Gaussian Mixture Filtering with Nonlinear Measurements Minimizing Forward Kullback-Leibler Divergence

Laz E., ORGUNER U.

Signal Processing, vol.208, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 208
  • Publication Date: 2023
  • Doi Number: 10.1016/j.sigpro.2023.108992
  • Journal Name: Signal Processing
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, PASCAL, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, zbMATH
  • Keywords: Nonlinear filtering, Gaussian mixture, Gaussian sum, Kullback-Leibler divergence, Newton?s method, KALMAN FILTER, UPDATE
  • Middle East Technical University Affiliated: Yes

Abstract

A Gaussian mixture filter is proposed for the state estimation of dynamical systems with nonlinear measurements. The filter is derived by solving an assumed density filtering problem where Kullback-Leibler (KL) divergence from the assumed posterior, which is a Gaussian mixture, to the true posterior (which we call forward KL divergence) is minimized. The approximate solution to this problem gives an iterative measurement update by which the weights, means and covariances of the assumed posterior are optimized. The resulting Gaussian mixture filter is shown to be a generalization of the (damped) posterior linearization filter to Gaussian mixture posteriors. The performance of the proposed filter is illustrated and compared to alternatives on a challenging example of target tracking in a sensor network and on an example of tracking with a radar. The results show that the proposed filter can outperform Gaussian filters as well as the Gaussian sum filter and the Gaussian sum particle filter yielding results very close to a bootstrap particle filter when the number of components in the assumed posterior is sufficiently large.