Author Type

Graduate Student

Date of Award

Spring 4-28-2026

Document Type

Dissertation

Publication Status

Version of Record

Submission Date

May 2026

Department

Computer and Electrical Engineering and Computer Science

College Granting Degree

College of Engineering and Computer Science

Department Granting Degree

Electrical Engineering and Computer Science

Degree Name

Doctor of Philosophy (PhD)

Thesis/Dissertation Advisor [Chair]

Dimitris Pados

Thesis/Dissertation Co-Chair

George Sklivanitis

Abstract

Modern autonomous systems operating in highly dynamic, non-stationary environments require reliable inference from short, potentially corrupted time-series measurements, where conventional statistical methods relying on large-sample support and stationarity assumptions become fundamentally inapplicable. This dissertation develops a unified, model-free theoretical framework for time-series analysis, with a particular application to signal Direction-of-Arrival (DoA) estimation, grounded in structured matrix decompositions under both the L2-norm and L1-norm formulations.

We first approach the problem from a conventional viewpoint by carrying out standard matrix analysis directly on Hankel-structured representations of time-series data. In this context, we demonstrate that L1-norm decompositions of Hankel matrices offer strong resistance to partially faulty or missing sensor measurements, yielding a principled framework for robust real-time monitoring and operation of autonomous systems. Pursuing this line of inquiry, we introduce a novel one-shot DoA estimator that operates directly on a single antenna-array sample via structured matrix representations and singular-value decomposition (SVD). Arguably surprisingly, the proposed estimator can achieve lower mean-square error, bias, and variance when compared against the classical Maximum Likelihood single-sample estimator under white Gaussian noise. The effectiveness of the proposed one-shot estimator is further validated using real-world massive MIMO measurements from the POWDER-RENEW platform.

Next, we depart from conventional decompositions of Hankel-structured representations and turn our attention to the general and broadly applicable problem of computing optimal structured Hankel and Toeplitz decompositions of arbitrary matrices, jointly enforcing the low-rank and the corresponding structure constraints. We develop accurate and computationally efficient algorithms for rank-1 Hankel and Toeplitz-structured decompositions under both the L2-norm and L1-norm formulations, and derive analytically grounded few-shot DoA estimators for practical sensing architectures in which the sensed array measurement matrix does not possess Hankel structure, while the underlying signal of interest inherently does. The proposed rank-1 estimators under the L2 and L1 norms are formally shown to be maximum-likelihood- optimal under white Gaussian and Laplace noise, respectively. Beyond theoretical guarantees and controlled simulations, the robustness of the L1-based estimator is further demonstrated using real-world outdoor Unmanned Aerial Vehicle (UAV) measurements.

Extending this framework to the multi-signal case, we further develop few-shot DoA estimators based on rank-K Hankel matrix decompositions under both the L2 and L1 norm formulations. Consistent with the proposed Hankel-sensing architecture, the rank-K estimator under the L2-norm retains its maximum-likelihood optimality under white Gaussian noise, while the L1-norm formulation yields a novel, robust estimator that is highly resilient to impulsive interference and remains maximum-likelihood optimal under Laplace noise. Extensive simulations demonstrate that the proposed methods achieve super-resolution capabilities, requiring significantly lower signal-to-noise ratio and attaining substantially higher probability of resolution compared to competing approaches.

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