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

arXiv: https://arxiv.org/abs/2411.06378 · HTML: https://mlsanity.com/paper/2411.06378/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 53 references that are in the map.
- First posted on arXiv 10 Nov 2024.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Objects as Points](https://mlsanity.com/paper/1904.07850/) (2019)
- [Simple Online and Realtime Tracking with a Deep Association Metric](https://mlsanity.com/paper/1703.07402/) (2017)
- [Simple Online and Realtime Tracking](https://mlsanity.com/paper/1602.00763/) (2016)
- [ByteTrack: Multi-Object Tracking by Associating Every Detection Box](https://mlsanity.com/paper/2110.06864/) (2021)
- [Performance Measures and a Data Set for Multi-Target, Multi-Camera Tracking](https://mlsanity.com/paper/1609.01775/) (2016)
- [HOTA: A Higher Order Metric for Evaluating Multi-Object Tracking](https://mlsanity.com/paper/2009.07736/) (2020)
- [MOT16: A Benchmark for Multi-Object Tracking](https://mlsanity.com/paper/1603.00831/) (2016)
- [TrackFormer: Multi-Object Tracking with Transformers](https://mlsanity.com/paper/2101.02702/) (2021)
- [FairMOT: On the Fairness of Detection and Re-Identification in Multiple Object Tracking](https://mlsanity.com/paper/2004.01888/) (2020)
- [Tracking Objects as Points](https://mlsanity.com/paper/2004.01177/) (2020)
- [Tracking without bells and whistles](https://mlsanity.com/paper/1903.05625/) (2019)
- [MOTR: End-to-End Multiple-Object Tracking with Transformer](https://mlsanity.com/paper/2105.03247/) (2021)
- [MOT20: A benchmark for multi object tracking in crowded scenes](https://mlsanity.com/paper/2003.09003/) (2020)
- [Observation-Centric SORT: Rethinking SORT for Robust Multi-Object Tracking](https://mlsanity.com/paper/2203.14360/) (2022)
- [Quasi-Dense Similarity Learning for Multiple Object Tracking](https://mlsanity.com/paper/2006.06664/) (2020)
- [DanceTrack: Multi-Object Tracking in Uniform Appearance and Diverse Motion](https://mlsanity.com/paper/2111.14690/) (2021)
- [Learning a Neural Solver for Multiple Object Tracking](https://mlsanity.com/paper/1912.07515/) (2019)
- [Track to Detect and Segment: An Online Multi-Object Tracker](https://mlsanity.com/paper/2103.08808/) (2021)
- [Detect to Track and Track to Detect](https://mlsanity.com/paper/1710.03958/) (2017)
- [MeMOT: Multi-Object Tracking with Memory](https://mlsanity.com/paper/2203.16761/) (2022)
- [TransMOT: Spatial-Temporal Graph Transformer for Multiple Object Tracking](https://mlsanity.com/paper/2104.00194/) (2021)
- [Hybrid-SORT: Weak Cues Matter for Online Multi-Object Tracking](https://mlsanity.com/paper/2308.00783/) (2023)
- [Exactly Sparse Gaussian Variational Inference with Application to Derivative-Free Batch Nonlinear State Estimation](https://mlsanity.com/paper/1911.08333/) (2019)
- [Multi-Robot Object SLAM Using Distributed Variational Inference](https://mlsanity.com/paper/2404.18331/) (2024)

## Built on by (most cited first, 3 of 3)

- [IMM-MOT: A Novel 3D Multi-object Tracking Framework with Interacting Multiple Model Filter](https://mlsanity.com/paper/2502.09672/) (2025)
- [Learning a Neural Association Network for Self-supervised Multi-Object Tracking](https://mlsanity.com/paper/2411.11514/) (2024)
- [FC-Track: Overlap-Aware Post-Association Correction for Online Multi-Object Tracking](https://mlsanity.com/paper/2603.12758/) (2026)

## Abstract (arXiv)

In this paper, we derive a new Kalman filter 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 update step in the same form as the Kalman filter but with 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 also propose an ambiguity check that associates only a subset of ambiguous measurements and states probabilistically, thus reducing the association time and preventing low-probability measurements from harming the estimation accuracy. Experiments in simulation show that our filter achieves lower tracking errors than the well-established joint probabilistic data association filter (JPDAF), while running at comparable rate. We also demonstrate the effectiveness of our filter in multi-object tracking (MOT) on multiple real-world datasets, including MOT17, MOT20, and DanceTrack. We achieve better higher order tracking accuracy (HOTA) than previous Kalman-filter methods and remain real-time. Associating only bounding boxes without deep features or velocities, our method ranks top-10 on both MOT17 and MOT20 in terms of HOTA. Given offline detections, our algorithm tracks at 250+ fps on a single laptop CPU. Code is available at https://github.com/hwcao17/pkf.