Initial orbit determination (IOD) is an important early step in the processing chain that makes sense of and reconciles the multiple optical observations of a resident space object. IOD methods generally operate on line-of-sight (LOS) vectors extracted from images of the object, hence the LOS vectors can be seen as discrete point samples of the raw optical measurements. Typically, the number of LOS vectors used by an IOD method is much smaller than the available measurements (\ie, the set of pixel intensity values), hence current IOD methods arguably under-utilize the rich information present in the data. In this paper, we propose a \emph{direct} IOD method called D-IOD that fits the orbital parameters directly on the observed streak images, without requiring LOS extraction. Since it does not utilize LOS vectors, D-IOD avoids potential inaccuracies or errors due to an imperfect LOS extraction step. Two innovations underpin our novel orbit-fitting paradigm: first, we introduce a novel non-linear least-squares objective function that computes the loss between the candidate-orbit-generated streak images and the observed streak images. Second, the objective function is minimized with a gradient descent approach that is embedded in our proposed optimization strategies designed for streak images. We demonstrate the effectiveness of D-IOD on a variety of simulated scenarios and challenging real streak images.

翻译：初始轨道确定（IOD）是处理链中的重要早期步骤，用于理解和协调对空间目标的多重光学观测。IOD方法通常基于从目标图像中提取的视线（LOS）向量进行操作，因此LOS向量可视为原始光学测量的离散点样本。通常，IOD方法使用的LOS向量数量远小于可用测量数据（即像素强度值集合），因此当前IOD方法在某种程度上未充分利用数据中蕴含的丰富信息。本文提出一种名为D-IOD的“直接”IOD方法，该方法直接对观测到的条纹图像拟合轨道参数，无需LOS提取。由于不依赖LOS向量，D-IOD避免了因LOS提取步骤不完善而导致的潜在不准确或误差。两个创新点支撑了这一新型轨道拟合范式：首先，我们引入了新颖的非线性最小二乘目标函数，该函数计算候选轨道生成的条纹图像与观测条纹图像之间的损失；其次，通过嵌入我们为条纹图像设计的优化策略中的梯度下降方法最小化该目标函数。我们在多种模拟场景及具有挑战性的真实条纹图像上验证了D-IOD的有效性。