Scalar-Measurement Attitude Estimation on SO(3) with Bias Compensation
Alessandro Melis, Tarek Bouazza, Hassan Alnahhal, Sifeddine Benahmed, Soulaimane Berkane, Tarek Hamel
AI summary
Problem
Conventional attitude estimators require complete 3D vector measurements from IMUs, which fails when directional data is sparse, noisy, or partially unavailable, while prior scalar-based methods lack bias handling and impose overly strict observability conditions.
Approach
The authors develop a deterministic nonlinear observer directly on the SO(3) manifold that fuses scalar measurements with a continuous Riccati equation to jointly estimate attitude and gyroscope bias, ensuring local exponential stability under derived observability conditions.
Key results
- Direct SO(3)-based observer design avoids high-dimensional embeddings
- Explicit gyroscope bias compensation within a deterministic Riccati framework
- Rigorous persistence-of-excitation conditions guaranteeing local exponential stability
- Proof that two scalar measurements suffice for dynamic estimation and three for static cases
Why it matters
Enables robust, low-cost attitude estimation for navigation and control systems when full vector sensor data is compromised or unavailable.
Abstract
Attitude estimation methods typically rely on full vector measurements from inertial sensors such as accelerom- eters and magnetometers. This paper shows that reliable estimation can also be achieved using only scalar measure- ments, which naturally arise either as components of vector readings or as independent constraints from other sensing modalities. We propose nonlinear deterministic observers on 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 con- sistent 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.