Clustering Methods for Particle Filters with Gaussian Mixture Models

New clustering methods are proposed to develop novel particle filters with Gaussian mixture models (PFGMM). In the PFGMM, the propagated samples are clustered to recover a Gaussian mixture model (GMM) using a clustering algorithm, which plays a fundamental role in the filter's performance. Two clustering methods are introduced that simultaneously minimize the covariance of each of the GMM components and maximize the likelihood function. Under the scenarios considered in this paper, it is shown through numerical simulation that the PFGMMs with the proposed clustering algorithms lead to better performance than the PFGMM employing the K-means or the expectation-maximization (EM) algorithms as well as the regularized particle filter (RPF) and the Gaussian sum particle filter (GSPF).