Since World War I, the area of acoustic undersea warfare has witnessed several research activities targeting the development of advanced systems to accurately detect and localize underwater moving targets. One of the main categories of these systems is the passive sound navigation and ranging (SONAR) that searches for the location of the ships and submarines by listening to the radiated noise produced by their propellers, machinery, and flow dynamics. The performance of the passive sonar highly depends on the particular array signal processing algorithms used in practice. Presently, one of the main challenges is to accurately estimate the target direction of arrival (DOA) in severe underwater environments. This thesis is proposed to enhance the DOA estimation in two distinct applications. This first application is to improve the spatial resolution of the uniform linear towed arrays. This is done by applying new spatial extrapolation techniques called 2D- and 3D- fast orthogonal search (FOS) for both uniform linear and rectangular arrays, respectively. The presented methods show better performance than the conventional methods with respect to signal to noise ratio (SNR), number of snapshots and angular separation. Moreover it reduces the computational complexity required by the spatial extrapolation methods based on linear prediction approach. The other application concerns with developing a new DOA estimation that provides better spatial spectrum than the one provided by conventional beamforming (CBF) when a nonuniform linear array of directional frequency analysis and recording (DIFAR) sonobuoys is employed. The introduced technique or the so called fourth order cumulant beamforming (FOCBF) and shows an outstanding performance compared to CBF especially in low SNR. Furthermore, a warping FOC-BF (WFOC-BF) method obtained by augmenting a warping beamforming technique with FOC-BF is proposed to reduce the required computational complexity by FOC-BF while preserving the same performance. / Thesis (Ph.D, Electrical & Computer Engineering) -- Queen's University, 2012-06-27 14:59:33.941