Abstract 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.

Highlights • Orbit maneuver-free approach to the angle-only relative orbit determination for is proposed. • Angles-only orbital observability problem is solved by using deep neural network to capture the nonlinearity of the dynamics. • The DNN frame including the network structure, data processing, and training algorithm for angles-only problem is designed. • The validity of the proposed algorithm is evaluated by digital simulations. • The sensitivities of the uncertainties and parameters are presented and discussed.