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

TL;DR

This paper introduces a modified complementary filter on SO(3) for attitude estimation using scalar measurements, achieving almost-global stability under certain conditions and demonstrating effectiveness in scenarios with limited sensing.

Contribution

It develops a new observer tailored for scalar measurements, extending classical filters to handle incomplete vector observations on SO(3).

Findings

Almost-global asymptotic stability under persistence of excitation.

Convergence guarantees for two-scalar measurement configurations.

Numerical results validate effectiveness in reduced sensing scenarios.

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.