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Convergence Results for the Gaussian Mixture Implementation of the Extended-Target PHD Filter and Its Extended Kalman Filtering Approximation

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  • Feng Lian
  • Chongzhao Han
  • Jing Liu
  • Hui Chen

Abstract

The convergence of the Gaussian mixture extended-target probability hypothesis density (GM-EPHD) filter and its extended Kalman (EK) filtering approximation in mildly nonlinear condition, namely, the EK-GM-EPHD filter, is studied here. This paper proves that both the GM-EPHD filter and the EK-GM-EPHD filter converge uniformly to the true EPHD filter. The significance of this paper is in theory to present the convergence results of the GM-EPHD and EK-GM-EPHD filters and the conditions under which the two filters satisfy uniform convergence.

Suggested Citation

  • Feng Lian & Chongzhao Han & Jing Liu & Hui Chen, 2012. "Convergence Results for the Gaussian Mixture Implementation of the Extended-Target PHD Filter and Its Extended Kalman Filtering Approximation," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-20, August.
    • Handle: RePEc:hin:jnljam:141727
    DOI: 10.1155/2012/141727
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