A GNSS Attitude Determination Algorithm Using Optimization Techniques on Riemannian Manifolds

Abstract

This paper presents a Global Navigation Satellite Systems (GNSS) attitude determination method based on Riemannian manifold optimization techniques. By noting that the solution set of the attitude determination problem is a Riemannian manifold, we formulate the problem as an optimization on the Riemannian manifold. We study the manifold geometry to design an efficient attitude determination algorithm. As a first step, we calculate a float solution using Riemannian manifold optimization to be used as the starting point for the integer search process. Since this solution makes full use of the geometrical constraints, it is expected to have an improvement over the popular least-squares estimator. To utilize the improved float solution, we propose a new decomposition of the objective function, which allows us to apply Riemannian optimization to the process of integer ambiguity resolution. Numerical simulations and actual experiments demonstrate that the proposed algorithm significantly outperforms state-of-the-art approaches for various system configurations.