University of Murcia, Department of Information and Communication Engineering, 30100 Murcia, Spain.
Sensors (Basel). 2019 Jan 3;19(1):149. doi: 10.3390/s19010149.
The problem of attitude estimation is broadly addressed using the Kalman filter formalism and unit quaternions to represent attitudes. This paper is also included in this framework, but introduces a new viewpoint from which the notions of "multiplicative update" and "covariance correction step" are conceived in a natural way. Concepts from manifold theory are used to define the moments of a distribution in a manifold. In particular, the mean and the covariance matrix of a distribution of unit quaternions are defined. Non-linear versions of the Kalman filter are developed applying these definitions. A simulation is designed to test the accuracy of the developed algorithms. The results of the simulation are analyzed and the best attitude estimator is selected according to the adopted performance metric.
使用卡尔曼滤波形式和单位四元数来表示姿态来广泛解决姿态估计问题。本文也包含在此框架内，但引入了一个新的观点，自然地从该观点来构想“乘法更新”和“协方差校正步骤”的概念。流形理论中的概念用于定义流形中分布的矩。特别地，定义了单位四元数分布的均值和协方差矩阵。应用这些定义开发了非线性版本的卡尔曼滤波器。设计了一个模拟来测试所开发算法的准确性。根据采用的性能指标分析模拟结果并选择最佳姿态估计器。
