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Convergence results for the Gaussian mixture implementation of the extended-target PHD filter and its extended Kalman filtering approximation. (English) Zbl 1251.93125

Summary: 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.

MSC:

93E11 Filtering in stochastic control theory
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