Rigid Body Geometric Attitude Estimator using Multi-rate Sensors

TL;DR

This paper introduces a geometric attitude estimator for rigid bodies that effectively fuses multi-rate sensor data using Lyapunov stability analysis, ensuring exponential stability and robustness to measurement noise.

Contribution

It develops a novel discrete-time Lyapunov-based filtering scheme for attitude estimation with multi-rate measurements, demonstrating almost global stability and noise robustness.

Findings

The estimator achieves exponential stability in noise-free conditions.

Simulation results confirm convergence to a bounded neighborhood under noisy measurements.

The approach effectively handles multi-rate sensor data for attitude determination.

Abstract

A geometric estimator is proposed for the rigid body attitude under multi-rate measurements using discrete-time Lyapunov stability analysis in this work. The angular velocity measurements are assumed to be sampled at a higher rate compared to the attitude. The attitude determination problem from two or more vector measurements in the body-fixed frame is formulated as Wahba's problem. In the case when measurements are absent, a discrete-time model for attitude kinematics is assumed in order to propagate the measurements. A discrete-time Lyapunov function is constructed as the sum of a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential energy-like term obtained from Wahba's cost function. A filtering scheme is obtained by discrete-time stability analysis using a suitable Lyapunov function. The analysis shows that the filtering scheme is exponentially stable in the absence of measurement noise and the domain of convergence is almost global. For a realistic evaluation of the scheme, numerical experiments are conducted with inputs corrupted by bounded measurement noise. Simulation results exhibit convergence of the estimated states to a bounded neighborhood of the actual states.