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

Douik, Ahmed; Liu, Xing; Ballal, Tarig; Al-Naffouri, Tareq Y.; Hassibi, Babak

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

Files

T-SP-24622-2019.pdf (3.87 MB)

Type

Article

Authors

Douik, Ahmed
Liu, Xing

Ballal, Tarig
Al-Naffouri, Tareq Y.

Hassibi, Babak

KAUST Department

Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program
Office of the VP
Physical Science and Engineering (PSE) Division

Online Publication Date

2019-12-13

Print Publication Date

2020

Date

2019-12-13

Abstract

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.

Citation

Douik, A., Liu, X., Ballal, T., Al-Naffouri, T. Y., & Hassibi, B. (2020). Precise 3-D GNSS Attitude Determination Based on Riemannian Manifold Optimization Algorithms. IEEE Transactions on Signal Processing, 68, 284–299. doi:10.1109/tsp.2019.2959226