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A new method for estimating the pose of a person in a marker-based visual motion capture system is presented. In such systems, certain markers are not detected at each time frame due to occlusion by the subject. It is proposed to estimate the person's pose subject to the constraint that non-detected markers remain occluded and that detected markers remain visible. In this paper, the complete posterior PDF for the person's pose is developed using the constraints mentioned above, as is a least squares solution for determining its maximum. It is shown that the new technique is able to correctly estimate a variety of poses in which many marker occlusions occur and in which typical motion capture systems fail.