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.

中文翻译：

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基于黎曼流形优化算法的精确 3-D GNSS 姿态确定

近年来，基于全球导航卫星系统（GNSS）的姿态确定因其高精度、低成本和实时性而得到广泛应用。本文提出了一种基于黎曼优化技术的新型 3-D GNSS 姿态确定方法。该论文首先利用天线几何形状和基线长度将 3-D GNSS 姿态确定问题重新表述为对非凸集的优化。由于解集是一个流形，在本手稿中，我们将问题表述为对黎曼流形的优化。流形几何的研究允许设计高效的一阶和二阶黎曼算法来解决 3-D GNSS 姿态确定问题。尽管问题不凸，所提出的算法保证全局收敛到优化问题的临界点。为了评估所提出框架的性能，为最具挑战性的姿态确定案例提供了数值模拟：独立、单历元和单频场景。数值结果表明，对于各种系统配置，所提出的算法在很大程度上优于最先进的方法，其复杂度低于通用非凸求解器，例如内点方法。