Scalar-Measurement Attitude Estimation on $\mathbf{SO}(3)$ with Bias Compensation

TL;DR

This paper introduces nonlinear observers for attitude estimation on SO(3) using only scalar measurements, demonstrating robustness to partial sensing and establishing fundamental observability results with experimental validation.

Contribution

It presents the first fundamental observability results showing two scalar measurements suffice for attitude estimation, and introduces bias-compensating observers on SO(3).

Findings

Robust attitude estimation with only scalar measurements.

Experimental validation shows small errors even with severe measurement loss.

Fundamental observability results for scalar measurements on SO(3).

Abstract

Attitude estimation methods typically rely on full vector measurements from inertial sensors such as accelerometers and magnetometers. This paper shows that reliable estimation can also be achieved using only scalar measurements, which naturally arise either as components of vector readings or as independent constraints from other sensing modalities. We propose nonlinear deterministic observers on $\mathbf{SO}(3)$ that incorporate gyroscope bias compensation and guarantee uniform local exponential stability under suitable observability conditions. A key feature of the framework is its robustness to partial sensing: accurate estimation is maintained even when only a subset of vector components is available. Experimental validation on the BROAD dataset confirms consistent performance across progressively reduced measurement configurations, with estimation errors remaining small even under severe information loss. To the best of our knowledge, this is the first work to establish fundamental observability results showing that two scalar measurements under suitable excitation suffice for attitude estimation, and that three are enough in the static case. These results position scalar-measurement-based observers as a practical and reliable alternative to conventional vector-based approaches.