  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.
