A Global, Continuous, and Exponentially Convergent Observer for Gyro Bias and Attitude of a Rigid Body

TL;DR

This paper introduces a novel 12-dimensional observer for rigid body gyro bias and attitude that guarantees global exponential convergence by operating outside the topological constraints of traditional methods, validated through indoor experiments.

Contribution

A new continuous, global, and exponentially convergent observer designed in matrix space, overcoming topological limitations of previous attitude observers on SO(3).

Findings

Observer achieves global exponential convergence.

Validated effectiveness through indoor landmark experiments.

Operates in matrix space, bypassing topological restrictions.

Abstract

We propose a 12-dimensional, global, continuous, and exponentially convergent observer for gyro bias and attitude of a rigid body. Any attitude observer developed on the special orthogonal group suffers from the topological restriction that prohibits global attractivity in continuous flow. In this paper, the observer is designed in the set of 3 by 3 real matrices, thus making the topological obstruction on the special orthogonal group irrelevant. The efficacy of the proposed approach against other attitude observers is illustrated by an indoor experiment utilizing visual landmarks.