Statistical Methods for Unexploded Ordnance Discrimination

We propose statistical processing methods and performance analysis techniques for discrimination and localization of Unexploded Ordnance (UXOs) using EMI sensors based on nonparametrically defined prior probability density functions for target-relevant features. In the first part of this thesis, new sets of UXO discrimination methods using these nonparametric prior models are introduced where we use kernel density estimation (KDE) methods to build a priori probability density functions (PDFs) for the vector of features used to classify Unexploded Ordnance items given electromagnetic induction (EMI) sensor data. This a priori information is then used to develop a new suite of estimation and classification algorithms. As opposed to the commonly used maximum likelihood (ML) parameter estimation methods, here we employ a maximum a posteriori (MAP) estimation algorithm that makes use of the KDE-generated PDFs. Similarly, we use the KDE priors to develop new suite of classification schemes operating in both “feature” space as well as “signal/data” space. In terms of featurebased methods, we construct a support vector machine (SVM) classifier and its extension to support M -ary classification. The KDE PDFs are also used to synthesize a MAP feature-based classifier. To address numerical challenges associated with the optimal, data-space Bayesian classifier, we have constructed several approximations, including one based on a Laplacian approximation and a new hybrid approach that makes use of ML estimates of the parameters not essential to classification. Generalized likelihood ratio tests employing the priors are also considered. Using both simulations and real field data, we observe significant improvement in classification performance due to the use of the KDE-based prior models. In second part of this thesis, we develop analytical performance analysis for the developed methods, where we derive analytical bounds on estimation and error performance including Cramer-Rao lower bounds (CRLB) and a Chernoff upper bound. The bounds are derived analytically and confirmed using Mont-Carlo simulations. Using the CRLBs the effect of unknown object geometry on estimation performance is analyzed. In third part of this work analytical bounds for error performance are used to optimize