GNSS Localization and Attitude Determination via Optimization Techniques on Riemannian Manifolds

Student thesis: Doctoral Thesis


Global Navigation Satellite Systems (GNSS)-based localization and attitude determination are essential for many navigation and control systems widely used in aircrafts, spacecrafts, vessels, automobiles, and other dynamic platforms. A GNSS receiver can generate pseudo-range and carrier-phase observations based on the signals transmitted from the navigation satellites. Since the accuracy of the carrier phase is two orders of magnitude higher than that of the pseudo-range, it is crucial to employ the precise GNSS data, the carrier phase, to perform a high-accuracy position or/and attitude estimate. The main challenge to fully utilizing carrier-phase observations is to successfully resolve the unknown integer parts (number of whole cycles), a process usually referred to as integer ambiguity resolution. Many methods have been developed to resolve integer ambiguities with different performance offerings. Under challenging environments with insufficient tracked satellites, significant multipath interference, and severe atmospheric effects, the existing methods might not be up to par regarding reliability and efficiency. First, we study the GNSS attitude determination problem in this thesis. A GNSS attitude model with nonlinear constraints about antenna-array geometry is used to incorporate a priori information rigorously. Given the characteristics of the employed nonlinear constraints, we formulate GNSS attitude determination as an optimization problem on a manifold. We propose three different attitude determination methods: the array-aided attitude determination based on an oriented sphere manifold, the Riemannian-manifold-based orthonormality-constrained attitude determination (RieMOCAD), and the constrained wrapped least squares (C-WLS) method. We also propose a joint solution for real-time kinematic positioning and attitude determination. Although without common parameters in the localization and attitude determination problems, the GNSS data of the two issues are correlated. We consider this correlation and treat GNSS localization and attitude determination as a joint problem instead of two independent issues, allowing us to leverage the prior information rigorously. Again, Riemannian optimization is applied to improve the performance of RTK positioning and attitude determination regarding the accuracy and ambiguity resolution.
Date of AwardMay 3 2023
Original languageEnglish (US)
Awarding Institution
  • Computer, Electrical and Mathematical Sciences and Engineering
SupervisorTareq Al-Naffouri (Supervisor)

Cite this