## Journal of Applied Mathematics

• J. Appl. Math.
• Volume 2012, Special Issue (2012), Article ID 141727, 20 pages.

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

#### 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.

#### Article information

Source
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 141727, 20 pages.

Dates
First available in Project Euclid: 3 January 2013

https://projecteuclid.org/euclid.jam/1357178255

Digital Object Identifier
doi:10.1155/2012/141727

Mathematical Reviews number (MathSciNet)
MR2956527

Zentralblatt MATH identifier
1251.93125

#### Citation

Lian, Feng; Han, Chongzhao; Liu, Jing; Chen, Hui. Convergence Results for the Gaussian Mixture Implementation of the Extended-Target PHD Filter and Its Extended Kalman Filtering Approximation. J. Appl. Math. 2012, Special Issue (2012), Article ID 141727, 20 pages. doi:10.1155/2012/141727. https://projecteuclid.org/euclid.jam/1357178255

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