Gotowa bibliografia na temat „Bernoulli hypothesis”

La poursuite multi-cibles a pour objet le suivi d'un ensemble de cibles mobiles à partir de données obtenues séquentiellement. Ce problème est particulièrement complexe du fait du nombre inconnu et variable de cibles, de la présence de bruit de mesure, de fausses alarmes, d'incertitude de détection et d'incertitude dans l'association de données. Les filtres PHD (Probability Hypothesis Density) constituent une nouvelle gamme de filtres adaptés à cette problématique. Ces techniques se distinguent des méthodes classiques (MHT, JPDAF, particulaire) par la modélisation de l'ensemble des cibles comme un ensemble fini aléatoire et par l'utilisation des moments de sa densité de probabilité. Dans la première partie, on s'intéresse principalement à la problématique de l'application des filtres PHD pour le filtrage multi-cibles maritime et aérien dans des scénarios réalistes et à l'étude des propriétés numériques de ces algorithmes. Dans la seconde partie, nous nous intéressons à l'étude théorique des processus de branchement liés aux équations du filtrage multi-cibles avec l'analyse des propriétés de stabilité et le comportement en temps long des semi-groupes d'intensités de branchements spatiaux. Ensuite, nous analysons les propriétés de stabilité exponentielle d'une classe d'équations à valeurs mesures que l'on rencontre dans le filtrage non-linéaire multi-cibles. Cette analyse s'applique notamment aux méthodes de type Monte Carlo séquentielles et aux algorithmes particulaires dans le cadre des filtres de Bernoulli et des filtres PHD.

The aim of the present dissertation is to address distributed tracking over a network of heterogeneous and geographically dispersed nodes (or agents) with sensing, communication and processing capabilities. Tracking is carried out in the Bayesian framework and its extension to a distributed context is made possible via an information-theoretic approach to data fusion which exploits consensus algorithms and the notion of Kullback–Leibler Average (KLA) of the Probability Density Functions (PDFs) to be fused. The first step toward distributed tracking considers a single moving object. Consensus takes place in each agent for spreading information over the network so that each node can track the object. To achieve such a goal, consensus is carried out on the local single-object posterior distribution, which is the result of local data processing, in the Bayesian setting, exploiting the last available measurement about the object. Such an approach is called Consensus on Posteriors (CP). The first contribution of the present work is an improvement to the CP algorithm, namely Parallel Consensus on Likelihoods and Priors (CLCP). The idea is to carry out, in parallel, a separate consensus for the novel information (likelihoods) and one for the prior information (priors). This parallel procedure is conceived to avoid underweighting the novel information during the fusion steps. The outcomes of the two consensuses are then combined to provide the fused posterior density. Furthermore, the case of a single highly-maneuvering object is addressed. To this end, the object is modeled as a jump Markovian system and the multiple model (MM) filtering approach is adopted for local estimation. Thus, the consensus algorithms needs to be re-designed to cope with this new scenario. The second contribution has been to devise two novel consensus MM filters to be used for tracking a maneuvering object. The novel consensus-based MM filters are based on the First Order Generalized Pseudo-Bayesian (GPB1) and Interacting Multiple Model (IMM) filters. The next step is in the direction of distributed estimation of multiple moving objects. In order to model, in a rigorous and elegant way, a possibly time-varying number of objects present in a given area of interest, the Random Finite Set (RFS) formulation is adopted since it provides the notion of probability density for multi-object states that allows to directly extend existing tools in distributed estimation to multi-object tracking. The multi-object Bayes filter proposed by Mahler is a theoretically grounded solution to recursive Bayesian tracking based on RFSs. However, the multi-object Bayes recursion, unlike the single-object counterpart, is affected by combinatorial complexity and is, therefore, computationally infeasible except for very small-scale problems involving few objects and/or measurements. For this reason, the computationally tractable Probability Hypothesis Density (PHD) and Cardinalized PHD (CPHD) filtering approaches will be used as a first endeavour to distributed multiobject filtering. The third contribution is the generalisation of the single-object KLA to the RFS framework, which is the theoretical fundamental step for developing a novel consensus algorithm based on CPHD filtering, namely the Consensus CPHD (CCPHD). Each tracking agent locally updates multi-object CPHD, i.e. the cardinality distribution and the PHD, exploiting the multi-object dynamics and the available local measurements, exchanges such information with communicating agents and then carries out a fusion step to combine the information from all neighboring agents. The last theoretical step of the present dissertation is toward distributed filtering with the further requirement of unique object identities. To this end the labeled RFS framework is adopted as it provides a tractable approach to the multi-object Bayesian recursion. The δ- GLMB filter is an exact closed-form solution to the multi-object Bayes recursion which jointly yields state and label (or trajectory) estimates in the presence of clutter, misdetections and association uncertainty. Due to the presence of explicit data associations in the δ-GLMB filter, the number of components in the posterior grows without bound in time. The fourth contribution of this thesis is an efficient approximation of the δ-GLMB filter, namely Marginalized δ-GLMB (Mδ-GLMB), which preserves key summary statistics (i.e. both the PHD and cardinality distribution) of the full labeled posterior. This approximation also facilitates efficient multi-sensor tracking with detection-based measurements. Simulation results are presented to verify the proposed approach. Finally, distributed labeled multi-object tracking over sensor networks is taken into account. The last contribution is a further generalization of the KLA to the labeled RFS framework, which enables the development of two novel consensus tracking filters, namely the Consensus Marginalized δ-Generalized Labeled Multi-Bernoulli (CM-δGLMB) and the Consensus Labeled Multi-Bernoulli (CLMB) tracking filters. The proposed algorithms provide a fully distributed, scalable and computationally efficient solution for multi-object tracking. Simulation experiments on challenging single-object or multi-object tracking scenarios confirm the effectiveness of the proposed contributions.