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The authors consider the problem of extended object tracking. An extended object is modelled as a set of point features in a target reference frame. The dynamics of the extended object are formulated in terms of the translation and rotation of the target reference frame relative to a fixed reference frame. This leads to realistic, yet simple, models for the object motion. It is assumed that the measurements of the point features are unlabelled, and contaminated with a high level of clutter, leading to measurement association uncertainty. Marginalising over all the association hypotheses may be computationally prohibitive for realistic numbers of point features and clutter measurements. The authors present an alternative approach within the context of particle filtering, where they augment the state with the unknown association hypothesis, and sample candidate values from an efficiently designed proposal distribution. This proposal elegantly captures the notion of a soft gating function. The performance of the algorithm is demonstrated on a challenging synthetic tracking problem, where the ground truth is known, in order to compare between different algorithms.