Graduation Semester and Year
Spring 2026
Language
English
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Aerospace Engineering
Department
Mechanical and Aerospace Engineering
First Advisor
Dr. Kamesh Subbarao
Abstract
Uncertainty quantification has gained significant attention in recent years as a research area in dynamical systems. Mathematical representations of the physical system, combined with an understanding of model uncertainties, enable the propagation of uncertainty in temporal space, which allows us to make informed decisions. However, what if the true dynamics of the system is unknown or too complex to define explicitly? In such cases, the system’s behavior can instead be inferred or learned from observed input–output data rather than from an analytical or physics-based model. To this end, this dissertation focuses on developing a data-driven framework for nonparametric dynamics modeling, uncertainty quantification, and state estimation of stochastic dynamical systems using Gaussian process regression (GPR), with applications to collision risk assessment in unmanned traffic systems.
The first part of this dissertation focuses on non-parametric modeling of dynamical systems and trajectory prediction using GPR. The novelty of this dissertation lies in developing a multi-output Gaussian process (MOGP) framework for modeling the dynamics of systems with correlated states. Building on the above, a GPR-based uncertainty quantification and propagation framework is established to advance uncertainty quantification. The GPR model quantifies predictive uncertainty in the target variable through its posterior predictive distribution, which combines a Gaussian process (GP) prior with the Gaussian likelihood.
The second part of the dissertation introduces a novel data-driven state estimation framework for stochastic dynamical systems that accounts for uncertain initial conditions and parametric variations. In this framework, the learned GPR dynamics model is employed to propagate uncertainty and obtain prior state estimates, which are subsequently updated through Bayesian filtering using measurement data.
The final part of the dissertation focuses on collision risk assessment for unmanned aircraft system traffic management (UTM) and advanced air mobility (AAM), two emerging paradigms in future aviation, where the collision risk is approximated through the three-sigma confidence ellipse of the predicted state distribution, enabling informed decision-making. Additionally, an open-source toolbox has also been developed to provide a unified framework for Gaussian process regression and Bayesian filtering.
The proposed frameworks are demonstrated for various application problems, including flight delay prediction, dynamics modeling, and state estimation of small unmanned aerial vehicles (sUAVs), assessment of collision risk in homogeneous and heterogeneous sUAV traffic, and other dynamical systems.
Keywords
Gaussian process regression, Uncertainty quantification, Stochastic dynamical systems, State estimation, Unmanned aircraft system traffic management, Advanced air mobility
Disciplines
Aerospace Engineering | Engineering | Mechanical Engineering | Multi-Vehicle Systems and Air Traffic Control | Navigation, Guidance, Control and Dynamics
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Khanal, Aakarshan, "Gaussian Process Regression–Based Uncertainty Quantification for Unmanned Aircraft System Traffic Management and Advanced Air Mobility Applications" (2026). Mechanical and Aerospace Engineering Dissertations. 4.
https://mavmatrix.uta.edu/mechaerospace_dissertations2/4
Included in
Mechanical Engineering Commons, Multi-Vehicle Systems and Air Traffic Control Commons, Navigation, Guidance, Control and Dynamics Commons
Comments
Degree granted by The University of Texas at Arlington