Symmetrizing measurement equations for association-free multi-target tracking via point set distances

We are tracking multiple targets based on noisy measurements. The targets are labeled, the measurements are unlabeled, and the association of measurements to targets is unknown. Our goal is association-free tracking, so the associations will never be determined as this is costly and impractical in many scenarios. By employing a permutation-invariant and differentiable point set distance measure, we derive a modified association-free multi-target measurement equation. It maintains the target identities but is invariant to permutations in the unlabeled measurements. Based on this measurement equation, we derive an efficient sample-based association-free multi-target Kalman filter. The proposed new approach is straightforward to implement and scalable.