A Pontryagin Neural Network Application to Tracklets Correlation of Optical Observations

The increasing interest in the X-GEO region is leading towards a significant increment in its population of satellites and debris. Consequently, there will be a demand for techniques capable of accurately identifying, correlating, and cataloging X-GEO objects. This paper introduces an innovative approach to solve tracklets correlation of optical observations via Pontryagin Neural Network (PoNN), which is a Physics-Informed Neural Network (PINN) trained to solve optimal control problems via indirect method and Pontryagin Minimum Principle. Within PoNN, the PINN framework called Extreme Theory of Functional Connections (X-TFC) is employed. PoNN is a particular kind of single-layer feed-forward neural network used to estimate the object’s state and costate, while solving an energy optimal control problem. Indeed, since no maneuvering objects are considered, the ballistic trajectory, solution of the successfully correlated tracklets, is assumed to be the one minimizing the control effort. The correlation is assessed through a criterion based on the Mahalanobis distance, involving the residuals on the observations and the DeltaV associated to the computed optimal trajectory. The proposed method is applied to angles-only observations of objects in Keplerian dynamics and tested on both simulated and real data. For the case of real data, the majority of the real topocentric right ascension and declination measurements have been provided by the telescopes of the Space4 Center at the University of Arizona.