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On the functional derivative with respect to the Dirac Delta

: Degen, C.; Streit, R.; Koch, W.


Institute of Electrical and Electronics Engineers -IEEE-; IEEE Aerospace and Electronic Systems Society -AESS-; International Society of Information Fusion -ISIF-:
10th Workshop on Sensor Data Fusion: Trends, Solutions, Applications, SDF 2015 : Bonn, Germany, October 6 - 8, 2015
Piscataway, NJ: IEEE, 2015
ISBN: 978-1-4673-7176-6
ISBN: 978-1-4673-7175-9
Workshop on Sensor Data Fusion (SDF) <10, 2015, Bonn>
Fraunhofer FKIE ()

It is a well-known fact that the distribution of the Bayes posterior point process is given by a ratio of functional derivatives (with respect to the Dirac delta) of a joint target-measurement probability generating functional. In the literature, functional derivatives with respect to the Dirac delta are often described as a heuristic. In this paper an existing definition of the functional derivative with respect to the Dirac delta using approximate identities is proven to be mathematically correct under general assumptions that are valid for almost all practical multitarget tracking applications.