Convergence Results for the Gaussian Mixture Implementation of the Extended‐Target PHD Filter and Its Extended Kalman Filtering Approximation
Feng Lian, Chongzhao Han, Jing Liu, Hui Chen · Journal of Applied Mathematics · 2012
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.