Signal Processing Methods in Riemannian Geometry with Application to Drone Detection

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 illegal activities. 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 drone detection and estimation techniques. 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. 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 angle-based hybrid-Brauer (ABHB) CFAR detector is based on the calculated angle on the Riemannian manifold between the Riemannian mean and median of the clutter-plus-noise Brauer bound and the THPD covariance matrix of the outliers. The direction of arrival estimation problem is formulated as a linear search optimization problem that searches for the minimum Riemannian distance between the Riemannian mean of all THPD covariance matrices residing on the manifold and the Hermitian positive definite (HPD) matrix for each of the steering vectors. The estimation of the interference-plus-noise covariance matrix is formulated as a linear combination of THPD covariance matrices where the weights of the linear combination operation are based on the Riemannian distance between the Riemannian mean and each THPD covariance matrix. The largest distance (potential target) will have zero weight and the smallest distance will have maximum weight. Simulations and real data analysis validate the robustness and performance of all techniques in low SINR and small sample size.