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.
However, the particular structure of PIOD, based on ELM, allows it to provide an accurate estimate without needing an initial guess. The only parameters to initialize are input weights and biases, which as per ELM theory, are initialized at random. This essentially removes the dependence of the solution on the initial guess. This is in stark contrast with batch least squares, which shows convergence sensitivity to initial guess, especially when estimating the state of satellites in cislunar space, which is becoming increasingly critical for the future of space exploration. Overall, this paper shows that physics informed neural networks are a powerful tool that can be employed for OD, which performs on par or better than existing least-squares techniques, without requiring any initial guess. Moreover, the flexibility of PINNs allows the method to be extended further using a more refined parameter selection algorithm, as well as adding functionality to account for maneuvering targets and perturbations.
Reference:
Scorsoglio, A., Ghilardi, L., & Furfaro, R. (2023). A Physic-Informed Neural Network Approach to Orbit Determination. The Journal of the Astronautical Sciences, 70(4), 1-30. DOI