On-board modeling of gravity fields of elongated asteroids using Hopfield neural networks

To rapidly model the gravity field near elongated asteroids, an intelligent inversion method using Hopfield neural networks (HNNs) is proposed to estimate on-orbit simplified model parameters. First, based on a rotating mass dipole model, the gravitational field of asteroids is characterized using a few parameters. To solve all the parameters of this simplified model, a stepped parameter estimation model is constructed based on different gravity field models. Second, to overcome linearization difficulties caused by the coupling of the parameters to be estimated and the system state, a dynamic parameter linearization technique is proposed such that all terms except the parameter terms are known or available. Moreover, the Lyapunov function of the HNNs is matched to the problem of minimizing parameter estimation errors. Equilibrium values of the Lyapunov function are used as estimated values. The proposed method is applied to natural elongated asteroids 216 Kleopatra, 951 Gaspra, and 433 Eros. Simulation results indicate that this method can estimate the simplified model parameters rapidly, and that the estimated simplified model provides a good approximation of the gravity field of elongated asteroids.