The following problem is considered: a group of point targets is observed via an imperfect sensor and one of the measurements chosen. The measurements of each target position is corrupted by an independent error, although every object is detected. Two processes then act to move and distort the group: one is a bulk effect that acts equally on all members of the group while the other is independent for each target. The group is observed again by a (possibly different) imperfect sensor which may not detect every target. The problem is to construct the posterior distribution of the chosen target's position, given the two sets of measurements. Probability models of the sensors and of the pattern distortion processes are assumed to be available. A formal general solution has been obtained for this problem. For the special linear-Gaussian case this reduces to a closed form analytic expression. To facilitate implementation, a hypothesis pruning technique is given. A simulation example illustrating performance is provided.
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