Aleksandar Jeremic

Landmine detection and localization using chemical sensor array processing

We develop methods for automatic detection and localization of landmines using chemical sensor arrays and statistical signal processing techniques. The transport of explosive vapors emanating from buried landmines is modeled as a diffusion process in a two-layered system consisting of ground and air. Measurement and statistical models are then obtained from the associated concentration distribution. We derive two detectors (the generalized likelihood ratio (GLR) test and the mean detector) and determine their performance in terms of the probabilities of false alarm and detection. To determine the unknown location of a landmine, we derive a maximum likelihood (ML) estimation algorithm and evaluate its performance by computing the Cramer-Rao bound (CRB). The results are applied to the design of chemical sensor arrays, satisfying criteria specified in terms of detection and estimation performance measures and for optimally selecting the number and positions of sensors and the number of time samples. To illustrate the potential of the proposed techniques in a realistic demining scenario, we derive a moving-sensor algorithm in which the stationary sensor array is replaced by a single moving sensor. Numerical examples are given to demonstrate the applicability of our results.

OFDM channel estimation in the presence of interference

We develop a frequency-domain channel estimation algorithm for single-user multiantenna orthogonal frequency division multiplexing (OFDM) wireless systems in the presence of synchronous interference. In this case, the synchronous interferers signal on each OFDM subcarrier is correlated in space with a rank one spatial covariance matrix. In addition, the interferers spatial covariance matrix is correlated in frequency based on the delay spread of the interferers channel. To reduce the number of unknown parameters we develop a structured covariance model that accounts for the structure resulting from the synchronous interference. To further reduce the number of unknown parameters, we model the covariance matrix using a priori known set of frequency-dependent functions of joint (global) parameters. We estimate the interference covariance parameters using a residual method of moments (RMM) estimator and the channel parameters by maximum likelihood (ML) estimation. Since our RMM estimates are invariant to the mean, this approach yields simple noniterative estimates of the covariance parameters while having optimal statistical efficiency. Hence, our algorithm outperforms existing channel estimators that do not account for the interference, and at the same time requires smaller number of pilots than the MANOVA method and thus has smaller overhead. Numerical results illustrate the applicability of the proposed algorithm.

Design of chemical sensor arrays for monitoring disposal sites on the ocean floor

We develop methods for automatic environmental monitoring of disposal sites on the deep ocean floor using chemical sensor arrays and statistical hypothesis testing. Such sites have been proposed to relocate dredge materials from harbors and shipping channels. The transport of pollutants is modeled as a diffusion process, and the measurement and statistical models are derived by exploiting the spatial and temporal evolution of the associated concentration distribution. We derive two detectors, the generalized likelihood ratio (GLR) test and the mean detector and determine their performance in terms of the probabilities of false alarm and detection, The results are applied to the design of chemical sensor arrays satisfying criteria specified in terms of these probabilities, and to optimally select a number of sensors and time samples. Numerical examples are used to demonstrate the applicability of our results.

Biochemical Transport Modeling and Bayesian Source Estimation in Realistic Environments

Early detection and estimation of the spread of a biochemical contaminant are major issues in many applications, such as homeland security and pollution monitoring. We present an integrated approach combining the measurements given by an array of biochemical sensors with a physical model of the dispersion and statistical analysis to solve these problems and provide system performance measures. We approximate the dispersion model of a contaminant in a realistic environment through numerical simulations of reflected stochastic diffusions describing the microscopic transport phenomena due to wind and chemical diffusion and use the Feynmann-Kac formula. We consider arbitrary complex geometries and account for wind turbulence. Numerical examples are presented for two real-world scenarios: an urban area and an indoor ventilation duct. Localizing the dispersive sources is useful for decontamination purposes and estimation of the cloud evolution. To solve the associated inverse problem, we propose a Bayesian framework based on a random field that is particularly powerful for localizing multiple sources with small amounts of measurements

OFDM channel estimation in the presence of asynchronous interference

We have recently proposed a frequency-domain channel estimation algorithm for a single-user orthogonal frequency division multiplexing (OFDM) wireless system in the presence of synchronous interference. However, the interference cyclic prefix does not usually align with the desired users cyclic prefix (i.e., the interferer is asynchronous) and thus a different approach is required. For an asynchronous interferer in a rich multipath environment, the received frequency-domain measurement is correlated in space with a full-rank covariance matrix on each subcarrier. Therefore, the synchronous algorithms may give poor detection performance since they assume reduced rank interference and use a smaller number of parameters. We overcome these problems by employing an appropriately structured model with a properly defined number of covariance parameters. We estimate the interference covariance parameters using a residual method of moments (RMM) estimator and the mean (i.e., the desired users channel) parameters by maximum likelihood (ML) estimation. Since the RMM estimates are invariant to the mean, we obtain simple non-iterative estimates of the covariance parameters while having optimal statistical efficiency. Numerical results illustrate the applicability of the proposed algorithm.

Electro-mechanical imaging of the heart using tagged MRI and ECG/MCG arrays

We develop a computational framework for estimating simultaneously mechanical properties (active stress, passive elasticities, and mechanical activation time) and electrical properties (current density and electrical activation time.) First, we present a method for estimating the mechanical properties, active stress and passive elasticity modulus, of the in vivo heart using magnetic resonance imaging (MRI) tissue-tagging and intra-ventricular pressure measurements. Next, we present an algorithm for estimating the current density of the heart using electrocardiography (ECG) and magnetocardiography (MCG) sensor arrays. Finally, we present an inverse electro-mechanical model based on the excitation-contraction coupling and dynamic analysis which includes inertial forces and moving mesh. The proposed model has significant potential for studying the coupling effects in the whole heart.

Estimating mechanical properties of the heart using dynamic modeling and magnetic resonance imaging

We present an algorithm for estimating active and passive mechanical properties of the heart using magnetic resonance imaging (MRI) tissue-tagging and blood pressure measurements. We combine physical modeling with a finite-element formulation and dynamic analysis, and apply non-linear optimization to estimate the unknown parameters. We assume that the myocardiums stiffness tensor is anisotropic and non-homogeneous.

Estimating current density in the heart using structured and unstructured covariance analysis

The inverse problem of electrocardiography can be defined as the determination of the electrical activity of the heart from measurements of the body-surface electromagnetic field. The solution to this inverse problem may ultimately improve the ability to detect and treat cardiac diseases early. We present an algorithm for estimating the current density of the heart using ECG and magnetocardiography (MCG) sensor arrays. We model the electrical activity of the heart using current density represented by a set of deterministic and stochastic spatio-temporal basis functions. In order to solve the corresponding Fredholm equation we apply the clement-free Galerkin method and compute the measurements as a function of the torso geometry and cardiac source. Then, we maximize the likelihood function to estimate the unknown parameters assuming a presence of spatially correlated Gaussian noise with unknown covariance matrix. Numerical examples illustrate the applicability of our results.