Instantaneous GNSS Ambiguity Resolution and Attitude Determination via Riemannian Manifold Optimization

Abstract

We present an ambiguity resolution method for Global Navigation Satellite System (GNSS)-based attitude determination. A GNSS attitude model with nonlinear constraints is used to rigorously incorporate a priori information. Given the characteristics of the employed nonlinear constraints, we formulate GNSS attitude determination as an optimization problem on a manifold. Then, Riemannian manifold optimization algorithms are utilized to aid ambiguity resolution based on a proposed decomposition of the objective function. The application of manifold geometry enables high-quality float solutions that are critical to reinforcing search-based integer ambiguity resolution in terms of efficiency, availability, and reliability. The proposed approach is characterized by a low computational complexity and a high probability of resolving the ambiguities correctly. The performance of the proposed ambiguity resolution method is tested through a series of simulations and real experiments. Comparisons with the principal benchmarks indicate the superiority of the proposed method as reflected by the high ambiguity resolution success rates.

Constrained Wrapped Least Squares: A Tool for High-Accuracy GNSS Attitude Determination

“…The distance of interest is always measured over the shorter (green) arc, which corresponds to respecting the half-cycle residual constraint (21). Given that only the fractional part of phase data is available, we can still measure the distance (on the unit circle) between the computed phase and the observed unwrapped phase (the observed wrapped phase plus the true integer value) using the fraction parts of the two phases, as emphasized by (27). Based on the above discussion, estimating unknowns using phase measurements can be achieved by matching the fractional part of the phase observations and those of the corresponding predictions.…”

“…Consequently, carrier-phase integer ambiguity resolution is a key and prime difficulty in precise attitude determination. Several ambiguity resolution methods have been proposed over the years, which can be categorized into motion-based methods [16]- [19] and search-based methods [2], [20]- [27]. Motion-based methods have no capacity for real-time solutions due to the requirement of motion information.…”