Bayesian Filtering for plan and activity recognition is challenging for scenarios that contain many observation equivalent entities (i.e. entities that produce the same observations). This is due to the combinatorial explosion in the number of hypotheses that need to be tracked. However, this class of problems exhibits a certain symmetry that can be exploited for state space representation and inference. We analyze current state of the art methods and find that none of them completely fits the requirements arising in this problem class. We sketch a novel inference algorithm that provides a solution by incorporating concepts from Lifted Inference algorithms, Probabilistic Multiset Rewriting Systems, and Computational State Space Models. Two experiments confirm that this novel algorithm has the potential to perform efficient probabilistic inference on this problem class.
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