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 trajectory-independent error state model, the linear Kalman filter is still effective for large initialization 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 initialization errors. Through substitution of the attitude prediction related term with the vector observation in body frame, a trajectory-independent measurement model is derived for MEKF. Meanwhile, the MEKFs with reference attitude error definition and with global state formulating on special Euclidean group have also been studied, with main focus on derivation of the trajectory-independent measurement models. Extensive Monte Carlo simulations and field test of attitude estimation implementations demonstrate that the performance of MEKFs can be much improved with trajectory-independent measurement models.
翻译:在本文中,众所周知的多复制扩展卡尔曼过滤器(MEKF)通过矢量观测重新调查,以进行姿态估测。从 Lie 群组理论可以看出,姿态估测模型是群状的,其误差状态模型应独立于轨迹。此外,有了这种轨迹独立的误差状态模型,线性卡尔曼过滤器仍然对大型初始误差有效。然而,传统的MEKF的测量模型取决于姿态预测,因此取决于轨迹。这也是传统MEKF的性能因大规模初始误差而退化的主要原因。通过在体体框中将与矢量观察有关的态度预测术语替换为对象,为MEKF制定了一个轨迹独立测量模型。与此同时,还研究了带有参考误差定义的MEKFs和关于Euclidean特殊组的全球状态的模型,主要侧重于产生依赖轨迹的测量模型。广泛的蒙特卡洛模拟和对姿态估测实施情况的实地测试表明,MEKFs的性能可以通过轨迹独立的测量模型大大改进。