# A Complete Derivation Of The Association Log-Likelihood Distance For Multi-Object Tracking

arXiv: https://arxiv.org/abs/1508.04124 · HTML: https://mlsanity.com/paper/1508.04124/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2015.

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

- [Collaborative Multi-Object Tracking with Conformal Uncertainty Propagation](https://mlsanity.com/paper/2303.14346/) (2023)
- [DeepHybrid: Deep Learning on Automotive Radar Spectra and Reflections for Object Classification](https://mlsanity.com/paper/2202.08519/) (2022)
- [Multi-Object Tracking based on Imaging Radar 3D Object Detection](https://mlsanity.com/paper/2406.01011/) (2024)

## Abstract (arXiv)

The Mahalanobis distance is commonly used in multi-object trackers for measurement-to-track association. Starting with the original definition of the Mahalanobis distance we review its use in association. Given that there is no principle in multi-object tracking that sets the Mahalanobis distance apart as a distinguished statistical distance we revisit the global association hypotheses of multiple hypothesis tracking as the most general association setting. Those association hypotheses induce a distance-like quantity for assignment which we refer to as association log-likelihood distance. We compare the ability of the Mahalanobis distance to the association log-likelihood distance to yield correct association relations in Monte-Carlo simulations. It turns out that on average the distance based on association log-likelihood performs better than the Mahalanobis distance, confirming that the maximization of global association hypotheses is a more fundamental approach to association than the minimization of a certain statistical distance measure.