High precise estimation and prediction of the target's attitude motion are key technologies for capturing and removing rotating space debris. In this article, a neural-network-enhanced Kalman filter (NNEKF) is proposed to improve the precision and robustness of attitude estimation algorithm. The main innovation of the NNEKF is to utilize virtual observations of the inertia characteristics to improve the filter's performances. The virtual observations are obtained using a neural network, which is offline trained using simulation data. In order to decrease the number of nodes of the network, the input data are preprocessed using the discrete Fourier transformation method. Moreover, by involving the characteristic frequencies in the input vector, the neural network can extract information from all the past observations, so as to grasp long-term characteristics of the dynamical system. Therefore, the NNEKF can provide more precise estimation of the target's moment of inertia, and furthermore improve the accuracy and robustness of attitude estimation and prediction. Simulation results indicate that the NNEKF can reduce the estimation errors by 39% compared with the conventional EKF method when using the same measurement data. And the accumulation errors of prediction using estimates of the NNEKF is just as 24% as the conventional EKF.

中文翻译：

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基于神经网络虚拟观测的旋转空间碎片鲁棒姿态估计

目标姿态运动的高精度估计和预测是捕获和清除旋转空间碎片的关键技术。在本文中，提出了一种神经网络增强卡尔曼滤波器（NNEKF）来提高姿态估计算法的精度和鲁棒性。NNEKF 的主要创新是利用对惯性特性的虚拟观察来提高滤波器的性能。虚拟观察是使用神经网络获得的，该网络使用模拟数据进行离线训练。为了减少网络的节点数，使用离散傅里叶变换方法对输入数据进行预处理。此外，通过在输入向量中包含特征频率，神经网络可以从所有过去的观察中提取信息，从而掌握动力系统的长期特征。因此，NNEKF可以提供更精确的目标转动惯量估计，​​进一步提高姿态估计和预测的准确性和鲁棒性。仿真结果表明，在使用相同的测量数据时，与传统的EKF方法相比，NNEKF可以减少39%的估计误差。并且使用 NNEKF 估计的预测累积误差与传统 EKF 一样只有 24%。仿真结果表明，在使用相同的测量数据时，与传统的EKF方法相比，NNEKF可以减少39%的估计误差。并且使用 NNEKF 估计的预测累积误差与传统 EKF 一样只有 24%。仿真结果表明，在使用相同的测量数据时，与传统的EKF方法相比，NNEKF可以减少39%的估计误差。并且使用 NNEKF 估计的预测累积误差与传统 EKF 一样只有 24%。