Signal Processing Methods in Riemannian Geometry with Application to Drone Detection

Abstract

The number of drones manufactured by many companies, such as DJI, Parrot, and 3D-Robotics, is always on the rise. Drones are widely used for commercial purposes, such as the delivery of goods, surveying and monitoring public places. On the other hand, drones can also be used to perform terrorist attacks or can be used to transport illegal drugs. Thus, a fast and reliable drone detection technique is very much needed to allow enough time for countermeasures in critical situations. Drones are considered complex targets which can range in size from 10 m 2 to 0.01 m 2 with symmetrical shape and fluctuating radar cross section (RCS), hence low signal-to-interference-plusnoise ratio (SINR). Current radar systems with classical signal processing techniques might fail to detect drones in low SINR environments with limited number of received snapshots. Multiple-input multiple-output (MIMO) radar systems with signal processing methods in Riemannian space can be exploited to improve the probability of drone detection, enhance the robustness of the direction of arrival estimation and improve the minimum variance distortionless response beamforming by estimating the interference-plus-noise covariance matrix in Riemannian space.This dissertation utilizes uniform linear array (ULA) MIMO radar systems and proposes two Riemannian geometry-based constant false alarm rate (CFAR) detectors, a direction of arrival estimation technique based on Riemannian mean and distance, and interference-plus-noise covariance matrix estimation for beamforming in a Riemannian space. All proposed techniques exploit the regularized Burg algorithm (RBA) to convert each range bin into a Toeplitz Hermitian positive definite (THPD) matrix, which represents a point on the Riemannian manifold. Although Toeplitz structure is generated from ULA configurations, non linear array configurations would produce non-Toeplitz covariance matrices even if RBA guarantee Toeplitz structure. The proposed Riemannian-Brauer matrix (RBM) CFAR detector is based on the Riemannian distance between the Riemannian mean of the clutter-plus-noise Brauer bound and the THPD covariance matrices of the outliers. Also, the proposed First and foremost, I would to thank ALLAH, the most gracious, the most merciful and the most beneficent for all His blessings and generosity all the time. Second, I would like to thank my wife for her encouragement, support, patience and motivation. Also, I would like to thank all my family for their support, especially my daughter Reina and son Hassan.