Multi-Sensor PHD by Space Partionning: Computation of a True Reference Density Within The PHD Framework

International audienceIn a previous paper, the authors proposed an extension of the Probability Hypothesis Density (PHD), a well-known method for singlesensor multi-target tracking problems in a Bayesian framework, to the multi-sensor case. The true expression of the multi-sensor data update PHD equation was constructed using finite sets statistics (FISST) derivative techniques on functionals defined onmulti-sensor observation and state space named "cross-terms". In this paper, an equivalent expression in a combinational form is provided, which allows an easier interpretation of the data update equation. Then, using the joint partitioning proposed by the authors in the previous paper, an exact multi-sensor multi-target PHD filter is efficiently propagated on a benchmark scenario involving 10 sensors and up to 10 simultaneous targets where the brute force approach would have been extremely burdensome. The availability of a true reference PHD then allows a validation of the classical iterated-corrector approximation method, albeit limited to the scope of the implemented scenario

Multi-target PHD filtering: proposition of extensions to the multi-sensor case

Common difficulties in multi-target tracking arise from the fact that the system state and the collection of measures are unordered and their size evolve randomly through time. The random finite set theory provides a powerful framework to cope with these issues. This document focuses more particularly on the PHD (Probability Hypothesis Density) filter proposed by Mahler. The first part of this report is a synthesis of Mahler's work and aims at providing a thorough description of the construction of the single-sensor PHD filter. Then, based on a few leads provided by Mahler, the second part proposes several extensions of this filter to the multi-sensor case.Le pistage multi-cible se trouve confronté au double problème suivant : l'état du système et la collection de mesures ne sont pas ordonnés et leurs dimensions varient aléatoirement au cours du temps. Dans ce contexte, l'utilisation des ensembles aléatoires finis apporte un cadre de résolution particulièrement pertinent et ce travail s'intéresse plus particulièrement au filtre PHD (Probability Hypothesis Density) introduit par Mahler. La première partie de ce rapport est une synthèse des travaux de Mahler et se veut pédagogique : elle reprend en détail la construction du filtre PHD mono-capteur. En se basant sur les éléments de solution proposés par Mahler, la deuxième partie propose des extensions du filtre au cas multi-capteur

Multi-target PHD filtering: proposition of extensions to the multi-sensor case

Common difficulties in multi-target tracking arise from the fact that the system state and the collection of measures are unordered and their size evolve randomly through time. The random finite set theory provides a powerful framework to cope with these issues. This document focuses more particularly on the PHD (Probability Hypothesis Density) filter proposed by Mahler. The first part of this report is a synthesis of Mahler's work and aims at providing a thorough description of the construction of the single-sensor PHD filter. Then, based on a few leads provided by Mahler, the second part proposes several extensions of this filter to the multi-sensor case.Le pistage multi-cible se trouve confronté au double problème suivant : l'état du système et la collection de mesures ne sont pas ordonnés et leurs dimensions varient aléatoirement au cours du temps. Dans ce contexte, l'utilisation des ensembles aléatoires finis apporte un cadre de résolution particulièrement pertinent et ce travail s'intéresse plus particulièrement au filtre PHD (Probability Hypothesis Density) introduit par Mahler. La première partie de ce rapport est une synthèse des travaux de Mahler et se veut pédagogique : elle reprend en détail la construction du filtre PHD mono-capteur. En se basant sur les éléments de solution proposés par Mahler, la deuxième partie propose des extensions du filtre au cas multi-capteur