An alternative to the Mahalanobis distance for determining optimal correspondences in data association
“An alternative to the Mahalanobis distance for determining optimal correspondences in data association”. J.L. Blanco, J. Gonzalez-Jimenez, J.A. Fernandez-Madrigal. IEEE Transactions on Robotics (T-RO), vol. 28, no.4, 980-986, 2012. (Bibtex, Draft PDF)
Abstract: The most common criteria for determining data association rely on minimizing the squared Mahalanobis distance (SMD) between observations and predictions. We hold that the SMD is just a heuristic, while the alternative matching likelihood (ML) is the optimal statistic to be maximized. Thorough experiments undoubtedly confirm this idea, with false positive reductions of up to 16%.
Related software: The 2d-slam-demo app; the data-association module in mrpt-slam.
This paper includes a rigorous review/tutorial on data association, discusses the underlying principles and demonstrates that the Mahalanobis distance is just an heuristic whose results can be improved with the proposed alternative.