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

2026-03-02

AI Summary

This work addresses the challenge that traditional attitude estimation methods rely on full vector measurements, whereas many practical scenarios provide only scalar observations. To overcome this limitation, the paper proposes a nonlinear deterministic observer on $\mathbf{SO}(3)$ that jointly estimates attitude and gyroscope bias using scalar measurements alone. Theoretical analysis establishes, for the first time, that attitude observability is guaranteed with merely two scalar measurements under sufficient excitation, and three suffice in static conditions. The method is validated on the BROAD dataset, demonstrating robust performance with low estimation error even under severely degraded measurement configurations, thereby highlighting its strong stability and practical applicability.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

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.

Problem

• attitude estimation
• scalar measurements
• SO(3)
• bias compensation
• observability

Innovation

• scalar measurements
• attitude estimation
• SO(3)
• bias compensation
• observability