Vasileios Maroulas

Improved particle filters for multi-target tracking

We present a novel approach for improving particle filters for multi-target tracking. The suggested approach is based on drift homotopy for stochastic differential equations. Drift homotopy is used to design a Markov Chain Monte Carlo step which is appended to the particle filter and aims to bring the particle filter samples closer to the observations while at the same time respecting the target dynamics. We have used the proposed approach on the problem of multi-target tracking with a nonlinear observation model. The numerical results show that the suggested approach can improve significantly the performance of a particle filter.

Distributed principal components analysis in sensor networks

Estimation of the principal eigenspace of a data covariance matrix is instrumental in applications such as data dimensionality reduction and denoising. In sensor networks the acquired data are spatially scattered which further calls for the development of distributed principal subspace estimation algorithms. Toward this end, the standard principal component analysis framework is reformulated as a separable constrained minimization problem which is solved by utilizing coordinate descent techniques combined with the alternating direction method of multipliers. Computationally simple local updating recursions are obtained that involve only single-hop inter-sensor communications and allow sensors to estimate the principal covariance eigenspace in a distributed fashion. Adaptive implementations are also considered that allow online information processing. Numerical tests demonstrate that the novel algorithm has the potential to achieve a considerably faster convergence rate and better steady-state estimation performance compared to existing alternatives.

Distributed spatio-temporal association and tracking of multiple targets using multiple sensors

The problem of tracking multiple targets using nonlinear observations acquired at multiple sensors is addressed by combining particle filtering (PF) with sparse matrix decomposition techniques. Sensors are spatially scattered, while the unknown number of targets may be time varying. A framework is put forth where norm-one regularized factorization is employed to decompose the sensor data covariance matrix into sparse factors whose support facilitates recovery of sensors that acquire informative measurements about the targets. This novel sensors-to-targets association scheme is integrated with PF mechanisms to perform accurate tracking. Precisely, distributed optimization techniques are employed to associate targets with sensors, and PF is integrated to perform target tracking using only the sensors selected by the sparse decomposition scheme. Different from existing alternatives, the novel algorithm can efficiently track and associate targets with sensors even in noisy settings. Extensive numerical tests are provided to demonstrate the tracking superiority of the proposed algorithm over existing approaches.

Dynamic Data Driven Sensor Network Selection and Tracking

Abstract The deployment of networks of sensors and development of pertinent information processing techniques can facilitate the requirement of situational awareness present in many defense/surveillance systems. Sensors allow the collection and distributed processing of information in a variety of environments whose structure is not known and is dynamically changing with time. A distributed dynamic data driven (DDDAS-based) framework is developed in this paper to address distributed multi-threat tracking under limited sensor resources. The acquired sensor data will be used to control the sensing part of the sensor network, and utilize only the sensing devices that acquire good quality measurements about the present targets. The DDDAS-based concept will be utilized to enable efficient sensor activation of only those parts of the network located close to a target/object. A novel combination of stochastic filtering techniques, drift homotopy and sparsity-inducing canonical correlation analysis (S-CCA) is utilized to dynamically identify the target-informative sensors and utilize them to perform improved drift-based particle filtering techniques that will allow robust, stable and accurate distributed tracking of multiple objects. Numerical tests demonstrate the effectiveness of the novel framework.

A multiobjective optimization framework for stochastic control of complex systems

This paper addresses the problem of minimizing the long-run expected average cost of a complex system consisting of subsystems that interact with each other and the environment. We treat the stochastic control problem as a multiobjective optimization problem of the one-stage expected costs of the subsystems, and we show that the control policy yielding the Pareto optimal solution is an optimal control policy that minimizes the average cost criterion for the entire system. For practical situations with constraints consistent to those we study here, our results imply that the Pareto control policy may be of value in deriving online an optimal control policy in complex systems.

Sequential Empirical Bayes Method for Filtering Dynamic Spatiotemporal Processes

We consider online prediction of a latent dynamic spatiotemporal process and estimation of the associated model parameters based on noisy data. The problem is motivated by the analysis of spatial data arriving in real-time and the current parameter estimates and predictions are updated using the new data at a fixed computational cost. Estimation and prediction is performed within an empirical Bayes framework with the aid of Markov chain Monte Carlo samples. Samples for the latent spatial field are generated using a sampling importance resampling algorithm with a skewed-normal proposal and for the temporal parameters using Gibbs sampling with their full conditionals written in terms of sufficient quantities which are updated online. The spatial range parameter is estimated by a novel online implementation of an empirical Bayes method, called herein sequential empirical Bayes method. A simulation study shows that our method gives similar results as an offline Bayesian method. We also find that the skewed-normal proposal improves over the traditional Gaussian proposal. The application of our method is demonstrated for online monitoring of radiation after the Fukushima nuclear accident.

K−means clustering on the space of persistence diagrams

A recent cohort of research aims to apply topological and geometric theory to data analysis. However, more effort is needed to incorporate statistical ideas and structure to these analysis methods. To this end, we present persistent homology clustering techniques through the perspective of data analysis. These techniques provide insight into the structure of the underlying dynamic and are able to recognize important shape properties such as periodicity, chaos, and multi-stability. Moreover, introducing quantitative structure on the topological data space allows for rigorous understanding of the datas geometry, a powerful tool for scrutinizing the morphology of the inherent dynamic. Additionally, we illustrate the advantages of these techniques and results through examples derived from dynamical systems applications.

On least-squares estimation for partially observed jump-diffusion processes

We propose a least-squares estimator for the intensity of the Poisson process in a partially observed stochastic system, where the signal evolves as a jump-diffusion process and the observation is a diffusion process. Precisely, we establish the consistency and a central limit theorem of the least-squares estimator when a negative drift coefficient for the jump-diffusion process is considered and data are streamed online ad infinitum as in a big data scenario. Simulation results are presented to support the theoretical landscape.

Decentralized sparsity-based multi-source association and state tracking

The problem of tracking multiple sources using observations acquired at spatially scattered sensors is considered here. Two different sensing architectures are studied: (i) a fusion-center based topology where sensors have a limited power budget; and (ii) an ad hoc architecture where sensors collaborate with neighboring nodes enabling in-network processing. A novel source-to-sensor association scheme and tracking is introduced by enhancing the standard Kalman filtering minimization formulation with norm-one regularization terms. In the fusion-based topology a pertinent transmission power constraint is introduced, while coordinate descent techniques are employed to recover the unknown sparse observation matrix, select pertinent sensors and subsequently track the source states. In the ad hoc topology, the centralized minimization problem is written in a separable way and the alternating direction method of multipliers is utilized to construct an in-network algorithmic tracking and association framework. Numerical tests demonstrate that the resulting schemes are capable to associate sources with sensors, and track the unknown sources while adhering to any imposed power constraints. HighlightsWe develop distributed source-to-sensor association scheme and tracking schemes.An norm-one regularized Kalman filter formulation is introduced.Ad hoc and fusion-center based sensor networks are considered.In-network processing via alternating direction method of multipliers.

Nonlandmark classification in paleobiology: computational geometry as a tool for species discrimination

Abstract. One important and sometimes contentious challenge in paleobiology is discriminating between species, which is increasingly accomplished by comparing specimen shape. While lengths and proportions are needed to achieve this task, finer geometric information, such as concavity, convexity, and curvature, plays a crucial role in the undertaking. Nonetheless, standard morphometric methodologies such as landmark analysis are not able to capture in a quantitative way these features and other important fine-scale geometric notions. Here we develop and implement state-of-the-art techniques from the emerging field of computational geometry to tackle this problem with the Mississippian blastoid Pentremites.We adapt a previously known computational framework to produce a measure of dissimilarity between shapes. More precisely, we compute “distances” between pairs of 3D surface scans of specimens by comparing a mix of global and fine-scale geometric measurements. This process uses the 3D scan of a specimen as a whole piece of data incorporating complete geometric information about the shape; as a result, scans used must accurately reflect the geometry of whole, undamaged, undeformed specimens. Using this information we are able to represent these data in clusters and ultimately reproduce and refine results obtained in previous work on species discrimination. Our methodology is landmark free, and therefore faster and less prone to human error than previous landmark-based methodologies.