In the field of in-situ gravimetry around asteroids, previous works have extensively utilised spherical harmonics gravity models. These models offer advantages because they are parameterised in terms of coefficients that can be incorporated into the estimation state of a filter. In line with this approach, there have been efforts to re-examine the gravity determination of the pioneer NEAR mission on asteroid 433 Eros. However, these models often prove inadequate within the body's circumscribing sphere, compromising their suitability for low-altitude operations such as descent and landing. Alternative models (e.g. mascon) that avoid accuracy losses within the circumscribing sphere present challenges when integrating into a filter-based approach. This is primarily due to the large number of parameters or the physical constraints associated with these alternative models. THOR proposes leveraging the concept of dynamical model compensation to estimate unmodeled empirical accelerations along the spacecraft trajectory. This process yields an on-orbit position-acceleration dataset that can be utilised to determine the parameters of a gravity model. Specifically, we have developed an optimised mascon model with physical consistency. This is specially relevant in scenarios where data is sparse and addressing physical constraints directly becomes imperative to ensure robust extrapolation in data less regions. In THOR, we have developed a novel optimiser that employs Adam gradient descent with constraints projection to ensure that masses remain positive and confined within the asteroid shape.
Regarding the topic of gravity field modeling, THOR has explored the concept of integrating robust physical models with data-driven neural networks. Researchers have devoted extensive efforts, with ongoing progress, to develop accurate yet lightweight gravity models for on-board autonomy. In THOR, pre-trained mascon models have been combined with physics-informed neural networks (PINNs). Mascon models offer a precise initial approximation to the asteroid's gravity field and effectively extrapolate the high-altitude profile where data is lacking. However, their learning capacity is constrained by the finite number of masses used, and errors may arise from mass placement near the surface. Recent advancements in PINN gravity models, demonstrated by J. Martin and H. Schaub, have showcased their capability to approximate highly complex patterns, such as surface gravity. Nonetheless, these authors observed neural networks' limitations in extrapolating patterns beyond data bounds, prompting the inclusion of low-fidelity analytical models (e.g. point mass) to prevent divergence. THOR proposes to enhance the low-fidelity analytic component with pre-trained mascon models, which exhibit accuracy except in areas very close to the surface. This approach enables continued learning of complex patterns by the PINN through the introduction of new basis functions. Currently, these models have been implemented in the open-source Basilisk astrodynamics framework to benefit the broader astrodynamics community. Preliminary results indicate a one-order-of-magnitude decrease in 1-day propagation errors for orbits around asteroid Eros with the fused model. We anticipate completing and submitting a journal version of this work after summer 2024.
