Complementary Filtering on SO(3) for Attitude Estimation with Scalar Measurements

2026-04-09

AI Summary

This work addresses the challenge of attitude estimation when only scalar inertial measurements—such as partial vector observations along a single body-fixed axis—are available. The authors propose a novel complementary filter formulated directly on the SO(3) manifold, wherein the innovation term is specifically restructured to accommodate the scalar output structure. They establish almost global asymptotic stability of the attitude estimate under the condition that at least three inertial vectors are measured along the same body axis, and further derive sufficient conditions for convergence in two distinct dual-scalar measurement configurations. Numerical experiments demonstrate that the proposed method maintains robustness and effectiveness even under severe sensor constraints or with emerging scalar sensing modalities.

Abstract

Attitude estimation using scalar measurements, corresponding to partial vectorial observations, arises naturally when inertial vectors are not fully observed but only measured along specific body-frame vectors. Such measurements arise in problems involving incomplete vector measurements or attitude constraints derived from heterogeneous sensor information. Building on the classical complementary filter on SO(3), we propose an observer with a modified innovation term tailored to this scalar-output structure. The main result shows that almost-global asymptotic stability is recovered, under suitable persistence of excitation conditions, when at least three inertial vectors are measured along a common body-frame vector, which is consistent with the three-dimensional structure of SO(3). For two-scalar configurations - corresponding either to one inertial vector measured along two body-frame vectors, or to two inertial vectors measured along a common body-frame vector - we further derive sufficient conditions guaranteeing convergence within a reduced basin of attraction. Different examples and numerical results demonstrate the effectiveness of the proposed scalar-based complementary filter for attitude estimation in challenging scenarios involving reduced sensing and/or novel sensing modalities.

Problem

• attitude estimation
• scalar measurements
• SO(3)
• incomplete vector observations
• complementary filtering

Innovation

• complementary filtering
• SO(3)
• scalar measurements
• attitude estimation
• almost-global asymptotic stability