Revisiting Functional Derivatives in Multi-object Tracking
Abstract
Probability generating functionals (PGFLs) are efficient and powerful tools for tracking independent objects in clutter. It was shown that PGFLs could be used for the elegant derivation of practical multi-object tracking algorithms, e.g., the probability hypothesis density (PHD) filter. However, derivations using PGFLs use the so-called functional derivatives whose definitions usually appear too complicated or heuristic, involving Dirac delta ``functions''. This paper begins by comparing different definitions of functional derivatives and exploring their relationships and implications for practical applications. It then proposes a rigorous definition of the functional derivative, utilizing straightforward yet precise mathematics for clarity. Key properties of the functional derivative are revealed and discussed.
Cite
@article{arxiv.2508.12982,
title = {Revisiting Functional Derivatives in Multi-object Tracking},
author = {Jan Krejčí and Ondřej Straka and Petr Girg and Jiří Benedikt},
journal= {arXiv preprint arXiv:2508.12982},
year = {2025}
}
Comments
submitted to SIAM Journal on Control and Optimization