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Precise 3-D GNSS Attitude Determination Based on Riemannian Manifold Optimization Algorithms

Douik, Ahmed and Liu, Xing and Ballal, Tarig and Al-Naffouri, Tareq Y. and Hassibi, Babak (2020) Precise 3-D GNSS Attitude Determination Based on Riemannian Manifold Optimization Algorithms. IEEE Transactions on Signal Processing, 68 . pp. 284-299. ISSN 1053-587X.

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In the past few years, Global Navigation Satellite Systems (GNSS) based attitude determination has been widely used thanks to its high accuracy, low cost, and real-time performance. This paper presents a novel 3-D GNSS attitude determination method based on Riemannian optimization techniques. The paper first exploits the antenna geometry and baseline lengths to reformulate the 3-D GNSS attitude determination problem as an optimization over a non-convex set. Since the solution set is a manifold, in this manuscript we formulate the problem as an optimization over a Riemannian manifold. The study of the geometry of the manifold allows the design of efficient first and second order Riemannian algorithms to solve the 3-D GNSS attitude determination problem. Despite the non-convexity of the problem, the proposed algorithms are guaranteed to globally converge to a critical point of the optimization problem. To assess the performance of the proposed framework, numerical simulations are provided for the most challenging attitude determination cases: the unaided, single-epoch, and single-frequency scenarios. Numerical results reveal that the proposed algorithms largely outperform state-of-the-art methods for various system configurations with lower complexity than generic non-convex solvers, e.g., interior point methods.

Item Type:Article
Related URLs:
URLURL TypeDescription
Douik, Ahmed0000-0001-7791-9443
Liu, Xing0000-0002-0506-6821
Ballal, Tarig0000-0003-4160-7514
Al-Naffouri, Tareq Y.0000-0001-6955-4720
Additional Information:© 2019 IEEE. Manuscript received January 28, 2019; revised November 6, 2019; accepted December 3, 2019. Date of publication December 11, 2019; date of current version January 10, 2020. The work of X. Liu, T. Ballal, and T. Y. Al-Naffouri is funded by the Center of NEOM Research at KAUST. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Caroline Chau. (Ahmed Douik and Xing Liu contributed equally to this work.)(Ahmed Douik and Xing Liu are co-first authors.)
Funding AgencyGrant Number
King Abdullah University of Science and Technology (KAUST)UNSPECIFIED
Subject Keywords:3-D GNSS attitude determination, GPS localization, integer ambiguity resolution, non-convex optimization, Riemannian manifolds
Record Number:CaltechAUTHORS:20191216-132407663
Persistent URL:
Official Citation:A. Douik, X. Liu, T. Ballal, T. Y. Al-Naffouri and B. Hassibi, "Precise 3-D GNSS Attitude Determination Based on Riemannian Manifold Optimization Algorithms," in IEEE Transactions on Signal Processing, vol. 68, pp. 284-299, 2020. doi: 10.1109/TSP.2019.2959226
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100301
Deposited By: Tony Diaz
Deposited On:16 Dec 2019 21:31
Last Modified:14 Jan 2020 21:17

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