Stochastic modeling of physical drag coefficient -- its impact on orbit prediction and space traffic management

TL;DR

This paper develops a neural network model to predict satellite drag coefficients, including uncertainty, to improve orbit prediction and space traffic management amidst increasing low-Earth space congestion.

Contribution

It introduces a deep neural network that predicts both mean and standard deviation of drag coefficients across satellite attitudes, calibrated with simulated physical data, extending prior work.

Findings

The neural network accurately predicts drag coefficient and its uncertainty.

Propagation of orbital errors shows significant impact from drag coefficient uncertainty.

Model improves orbit prediction accuracy for space traffic management.

Abstract

Ambitious satellite constellation projects by commercial entities and the ease of access to space in recent times have led to a dramatic proliferation of low-Earth space traffic. It jeopardizes space safety and long-term sustainability, necessitating better space traffic management (STM). Correct modeling of uncertainties in force models and orbital states, among other things, is an essential part of STM. For objects in the low-Earth orbit (LEO) region, the uncertainty in the orbital dynamics mainly emanate from limited knowledge of the atmospheric drag-related parameters and variables. In this paper, which extends the work by Paul et al. [2021], we develop a feed-forward deep neural network model for the prediction of the satellite drag coefficient for the full range of satellite attitude (i.e., satellite pitch $\in$ ($-90^0$, $+90^0$) and satellite yaw $\in$ ($0^0$, $+360^0$)). The model simultaneously predicts the mean and the standard deviation and is well-calibrated. We use numerically simulated physical drag coefficient data for training our neural network. The numerical simulations are carried out using the test particle Monte Carlo method using the diffuse reflection with incomplete accommodation gas-surface interaction model. Modeling is carried out for the well-known CHAllenging Minisatellite Payload (CHAMP) satellite. Finally, we use the Monte Carlo approach to propagate CHAMP over a three-day period under various modeling scenarios to investigate the distribution of radial, in-track, and cross-track orbital errors caused by drag coefficient uncertainty.