# A Discrete-Time Attitude Observer on SO(3) for Vision and GPS Fusion

## TL;DR

This paper introduces a discrete-time geometric attitude observer that fuses monocular vision and GPS data to improve orientation estimation accuracy and stability, effectively reducing drift and directly estimating North-East-Down frame orientation.

## Contribution

It presents a novel attitude observer with rigorous stability analysis that fuses vision and GPS data, ensuring exponential convergence and robustness to large initial errors.

## Key findings

- Observer effectively reduces visual odometry drift
- Successfully estimates North-East-Down orientation
- Converges exponentially to true attitude

## Abstract

This paper proposes a discrete-time geometric attitude observer for fusing monocular vision with GPS velocity measurements. The observer takes the relative transformations obtained from processing monocular images with any visual odometry algorithm and fuses them with GPS velocity measurements. The objectives of this sensor fusion are twofold; first to mitigate the inherent drift of the attitude estimates of the visual odometry, and second, to estimate the orientation directly with respect to the North-East-Down frame. A key contribution of the paper is to present a rigorous stability analysis showing that the attitude estimates of the observer converge exponentially to the true attitude and to provide a lower bound for the convergence rate of the observer. Through experimental studies, we demonstrate that the observer effectively compensates for the inherent drift of the pure monocular vision based attitude estimation and is able to recover the North-East-Down orientation even if it is initialized with a very large attitude error.