NON-LINEAR ASPECTS OF THROUGH-WALL RADAR IMAGING AND OBJECT CHARACTERIZATION AND TRACKING

Abstract

Through-the-wall radar imaging is an application that is gaining more and more attention due to its large applicability and underlying mathematical challenges. In this thesis, we investigate techniques aimed at identifying, characterizing and tracking targets of interest hidden behind walls starting from through-the-wall measurements performed by deploying electromagnetic antennas around a monitored building. This might help police forces and rescue teams in surveillance and salvage operations by recognizing hostile or criminal activities, and could save lives by preventing them from entering a dangerous situation blindly. The identification of the targets is formulated in mathematical terms as an inverse scattering problem which, being non-linear and generally ill-posed, is difficult to address. Adjoint voxel-based reconstruction algorithms are analyzed to rapidly obtain an approximation of the target positions whereas more sophisticated level set-based shape reconstructions are considered to retrieve information about their geometry and physical properties. The effectiveness of these methods is confirmed by performing numerical experiments in 2D and 3D, balancing the realism of the simulated setups with the corresponding computational costs. In addition, the possibility of using a linear combination of Radial Basis Functions to represent the level set function associated with the system is explored. This defines a parametric framework in which the evolution of the latter function is reduced to an optimization task over discrete artificial time. Therefore, to promote fast reconstructions, first-order and quasi-Newton stochastic optimization algorithms are evaluated and compared. When moving targets enter the monitored building, the task of following their motions in almost real-time is addressed by adopting a Bayesian inference approach that combines adjoint reconstructions equipped with an optimally truncated sparsity regularization and a Kalman filter. Numerical experiments show that accurate trajectory estimations are attainable provided that reliable kinematic models are available a priori to describe the expected target dynamics. Relaxing this hypothesis motivates the development of an innovative tracking approach based on deep learning and enhanced by considerations suggested by the inverse problem theory. Inspired by the concept of model bagging and rewriting the localization task as a classification problem, a combination of independent networks is employed to accurately retrieve the unknown motions directly from through-the-wall measurements.

Date of Award	1 Aug 2022
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Oliver Dorn (Supervisor) & Sean Holman (Supervisor)