Design of Globally Exponentially Convergent Continuous Observers for Velocity Bias and State for Systems on Real Matrix Groups

TL;DR

This paper introduces globally exponentially convergent continuous observers for systems on matrix Lie groups, enabling simultaneous estimation of system states and velocity biases from landmark measurements.

Contribution

It presents a novel observer design that embeds systems on Lie groups into Euclidean space for improved estimation of states and biases.

Findings

Observers achieve global exponential convergence.

Method applied to special Euclidean group SE(3).

Effective bias and state estimation demonstrated.

Abstract

We propose globally exponentially convergent continuous observers for invariant kinematic systems on finite-dimensional matrix Lie groups. Such an observer estimates, from measurements of landmarks, vectors and biased velocity, both the system state and the unknown constant bias in velocity measurement, where the state belongs to the state-space Lie group and the velocity to the Lie algebra of the Lie group. The main technique is to embed a given system defined on a matrix Lie group into Euclidean space and build observers in the Euclidean space. The theory is illustrated with the special Euclidean group in three dimensions.