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

Radar Optimal Times Detection Allocation in Multitarget Environment

International audienceThis paper deals with the problem of the management of Electronically Steered Antenna (ESA) in multitarget environments. Radars are used to detect, locate and identify targets. In this paper we focus on the detection of several aerial targets in a fixed given time. The difficulty of such detection lies in the fact that targets may be located anywhere in the space, but radars can only observe a limited part of it at a time. As a result, it is necessary to change their axis position over time. This paper describes the main steps to derive an optimal radar management in this context: the modeling of the radar, the determination of a criterion based on the target detection probability and the temporal optimization process leading to sensor management strategy. An optimization solution is presented for several contexts and several hypotheses about prior knowledge concerning the targets' locations. First, we propose a method for the optimization of the radar detection probability in a single target environment. It consists in the decomposition of the detection step into an optimal number of independent elementary detections. Then, in a multitarget context with deterministic prior knowledge, we present an optimal time allocation method which is based on the results of non linear programming. Finally, in a multitarget context with probabilistic prior knowledge, results in Search Theory are used to determine an optimal temporal allocation

Time Allocation of a Set of Radars in a Multitarget Environment

International audienceThe question tackled here is the time allocation of radars in a multitarget environment. At a given time radars can only observe a limited part of the space; it is therefore necessary to move their axis with respect to time, in order to be able to explore the overall space facing them. Such sensors are used to detect, to locate and to identify targets which are in their surrounding aerial space. In this paper we focus on the detection schema when several targets need to be detected by a set of delocalized radars. This work is based on the modelling of the radar detection performances in terms of probability of detection and on the optimization of a criterion based on detection probabilities. This optimization leads to the derivation of allocation strategies and is made for several contexts and several hypotheses about the targets locations

Fusion de capteurs potentiellement défaillants par filtrage particulaire

Cet article s'intéresse à l'estimation bayésienne d'un vecteur d'état à l'aide de données multicapteur obtenues séquentiellement, en considérant que les capteurs sont potentiellement défaillants. Un état augmenté avec les variables indicatrices de validité et les coefficients de fiabilité de chaque capteur est estimé par un algorithme de Monte Carlo séquentiel (aussi appelé filtre particulaire). Une attention particulière est portée au choix des fonctions d'importance. Un exemple est fourni montrant l'amélioration de l'estimation en présence de capteurs défaillants par rapport à un filtre particulaire classique

Optimal Policies Search for Sensor Management

International audienceThis paper introduces a new approach to solve sensor management problems. Classically sensor management problems can be well formalized as Partially-Observed Markov Decision Processes (POMPD). The original approach developped here consists in deriving the optimal parameterized policy based on a stochastic gradient estimation. We assume in this work that it is possible to learn the optimal policy off-line (in simulation ) using models of the environement and of the sensor(s). The learned policy can then be used to manage the sensor(s). In order to approximate the gradient in a stochastic context, we introduce a new method to approximate the gradient, based on Infinitesimal Perturbation Approximation (IPA). The effectiveness of this general framework is illustrated by the managing of an Electronically Scanned Array Radar. First simulations results are finally proposed

Dirichlet Process Mixtures for Density Estimation in Dynamic Nonlinear Modeling: Application to GPS Positioning in Urban Canyons

International audienceIn global positioning systems (GPS), classical localization algorithms assume, when the signal is received from the satellite in line-of-sight (LOS) environment, that the pseudorange error distribution is Gaussian. Such assumption is in some way very restrictive since a random error in the pseudorange measure with an unknown distribution form is always induced in constrained environments especially in urban canyons due to multipath/masking effects. In order to ensure high accuracy positioning, a good estimation of the observation error in these cases is required. To address this, an attractive flexible Bayesian nonparametric noise model based on Dirichlet process mixtures (DPM) is introduced. Since the considered positioning problem involves elements of non-Gaussianity and nonlinearity and besides, it should be processed on-line, the suitability of the proposed modeling scheme in a joint state/parameter estimation problem is handled by an efficient Rao-Blackwellized particle filter (RBPF). Our approach is illustrated on a data analysis task dealing with joint estimation of vehicles positions and pseudorange errors in a global navigation satellite system (GNSS)-based localization context where the GPS information may be inaccurate because of hard reception conditions

Application of the TBM to the communication nodes localization using proximity measures

Materials localization on a site under contruction (a building for instance) is very important from an economical point of view. RFID systems and localization systems as GPS allow to treat such a problem in the more general context of randomly distributed communication nodes localization. When the nodes are moving the problem is still more complicated. The work exposed in this paper shows how the Transferable Belief Model be used for the detection of potential movements. This study also show how to deal with the calculation.La localisation de matériaux sur un site de construction est d'un intérêt économique de premier ordre. L'utilisation de systèmes RFID (Radio Frequency IDentification) et de dispositifs de localisation par satellite permettent de traiter ce problème dans le cadre, plus général, de la localisation de noeuds de communication distribués aléatoirement. Lorsque ces noeuds peuvent se déplacer de façon aléatoire, la problématique s'en trouve encore complexifiée. Les travaux exposés dans cet article montrent comment la modélisation, dans le cadre du Modèle de Croyance Transférable, de l'imprécision et de l'incertitude inhérentes au problème permet d'y apporter une solution. L'utilisation du conflit permet tout particulièrement de détecter, puis de prendre en compte, le mouvement d'un noeud de communication. L'étude proposée montre également comment il est possible de conduire les calculs de façon à ne pas être confronté à une explosion combinatoire

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

Conception et realisation d'un vehicule automatique

SIGLET 55003 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc