Revisiting Functional Derivatives in Multi-object Tracking
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909864483094528 |
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| author | Krejčí, Jan Straka, Ondřej Girg, Petr Benedikt, Jiří |
| author_facet | Krejčí, Jan Straka, Ondřej Girg, Petr Benedikt, Jiří |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12982 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Revisiting Functional Derivatives in Multi-object Tracking Krejčí, Jan Straka, Ondřej Girg, Petr Benedikt, Jiří Systems and Control Other Statistics 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. |
| title | Revisiting Functional Derivatives in Multi-object Tracking |
| topic | Systems and Control Other Statistics |
| url | https://arxiv.org/abs/2508.12982 |