# Attitude Tracking Algorithm Using GNSS Measurements from Short Baselines

## TL;DR

The paper introduces a new GNSS-based method for tracking attitude using short baselines that is computationally efficient and maintains accuracy.

## Contribution

A novel GNSS attitude tracking algorithm is proposed that reduces computational complexity while preserving accuracy.

## Key findings

- The proposed algorithm reduces computational complexity without sacrificing accuracy in attitude determination.
- An a priori error model for GNSS measurements provides a geometrically intuitive interpretation of errors.
- The algorithm performs well on real datasets with sub-meter baselines.

## Abstract

What are the main findings?
We present a novel GNSS-based attitude tracking method for short baselines that significantly reduces computational complexity without compromising the accuracy achieved by established algorithms.We introduce an a priori error model for GNSS measurement errors that lends itself to a clear and intuitive geometric interpretation.

We present a novel GNSS-based attitude tracking method for short baselines that significantly reduces computational complexity without compromising the accuracy achieved by established algorithms.

We introduce an a priori error model for GNSS measurement errors that lends itself to a clear and intuitive geometric interpretation.

What is the implication of the main finding?
By improving computational efficiency in integer ambiguity resolution, the proposed method simplifies the implementation of real-time attitude tracking algorithms, especially in systems that combine GNSS with data from other sensors.

By improving computational efficiency in integer ambiguity resolution, the proposed method simplifies the implementation of real-time attitude tracking algorithms, especially in systems that combine GNSS with data from other sensors.

The paper addresses the problem of attitude determination using Global Navigation Satellite System (GNSS) measurements from multiple antennas mounted on a navigation platform. To achieve attitude determination by GNSS with typical accuracy down to tenths of a degree for one-meter baselines, GNSS phase measurements are employed. A key challenge with phase measurements is the presence of unknown integer ambiguities. Consequently, the attitude determination problem traditionally reduces to a nonlinear, non-convex optimization problem with integer constraints. No closed-form solution to this problem is known, and its real-time calculation is computationally intensive. Given an a priori initial attitude approximation, we propose a new algorithm for attitude tracking based on the reduction of the nonlinear orthogonality-constrained attitude estimation problem to a linear integer least squares problem, for which numerical methods are well known and computationally much less demanding. Additionally, a simple a priori model for GNSS measurement error variance is introduced, grounded on the geometry of satellite signal propagation through vacuum and the Earth’s atmosphere, providing a clear physical interpretation. Applying the algorithm to a real dataset collected from a quasi-static multi-antenna, multi-GNSS system with sub-meter baselines, we obtain promising results.