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The problem is joint detection and tracking of a non-point or extended moving object, characterised by multiple feature points, which can result in detections. Owing to imperfect detection, only some of the feature points are detected and in addition, false alarms [or clutter] can also be present. Standard tracking techniques assume point objects, that is at most one detection per object, and hence are not adequate for this problem. This study presents a principled theoretical solution in the form of the Bayes filter, referred to as the Bernoulli filter for an extended object. The derivation follows the random set filtering framework introduced by Mahler. The filter is implemented approximately as a particle filter and subsequently applied both to simulated data and a real video sequence.