Sequential Monte Carlo Methods for Crowd and Extended Object Tracking and Dealing with Tall Data

The Bayesian methodology is able to deal with a number of challenges in object tracking, especially with uncertainties in the system dynamics and sensor characteristics. However, model complexities can result in non-analytical expressions which require computationally cumbersome approximate solutions. In this thesis computationally efficient approximate methods for object tracking with complex models are developed. One such complexity is when a large group of objects, referred to as a crowd, is required to be tracked. A crowd generates multiple measurements with uncertain origin. Two solutions are proposed, based on a box particle filtering approach and a convolution particle filtering approach. Contributions include a theoretical derivation for the generalised likelihood function for the box particle filter, and an adaptive convolution particle filter able to resolve the data association problem without the measurement rates. The performance of the two filters is compared over a realistic scenario for a large crowd of pedestrians. Extended objects also generate a variable number of multiple measurements. In contrast with point objects, extended objects are characterised with their size or volume. Multiple object tracking is a notoriously challenging problem due to complexities caused by data association. An efficient box particle filter method for multiple extended object tracking is proposed, and for the first time it is shown how interval based approaches can deal efficiently with data association problems and reduce the computational complexity of the data association. The performance of the method is evaluated on real laser rangefinder data. Advances in digital sensors have resulted in systems being capable of accumulating excessively large volumes of data. Three efficient Bayesian inference methods are developed for object tracking when excessively large numbers of measurements may otherwise cause standard algorithms to be inoperable. The underlying mechanics of these methods are adaptive subsampling and the expectation propagation algorithm

Bias in particle tracking acceleration measurement

We investigate sources of error in acceleration statistics from Lagrangian Particle Tracking (LPT) data and demonstrate techniques to eliminate or minimise bias errors introduced during processing. Numerical simulations of particle tracking experiments in isotropic turbulence show that the main sources of bias error arise from noise due to position uncertainty and selection biases introduced during numerical differentiation. We outline the use of independent measurements and filtering schemes to eliminate these biases. Moreover, we test the validity of our approach in estimating the statistical moments and probability densities of the Lagrangian acceleration. Finally, we apply these techniques to experimental particle tracking data and demonstrate their validity in practice with comparisons to available data from literature. The general approach, which is not limited to acceleration statistics, can be applied with as few as two cameras and permits a substantial reduction in the spatial resolution and sampling rate required to adequately measure statistics of Lagrangian acceleration

Generalized Kernel-based Visual Tracking

In this work we generalize the plain MS trackers and attempt to overcome standard mean shift trackers' two limitations. It is well known that modeling and maintaining a representation of a target object is an important component of a successful visual tracker. However, little work has been done on building a robust template model for kernel-based MS tracking. In contrast to building a template from a single frame, we train a robust object representation model from a large amount of data. Tracking is viewed as a binary classification problem, and a discriminative classification rule is learned to distinguish between the object and background. We adopt a support vector machine (SVM) for training. The tracker is then implemented by maximizing the classification score. An iterative optimization scheme very similar to MS is derived for this purpose.Comment: 12 page

Source detection using a 3D sparse representation: application to the Fermi gamma-ray space telescope

The multiscale variance stabilization Transform (MSVST) has recently been proposed for Poisson data denoising. This procedure, which is nonparametric, is based on thresholding wavelet coefficients. We present in this paper an extension of the MSVST to 3D data (in fact 2D-1D data) when the third dimension is not a spatial dimension, but the wavelength, the energy, or the time. We show that the MSVST can be used for detecting and characterizing astrophysical sources of high-energy gamma rays, using realistic simulated observations with the Large Area Telescope (LAT). The LAT was launched in June 2008 on the Fermi Gamma-ray Space Telescope mission. The MSVST algorithm is very fast relative to traditional likelihood model fitting, and permits efficient detection across the time dimension and immediate estimation of spectral properties. Astrophysical sources of gamma rays, especially active galaxies, are typically quite variable, and our current work may lead to a reliable method to quickly characterize the flaring properties of newly-detected sources.Comment: Accepted. Full paper will figures available at http://jstarck.free.fr/aa08_msvst.pd

Bibliographic Review on Distributed Kalman Filtering

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area