A Physic-Informed Neural Network Approach to Orbit Determination

This paper introduces a method for solving orbit determination problems named Physics Informed Orbit Determination. We use a particular kind of single-layer, feed-forward neural network with random input weights and biases called Extreme Learning Machines to estimate the spacecraft’s state. The least-squares estimate is used as the baseline for the loss function, to which a regularizing term based on the differential equations modeling the dynamics of the problem is added. This ensures that the learned relationship between input and output is compliant with the physics of the problem while also fitting the observation data. The method works with range/range-rate or angular observations, either in Keplerian or non-Keplerian dynamics. The method is tested on synthetically generated data, with and without perturbations. The results are comparable with the batch least-squares solution, with the advantage of not requiring an initial guess and solving for the entire trajectory without any integration.