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Joint multi-target detection and tracking is a challenging problem due to several factors such as the number of targets being an unknown time-varying random parameter, and the target generated measurements being obscured by clutter. The theory of random finite sets permits an elegant formulation of the joint multi-target detection and tracking problem in a Bayesian framework, in particular, the random finite set formalism leads to the probability hypothesis density (PHD) filtering method, which realizes Bayesian joint detection and tracking in a suboptimal but numerically tractable manner. In this paper the PHD filter is applied to jointly detect and track multiple maneuvering targets. The tracking performance fidelity of the PHD filter is demonstrated by numerical results.