针对不完整姿态观测，提出改进型滤波器实现稳定姿态估计。
Complementary Filtering on SO(3) for Attitude Estimation with Scalar Measurements
- 基于旋转群SO(3)设计新滤波器，适配仅测量标量的场景
- 三标量测量下可实现几乎全局稳定，两标量时在较小范围内收敛
- 适用于低感知或新型传感器的复杂姿态估计任务
利用标量测量进行姿态估计，对应于惯性矢量在特定机体坐标系方向上的部分观测。这类测量常见于向量观测不全或由异构传感器信息推导出的姿态约束问题中。本文在经典SO(3)互补滤波基础上，提出一种针对标量输出结构的改进观测器，其创新项经重构以适配该测量形式。主要结果表明，在至少三个惯性矢量沿同一机体矢量测量，且满足激励持续性条件下，可恢复几乎全局渐近稳定性，符合SO(3)的三维结构特性。对于双标量配置——即一个惯性矢量沿两个机体矢量测量，或两个惯性矢量沿同一机体矢量测量——进一步推导了保证收敛的充分条件，收敛域缩小但依然有效。多个实例与数值结果验证了所提标量互补滤波器在传感受限或新型传感模态下的有效性。
原文摘要 · Abstract (English)
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.
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