PKF: Probabilistic Data Association Kalman Filter for Multi-Object Tracking

In this letter, we derive a new Kalman filter (KF) with probabilistic data association between measurements and states. We formulate a variational inference problem to approximate the posterior density of the state conditioned on the measurement data. We view the unknown data association as a latent variable and apply Expectation Maximization (EM) to obtain a filter with the update step in the same form as the Kalman filter but with an expanded measurement vector of all potential associations. We show that the association probabilities can be computed as permanents of matrices with measurement likelihood entries. We name our probabilistic data association Kalman filter the PKF with P emphasizing both the probabilistic nature of the data association and the matrix permanent computation of the association weights. We compare PKF with the well-established Probabilistic Multi-Hypothesis Tracking (PMHT) and Joint Probabilistic Data Association Filter (JPDAF) in both theory and simulated experiments. The experiments show that we can achieve lower tracking errors than both. We also demonstrate the effectiveness of our filter in multi-object tracking (MOT) on multiple real-world datasets, including MOT17, MOT20, and DanceTrack. We can achieve comparable tracking results with previous KF-based methods without using velocities or doing multi-stage data association and remain real-time. We further show that our PKF can serve as a backbone for other KF-based trackers by applying it to a method that uses varieties of features for association, and improving its results.