Constructive Equivariant Observer Design for Inertial Velocity-Aided Attitude

TL;DR

This paper introduces a novel non-linear observer for inertial velocity-aided attitude estimation that guarantees almost global convergence by leveraging Lie group symmetries, outperforming existing methods in stability and robustness.

Contribution

It presents the first observer with almost global convergence for inertial VAA, exploiting Lie group symmetries for improved stability and global validity.

Findings

Observer achieves almost global asymptotic stability.

Estimation error converges to zero from poor initial conditions.

Simulation confirms robustness and convergence performance.

Abstract

Inertial Velocity-Aided Attitude (VAA), the estimation of the velocity and attitude of a vehicle using gyroscope, accelerometer, and inertial-frame velocity (e.g. GPS velocity) measurements, is an important problem in the control of Remotely Piloted Aerial Systems (RPAS). Existing solutions provide limited stability guarantees, relying on local linearisation, high gain design, or assuming specific trajectories such as constant acceleration of the vehicle. This paper proposes a novel non-linear observer for inertial VAA with almost globally asymptotically and locally exponentially stable error dynamics. The approach exploits Lie group symmetries of the system dynamics to construct a globally valid correction term. To the authors' knowledge, this construction is the first observer to provide almost global convergence for the inertial VAA problem. The observer performance is verified in simulation, where it is shown that the estimation error converges to zero even with an extremely poor initial condition.