey, CA
Pages:	393 - 406
Cite this article:	Psiaki, M.L., "The "Blob" Filter: Gaussian Mixture Nonlinear Filtering with Re-Sampling for Mixand Narrowing," Proceedings of IEEE/ION PLANS 2014, Monterey, CA, May 2014, pp. 393-406. https://doi.org/10.1109/PLANS.2014.6851397
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