Unscented Kalman Filter for Determination of Spacecraft Attitude Using Different Attitude Parameterizations and Real Data

ABSTRACT The non-linear estimators are certainly the most important algorithms applied to real problems, especially those involving the attitude estimation of spacecraft. The purpose of this paper was to use real data of sensors to analyze the behavior of Unscented Kalman Filter (UKF) in attitude estimation problems when it is represented in different ways and compare it with the standard estimator for non-linear estimation problems. The robustness of the estimation was performed when this was subjected to imprecise initial conditions. The attitude parametrization was described in Euler angles, quaternion and quaternion incremental. The satellite China-Brazil Earth Resources Satellite and measurements provided by the Satellite Control Center of the Instituto Nacional de Pesquisas Espaciais were considered in the study. The results indicate that the behaviors for both estimators were equivalent for such parameterizations under the same conditions. However, comparing the Unscented Kalman Filter with the standard filter for non-linear systems, Extended Kalman Filter (EKF), it was observed that, in the presence of inaccurate initial conditions, the Unscented Kalman Filter presented a fast convergence whereas Extended Kalman Filter had problems and only converged later on.

摘要 非线性估计器无疑是应用于实际问题的核心算法之一，尤其在航天器姿态估计相关场景中应用广泛。本文旨在利用传感器实测数据，分析无迹卡尔曼滤波（Unscented Kalman Filter，UKF）以不同形式表征时在姿态估计问题中的性能表现，并将其与针对非线性估计问题的标准估计器进行对比。研究针对估计过程面临不精确初始条件的情况，验证了其估计鲁棒性。本次研究采用欧拉角、四元数以及四元数增量三种形式对姿态参数化方案进行描述，选用中巴地球资源卫星（China-Brazil Earth Resources Satellite）的相关数据，以及巴西国家空间研究院（Instituto Nacional de Pesquisas Espaciais）卫星控制中心提供的测量数据开展实验。结果表明，在相同实验条件下，两种估计器针对上述参数化方案的性能表现相当。然而，将无迹卡尔曼滤波与针对非线性系统的标准滤波器——扩展卡尔曼滤波（Extended Kalman Filter，EKF）进行对比时，可以观察到：在初始条件不精确的情况下，无迹卡尔曼滤波能够实现快速收敛，而扩展卡尔曼滤波则存在收敛延迟问题，仅能在较晚阶段完成收敛。