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.

翻译：利用标量测量值进行姿态估计（对应于部分矢量观测）在惯性矢量未被完全观测，而仅沿特定体坐标系矢量进行测量时自然出现。此类测量常见于涉及不完整矢量测量或源自异构传感器信息的姿态约束问题中。基于经典SO(3互补滤波器，我们提出一种观测器，其包含针对这种标量输出结构定制的改进创新项。主要结果表明：在满足适当持续激励条件的假设下，当至少三个惯性矢量沿共同体坐标系矢量测量时——这与SO(3的三维结构一致——可恢复几乎全局渐近稳定性。针对双标量构型（即一个惯性矢量沿两个体坐标系矢量测量，或两个惯性矢量沿共同体坐标系矢量测量），我们进一步推导了保证在缩小吸引域内收敛的充分条件。通过不同算例与数值结果，展示了所提出的基于标量互补滤波器在涉及降级传感和/或新型传感模式的挑战场景中的有效性。