Data-Driven Orbit Determination for Low-Earth Orbit Space Debris Using Ground-Based Measurements

Fast and accurate orbit determination for Low-Earth Orbit (LEO) space debris using ground-based measurements presents a significant challenge due to the sparsity of observations, which leads to high nonlinearity. Classical orbit determination methods, such as the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), Particle Filter (PF), Gaussian Mixture Filter (GMF), have been widely employed. However, for highly nonlinear systems, the accuracy of EKF and UKF is constrained by linearization errors and the Gaussian assumption, respectively. Moreover, PF and GMF require large number of particles or Gaussian components to achieve sufficient accuracy, resulting in high computational costs. Motivated by recent advancements in deep learning, this study investigates the potential of the data-driven filter in the LEO orbit determination task. The Data-driven Autoregressive nonlinear Filter (DAF), which is proposed recently, has demonstrated promise in handling high nonlinearities. In this paper, we train the DAF using the distance and direction measurements obtained from the ground station for different debris, without access to the true states of the debris. During the inference phase, the DAF relies entirely on the well-trained neural network to estimate the states of debris that are not encountered during training. Simulation results demonstrate that when the system nonlinearity is high enough, our proposed method can achieve higher accuracy compared to the classical filters while offering competitive computational efficiency, as it eliminates the need for numerical integration. To the best of our knowledge, this study represents the first attempt to apply a data-driven filter to orbit determination, providing an alternative to existing methods.