Where are my colleagues?: Tracking and Counting Multiple Persons using Lifted Marginal Filtering

Abstract

Tracking multiple targets with anonymous sensors (e.g. presence sensors) leads to a combinatorial explosion in the number of possible siuations (hypotheses) that need to be tracked, due to the uncertainty of the association of identities to observed tracks. We propose a novel Bayesian filtering algorithm that can solve this problem by employing a compact state representation. A single lifted state represents a uniform distribution over all possible identity-track associations. The state representation and dynamics is based on Multiset Rewriting Systems and Lifted Probabilistic Inference. We show that Bayesian filtering using this representation is possible without resorting to ground states. This is demonstrated for a person tracking scenario in an office environment where up to seven persons are observed with presence sensors. Our approach naturally allows to simultaneously track persons and estimate their total number. The number of hypotheses is several orders of magnitude smaller than using a ground state representation.