First-moment multi-object forward-backward smoothing

Daniel E. Clark

Research output: Chapter in Book/Report/Conference proceedingConference contribution

13 Citations (Scopus)


The optimal solution to the problem of detecting, tracking and identifying multiple targets can be found through a direct generalisation of the Bayes filter to multi-object systems using Mahler's Finite Set Statistics. Due to the inherent complexity of the multi-object Bayes filter, Mahler proposed to propagate the first-order multi-object moment density, known as the Probability Hypothesis Density (PHD), instead of the multi-object posterior. This was derived using the concept of the probability generating functional (p.g.fl.) from point process theory. In this paper, I derive multi-object first-moment smoothers for forward-backward smoothing through a new formulation of the p.g.fl. smoother which takes advantage of the p.g.fl. Bayes update. This formulation permits the straightforward derivation of first-moment multi-object smoothers, including the PHD smoother.

Original languageEnglish
Title of host publication13th Conference on Information Fusion, Fusion 2010
Publication statusPublished - 2010
Event13th Conference on Information Fusion - Edinburgh, United Kingdom
Duration: 26 Jul 201029 Jul 2010


Conference13th Conference on Information Fusion
Abbreviated titleFusion 2010
Country/TerritoryUnited Kingdom


  • Finite Set Statistics (FISST)
  • Forward-backward smoothing
  • Multi-object estimation
  • Probability Hypothesis Density (PHD) filters


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