Collaborative Information Processing in Wireless Sensor Networks for Diffusive Source Estimation

In this dissertation, we address the issue of collaborative information processing for diffusive source parameter estimation using wireless sensor networks (WSNs) capable of sensing in dispersive medium/environment, from signal processing perspective. We begin the dissertation by focusing on the mathematical formulation of a special diffusion phenomenon, i.e., an underwater oil spill, along with statistical algorithms for meaningful analysis of sensor data leading to efficient estimation of desired parameters of interest. The objective is to obtain an analytical solution to the problem, rather than using non-model based sophisticated numerical techniques. We tried to make the physical diffusion model as much appropriate as possible, while maintaining some pragmatic and reasonable assumptions for the simplicity of exposition and analytical derivation. The dissertation studies both source localization and tracking for static and moving diffusive sources respectively. For static diffusive source localization, we investigate two parametric estimation techniques based on the maximum-likelihood (ML) and the best linear unbiased estimator (BLUE) for a special case of our obtained physical dispersion model. We prove the consistency and asymptotic normality of the obtained ML solution when the number of sensor nodes and samples approach infinity, and derive the Cramer-Rao lower bound (CRLB) on its performance. In case of a moving diffusive source, we propose a particle filter (PF) based target tracking scheme for moving diffusive source, and analytically derive the posterior Cramer-Rao lower bound (PCRLB) for the moving source state estimates as a theoretical performance bound. Further, we explore nonparametric, machine learning based estimation technique for diffusive source parameter estimation using Dirichlet process mixture model (DPMM). Since real data are often complicated, no parametric model is suitable. As an alternative, we exploit the rich tools of nonparametric Bayesian methods, in particular the DPMM, which provides us with a flexible and data-driven estimation process. We propose DPMM based static diffusive source localization algorithm and provide analytical proof of convergence. The proposed algorithm is also extended to the scenario when multiple diffusive sources of same kind are present in the diffusive field of interest. Efficient power allocation can play an important role in extending the lifetime of a resource constrained WSN. Resource-constrained WSNs rely on collaborative signal and information processing for efficient handling of large volumes of data collected by the sensor nodes. In this dissertation, the problem of collaborative information processing for sequential parameter estimation in a WSN is formulated in a cooperative game-theoretic framework, which addresses the issue of fair resource allocation for estimation task at the Fusion center (FC). The framework allows addressing either resource allocation or commitment for information processing as solutions of cooperative games with underlying theoretical justifications. Different solution concepts found in cooperative games, namely, the Shapley function and Nash bargaining are used to enforce certain kinds of fairness among the nodes in a WSN

Sparse EEG Source Localization Using Bernoulli Laplacian Priors

International audienceSource localization in electroencephalography has received an increasing amount of interest in the last decade. Solving the underlying ill-posed inverse problem usually requires choosing an appropriate regularization. The usual l2 norm has been considered and provides solutions with low computational complexity. However, in several situations, realistic brain activity is believed to be focused in a few focal areas. In these cases, the l2 norm is known to overestimate the activated spatial areas. One solution to this problem is to promote sparse solutions for instance based on the l1 norm that are easy to handle with optimization techniques. In this paper, we consider the use of an l0 + l1 norm to enforce sparse source activity (by ensuring the solution has few nonzero elements) while regularizing the nonzero amplitudes of the solution. More precisely, the l0 pseudonorm handles the position of the non zero elements while the l1 norm constrains the values of their amplitudes. We use a Bernoulli–Laplace prior to introduce this combined l0 + l1 norm in a Bayesian framework. The proposed Bayesian model is shown to favor sparsity while jointly estimating the model hyperparameters using a Markov chain Monte Carlo sampling technique. We apply the model to both simulated and real EEG data, showing that the proposed method provides better results than the l2 and l1 norms regularizations in the presence of pointwise sources. A comparison with a recent method based on multiple sparse priors is also conducted

RSSI-Based Self-Localization with Perturbed Anchor Positions

We consider the problem of self-localization by a resource-constrained mobile node given perturbed anchor position information and distance estimates from the anchor nodes. We consider normally-distributed noise in anchor position information. The distance estimates are based on the log-normal shadowing path-loss model for the RSSI measurements. The available solutions to this problem are based on complex and iterative optimization techniques such as semidefinite programming or second-order cone programming, which are not suitable for resource-constrained environments. In this paper, we propose a closed-form weighted least-squares solution. We calculate the weights by taking into account the statistical properties of the perturbations in both RSSI and anchor position information. We also estimate the bias of the proposed solution and subtract it from the proposed solution. We evaluate the performance of the proposed algorithm considering a set of arbitrary network topologies in comparison to an existing algorithm that is based on a similar approach but only accounts for perturbations in the RSSI measurements. We also compare the results with the corresponding Cramer-Rao lower bound. Our experimental evaluation shows that the proposed algorithm can substantially improve the localization performance in terms of both root mean square error and bias.Comment: Accepted for publication in 28th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (IEEE PIMRC 2017

State-space solutions to the dynamic magnetoencephalography inverse problem using high performance computing

Determining the magnitude and location of neural sources within the brain that are responsible for generating magnetoencephalography (MEG) signals measured on the surface of the head is a challenging problem in functional neuroimaging. The number of potential sources within the brain exceeds by an order of magnitude the number of recording sites. As a consequence, the estimates for the magnitude and location of the neural sources will be ill-conditioned because of the underdetermined nature of the problem. One well-known technique designed to address this imbalance is the minimum norm estimator (MNE). This approach imposes an $L^2$ regularization constraint that serves to stabilize and condition the source parameter estimates. However, these classes of regularizer are static in time and do not consider the temporal constraints inherent to the biophysics of the MEG experiment. In this paper we propose a dynamic state-space model that accounts for both spatial and temporal correlations within and across candidate intracortical sources. In our model, the observation model is derived from the steady-state solution to Maxwell's equations while the latent model representing neural dynamics is given by a random walk process.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS483 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Geometric Approach to Sound Source Localization from Time-Delay Estimates

This paper addresses the problem of sound-source localization from time-delay estimates using arbitrarily-shaped non-coplanar microphone arrays. A novel geometric formulation is proposed, together with a thorough algebraic analysis and a global optimization solver. The proposed model is thoroughly described and evaluated. The geometric analysis, stemming from the direct acoustic propagation model, leads to necessary and sufficient conditions for a set of time delays to correspond to a unique position in the source space. Such sets of time delays are referred to as feasible sets. We formally prove that every feasible set corresponds to exactly one position in the source space, whose value can be recovered using a closed-form localization mapping. Therefore we seek for the optimal feasible set of time delays given, as input, the received microphone signals. This time delay estimation problem is naturally cast into a programming task, constrained by the feasibility conditions derived from the geometric analysis. A global branch-and-bound optimization technique is proposed to solve the problem at hand, hence estimating the best set of feasible time delays and, subsequently, localizing the sound source. Extensive experiments with both simulated and real data are reported; we compare our methodology to four state-of-the-art techniques. This comparison clearly shows that the proposed method combined with the branch-and-bound algorithm outperforms existing methods. These in-depth geometric understanding, practical algorithms, and encouraging results, open several opportunities for future work.Comment: 13 pages, 2 figures, 3 table, journa