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

机译：基于黎曼流形优化算法的精确3-D GNSS姿态确定

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摘要

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.
机译：在过去的几年中，基于全球导航卫星系统（GNSS）的姿态确定由于其高精度，低成本和实时性能而得到了广泛的应用。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。本文首先利用天线的几何形状和基线长度来重新构造3-D GNSS姿态确定问题，作为对非凸集的优化。由于解集是流形，因此在本手稿中，我们将问题表述为在黎曼流形上的优化。对歧管几何形状的研究允许设计有效的一阶和二阶黎曼算法来解决3-D GNSS姿态确定问题。尽管存在问题的非凸性，但仍可以保证所提出的算法全局收敛到优化问题的关键点。为了评估所提出框架的性能，针对最具挑战性的姿态确定情况提供了数值模拟：独立，单历元和单频方案。数值结果表明，对于各种系统配置，所提出的算法在性能上大大优于最新的方法，其复杂度要比通用的非凸型求解器（例如内点法）低。

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