A Box Particle Filter for Stochastic and Set-theoretic Measurements with Association Uncertainty

This work develops a novel estimation approach for nonlinear dynamic stochastic systems by combining the sequential Monte Carlo method with interval analysis. Unlike the common pointwise measurements, the proposed solution is for problems with interval measurements with association uncertainty. The optimal theoretical solution can be formulated in the framework of random set theory as the Bernoulli filter for interval measurements. The straightforward particle filter implementation of the Bernoulli filter typically requires a huge number of particles since the posterior probability density function occupies a significant portion of the state space. In order to reduce the number of particles, without necessarily sacrificing estimation accuracy, the paper investigates an implementation based on box particles. A box particle occupies a small and controllable rectangular region of non-zero volume in the target state space. The numerical results demonstrate that the filter performs remarkably well: both target state and target presence are estimated reliably using a very small number of box particles

Parallelized Particle and Gaussian Sum Particle Filters for Large Scale Freeway Traffic Systems

Large scale traffic systems require techniques able to: 1) deal with high amounts of data and heterogenous data coming from different types of sensors, 2) provide robustness in the presence of sparse sensor data, 3) incorporate different models that can deal with various traffic regimes, 4) cope with multimodal conditional probability density functions for the states. Often centralized architectures face challenges due to high communication demands. This paper develops new estimation techniques able to cope with these problems of large traffic network systems. These are Parallelized Particle Filters (PPFs) and a Parallelized Gaussian Sum Particle Filter (PGSPF) that are suitable for on-line traffic management. We show how complex probability density functions of the high dimensional trafc state can be decomposed into functions with simpler forms and the whole estimation problem solved in an efcient way. The proposed approach is general, with limited interactions which reduces the computational time and provides high estimation accuracy. The efciency of the PPFs and PGSPFs is evaluated in terms of accuracy, complexity and communication demands and compared with the case where all processing is centralized

Filtrage ensembliste multi-hypothèse sur des données intervalles : Application à la localisation

Le filtrage particulaire est une méthode utilisée pour l'estimation d'état des systèmes dynamiques. L'un des inconvénients majeurs de ce type de filtrage est la nécessité d'utiliser un grand nombre de particules pour explorer les régions de forte vraisemblance et éviter ainsi une divergence éventuelle du filtre. Dans cet article, nous proposons un algorithme hybride basé simultanément sur le filtrage particulaire et l'analyse par intervalles. La méthode proposée permet de réduire significativement le nombre de particules par rapport au filtrage particulaire classique et de répondre ainsi aux applications temps réel. Des résultats sur un problème de localisation d'un mobile montrent l'utilité et l'efficacité de la méthode proposée

Localisation of an Unknown Number of Land Mines Using a Network of Vapour Detectors

We consider the problem of localising an unknown number of land mines using concentration information provided by a wireless sensor network. A number of vapour sensors/detectors, deployed in the region of interest, are able to detect the concentration of the explosive vapours, emanating from buried land mines. The collected data is communicated to a fusion centre. Using a model for the transport of the explosive chemicals in the air, we determine the unknown number of sources using a Principal Component Analysis (PCA)-based technique. We also formulate the inverse problem of determining the positions and emission rates of the land mines using concentration measurements provided by the wireless sensor network. We present a solution for this problem based on a probabilistic Bayesian technique using a Markov chain Monte Carlo sampling scheme, and we compare it to the least squares optimisation approach. Experiments conducted on simulated data show the effectiveness of the proposed approach

Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking

This work presents the current state-of-the-art in techniques for tracking a number of objects moving in a coordinated and interacting fashion. Groups are structured objects characterized with particular motion patterns. The group can be comprised of a small number of interacting objects (e.g. pedestrians, sport players, convoy of cars) or of hundreds or thousands of components such as crowds of people. The group object tracking is closely linked with extended object tracking but at the same time has particular features which differentiate it from extended objects. Extended objects, such as in maritime surveillance, are characterized by their kinematic states and their size or volume. Both group and extended objects give rise to a varying number of measurements and require trajectory maintenance. An emphasis is given here to sequential Monte Carlo (SMC) methods and their variants. Methods for small groups and for large groups are presented, including Markov Chain Monte Carlo (MCMC) methods, the random matrices approach and Random Finite Set Statistics methods. Efficient real-time implementations are discussed which are able to deal with the high dimensionality and provide high accuracy. Future trends and avenues are traced. © 2013 Elsevier Inc. All rights reserved

Group object structure and state estimation in the presence of measurement origin uncertainty.

This paper proposes a technique for motion and group structure estimation of moving targets based on evolving graph networks in the presence of measurement origin uncertainty. The proposed method, through an evolving graph model, allows to jointly estimate the group target and the group structure with the uncertainty. The performance of the algorithm is evaluated and results with real ground moving target indicator data are presented

Bernoulli Particle/Box-Particle Filters for Detection and Tracking in the Presence of Triple Measurement Uncertainty

This work presents sequential Bayesian detection and estimation methods for nonlinear dynamic stochastic systems using measurements affected by three sources of uncertainty: stochastic, set-theoretic and data association uncertainty. Following Mahler’s framework for information fusion, the paper develops the optimal Bayes filter for this problem in the form of the Bernoulli filter for interval measurements. Two numerical implementations of the optimal filter are developed. The first is the Bernoulli particle filter (PF), which turns out to require a large number of particles in order to achieve a satisfactory performance. For the sake of reduction in the number of particles, the paper also develops an implementation based on box particles, referred to as the Bernoulli Box-PF. A box particle is a random sample that occupies a small and controllable rectangular region of non-zero volume in the target state space. Manipulation of boxes utilizes the methods of interval analysis. The two implementations are compared numerically and found to perform remarkably well: the target is reliably detected and the posterior probability density function of the target state is estimated accurately. The Bernoulli Box-PF, however, when designed carefully, is computationally more efficient

Dynamic clustering and belief propagation for distributed inference in random sensor networks with deficient links.

A fundamental issue in real-world monitoring network systems is the choice of sensors to track local events. Ideally, the sensors work together, in a distributed manner, to achieve a common mission-specific task. This paper develops a framework for distributed inference based on dynamic clustering and belief propagation in sensor networks with deficient links. We investigate this approach for dynamic clustering of sensor nodes combined with belief propagation for the purposes of object tracking in sensor networks with and without deficient links. We demonstrate the efficiency of our approach over an example of hundreds randomly deployed sensors

A Sequential Monte Carlo Approach for Extended Object Tracking in the Presence of Clutter

Extended objects are characterised with multiple measurements originated from ifferent locations of the object surface. This paper presents a novel Sequential Monte Carlo (SMC) approach for extended object tracking in the presence of clutter. The problem is formulated for general nonlinear problems. The main contribution of this work is in the derivation of the likelihood function for nonlinear measurement functions, with sets of measurements belonging to a bounded region. Simulation results are presented when the object is surrounded by a circular region. Accurate estimation results are presented both for the object kinematic state and object extent