Angles-only relative orbit determination for space situational awareness is subjected to a well-known range observability problem, that is, the range between two spacecraft is weakly observable or unobservable. However, in previous studies, the solutions to this problem using nonlinear relative motion dynamics have been limited by the computational complexity and long arc of observation. To this end, this study develops a simple and fast algorithm to address the angles-only relative orbit determination problem by exploiting a deep neural network (DNN), which has a significantly strong capability of capturing nonlinearity. Emphasis is placed on the construction of a nonlinear mapping model from the line-of-sight angles to the relative orbit state by training the designed DNN. First, a training dataset generator including nonlinear relative motion dynamics and a line-of-sight measurement model is established to generate the training data for the DNN. Second, the DNN frame, including the network structure, data processing, and network training algorithm for angles-only relative orbit determination, is designed. Subsequently, a digital simulation system comprising error models, reference missions and trajectories, and computation models for error estimation is established. Thus, the anti-noise and generalization performance of the nonlinear mapping model on GEO-type orbits are verified using digital simulations. The results indicate that the proposed algorithm is effective, whereby the estimation accuracy for the relative position is generally better than that for the relative velocity. In the case of a co-elliptical orbit, the estimated errors of distance and velocity in each direction are less than 9.7% and 48.2%, respectively, whereas the maximum average errors are approximately 1.1% and 4.2%, respectively, where only three sets of angle measurements with an interval of 600 s are available. However, in the case of a non-coplanar orbit, the interval between angles can be decreased to 50 s, when the corresponding estimated error of distance in each direction is less than 9.9%, and the maximum average error is approximately 1.1%. Additionally, the sensitivity of the proposed algorithm to the arc length, number, and interval of the measurements is analyzed.

用于空间态势感知的仅角度相对轨道确定存在一个众所周知的距离可观测性问题，即两个航天器之间的距离是弱可观测或不可观测的。然而，在以往的研究中，使用非线性相对运动动力学来解决这个问题的方法受到计算复杂性和观测弧长的限制。为此，本研究开发了一种简单快速的算法，通过利用深度神经网络 (DNN) 来解决仅角度的相对轨道确定问题，该网络具有很强的非线性捕获能力。重点是通过训练设计的 DNN，构建从视线角度到相对轨道状态的非线性映射模型。第一的，建立包含非线性相对运动动力学和视线测量模型的训练数据集生成器，以生成用于 DNN 的训练数据。其次，设计了DNN框架，包括仅角度相对轨道确定的网络结构、数据处理和网络训练算法。随后，建立了一个包括误差模型、参考任务和轨迹以及用于误差估计的计算模型的数字仿真系统。因此，利用数字仿真验证了非线性映射模型在 GEO 型轨道上的抗噪声和泛化性能。结果表明，该算法是有效的，相对位置的估计精度普遍优于相对速度的估计精度。在共椭圆轨道的情况下，每个方向的距离和速度估计误差分别小于 9.7% 和 48.2%，而最大平均误差分别约为 1.1% 和 4.2%，其中只有 3 组间隔为 600 s 的角度测量值可用的。但是，在非共面轨道的情况下，当相应的各方向距离估计误差小于9.9%，最大平均误差约为1.1%时，角度间隔可以减小到50 s。此外，分析了所提出算法对弧长、数量和测量间隔的敏感性。其中只有三组间隔为 600 秒的角度测量可用。但是，在非共面轨道的情况下，当相应的各方向距离估计误差小于9.9%，最大平均误差约为1.1%时，角度间隔可以减小到50 s。此外，分析了所提出算法对弧长、数量和测量间隔的敏感性。其中只有三组间隔为 600 秒的角度测量可用。但是，在非共面轨道的情况下，当相应的各方向距离估计误差小于9.9%，最大平均误差约为1.1%时，角度间隔可以减小到50 s。此外，分析了所提出算法对弧长、数量和测量间隔的敏感性。