Theses and Dissertations
This collection includes both ASU Theses and Dissertations, submitted by graduate students, and the Barrett, Honors College theses submitted by undergraduate students.
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- Creators: Turaga, Pavan
Recursive Bayesian Estimation on Projective Spaces: Theoretical Foundations and Practical Algorithms
Description
This thesis develops geometrically and statistically rigorous foundations for multivariate analysis and bayesian inference posed on grassmannian manifolds. Requisite to the development of key elements of statistical theory in a geometric realm are closed-form, analytic expressions for many differential geometric objects, e.g., tangent vectors, metrics, geodesics, volume forms. The first part of this thesis is devoted to a mathematical exposition of these. In particular, it leverages the classical work of Alan James to derive the exterior calculus of differential forms on special grassmannians for invariant measures with respect to which integration is permissible. Motivated by various multi-sensor remote sensing applications, the second part of this thesis describes the problem of recursively estimating the state of a dynamical system propagating on the Grassmann manifold. Fundamental to the bayesian treatment of this problem is the choice of a suitable probability distribution to a priori model the state. Using the Method of Maximum Entropy, a derivation of maximum-entropy probability distributions on the state space that uses the developed geometric theory is characterized. Statistical analyses of these distributions, including parameter estimation, are also presented. These probability distributions and the statistical analysis thereof are original contributions. Using the bayesian framework, two recursive estimation algorithms, both of which rely on noisy measurements on (special cases of) the Grassmann manifold, are the devised and implemented numerically. The first is applied to an idealized scenario, the second to a more practically motivated scenario. The novelty of both of these algorithms lies in the use of thederived maximumentropy probability measures as models for the priors. Numerical simulations demonstrate that, under mild assumptions, both estimation algorithms produce accurate and statistically meaningful outputs. This thesis aims to chart the interface between differential geometry and statistical signal processing. It is my deepest hope that the geometric-statistical approach underlying this work facilitates and encourages the development of new theories and new computational methods in geometry. Application of these, in turn, will bring new insights and bettersolutions to a number of extant and emerging problems in signal processing.
ContributorsCrider, Lauren N (Author) / Cochran, Douglas (Thesis advisor) / Kotschwar, Brett (Committee member) / Scharf, Louis (Committee member) / Taylor, Thomas (Committee member) / Turaga, Pavan (Committee member) / Arizona State University (Publisher)
Created2021
Description
Millimeter-wave (mmWave) and sub-terahertz (sub-THz) systems aim to utilize the large bandwidth available at these frequencies. This has the potential to enable several future applications that require high data rates, such as autonomous vehicles and digital twins. These systems, however, have several challenges that need to be addressed to realize their gains in practice. First, they need to deploy large antenna arrays and use narrow beams to guarantee sufficient receive power. Adjusting the narrow beams of the large antenna arrays incurs massive beam training overhead. Second, the sensitivity to blockages is a key challenge for mmWave and THz networks. Since these networks mainly rely on line-of-sight (LOS) links, sudden link blockages highly threaten the reliability of the networks. Further, when the LOS link is blocked, the network typically needs to hand off the user to another LOS basestation, which may incur critical time latency, especially if a search over a large codebook of narrow beams is needed. A promising way to tackle both these challenges lies in leveraging additional side information such as visual, LiDAR, radar, and position data. These sensors provide rich information about the wireless environment, which can be utilized for fast beam and blockage prediction. This dissertation presents a machine-learning framework for sensing-aided beam and blockage prediction. In particular, for beam prediction, this work proposes to utilize visual and positional data to predict the optimal beam indices. For the first time, this work investigates the sensing-aided beam prediction task in a real-world vehicle-to-infrastructure and drone communication scenario. Similarly, for blockage prediction, this dissertation proposes a multi-modal wireless communication solution that utilizes bimodal machine learning to perform proactive blockage prediction and user hand-off. Evaluations on both real-world and synthetic datasets illustrate the promising performance of the proposed solutions and highlight their potential for next-generation communication and sensing systems.
ContributorsCharan, Gouranga (Author) / Alkhateeb, Ahmed (Thesis advisor) / Chakrabarti, Chaitali (Committee member) / Turaga, Pavan (Committee member) / Michelusi, Nicolò (Committee member) / Arizona State University (Publisher)
Created2024