In this paper, the well-known multiplicative extended Kalman filter (MEKF) is re-investigated for attitude estimation using vector observations. From the Lie group theory, it is shown that the attitude estimation model is group-affine and its error state model should be trajectory-independent. Moreover, with such a trajectory-independent error state model, the linear Kalman filter is still effective for large initialisation errors. However, the measurement model of the traditional MEKF is dependent on the attitude prediction, which is therefore trajectory-dependent. This is also the main reason why the performance of traditional MEKF is degraded for large initialisation errors. Through substitution of the attitude prediction related term with vector observations in the body frame, a trajectory-independent measurement model is derived for MEKF. Meanwhile, MEKFs with reference attitude error definition and with global state formulating on special Euclidean group have also been studied, with the main focus on derivation of the trajectory-independent measurement models. Extensive Monte Carlo simulations of spacecraft attitude estimation implementations demonstrate that the performance of MEKFs can be much improved with trajectory-independent measurement models.

在本文中，著名的乘法扩展卡尔曼滤波器 (MEKF) 被重新研究用于使用矢量观测的姿态估计。从李群理论可以看出，姿态估计模型是群仿射的，其误差状态模型应该是轨迹无关的。此外，对于这种与轨迹无关的误差状态模型，线性卡尔曼滤波器对于较大的初始化误差仍然有效。然而，传统MEKF的测量模型依赖于姿态预测，因此是轨迹相关的。这也是传统 MEKF 的性能因较大的初始化错误而下降的主要原因。通过将姿态预测相关项替换为身体坐标系中的矢量观测值，推导了MEKF 的轨迹无关测量模型。同时，还研究了具有参考姿态误差定义和在特殊欧几里德群上制定全局状态的 MEKF，主要侧重于轨迹无关测量模型的推导。航天器姿态估计实施的广泛蒙特卡罗模拟表明，MEKF 的性能可以通过与轨迹无关的测量模型得到很大改善。