On the Design of Attitude Observers on the Special Orthogonal Group $SO(3)$

TL;DR

This paper analyzes and improves nonlinear attitude estimation filters on $SO(3)$, providing explicit solutions, stability insights, and robustness comparisons, with simulations confirming enhanced performance of the proposed filters.

Contribution

The paper derives explicit solutions for attitude estimation error dynamics and introduces improved nonlinear filters with state-dependent gains for better robustness and stability.

Findings

Explicit solution for attitude error dynamics without measurement errors.

Improved stability and robustness of new filters over traditional ones.

Simulation results confirm theoretical robustness and performance enhancements.

Abstract

We revisit the nonlinear complimentary filter on $SO(3)$, previously proposed in the literature, and provide the (time-explicit) solution to the matrix ODE governing the attitude estimation error in the absence of measurement errors. The stability and performance properties of this filter can be easily deduced from the obtained closed-from solution. Thereafter, we consider two nonlinear complimentary filters (with state-dependent gains) which are shown to exhibit improved stability and performance proprieties compared to the traditional filter. We perform robustness analysis for the three discussed attitude filters on $SO(3)$ with respect to attitude and angular velocity measurement errors. Specifically, we show that the state-dependent-gain filters may exhibit improved robustness to gyro measurement disturbances and a better disturbance attenuation levels. Simulation results are performed to confirm the obtained theoretical results.