Duane DeSieno, Data Fusion & Neural Networks, LLC
Keywords: Neural networks, Enhanced orbit propagation, Trajectory propagation, Machine Learning
Abstract:
In astrodynamics, propagation refers to the process of predicting the future position and velocity (state) of an object in space, such as a satellite, spacecraft, or celestial body, based on its current state and the physical forces acting upon it. The future state can be estimated using two basic methodologies, numerical propagation and semi-analytical propagation.
A numerical propagator integrates the forces acting on the spacecraft over time. The accuracy of such a propagator depends heavily on the modeled physical forces it considers. The primary forces modeled in a numerical propagator are gravitational forces. The primary force model is the central body gravity of the Earth. This force is modeled using spherical harmonics including high order terms to account for irregularities in earth gravitational field. Third body gravity force models have also been produced for the influences of other celestial bodies, such as the Moon, the Sun, and planets, which perturb the satellite’s orbit. However, in the real world, there are other factors that influence the motion of the spacecraft. These factors include the atmospheric drag, solar radiation pressure (space weather), Earth’s albedo and Earth’s infrared radiation, the Earth’s magnetic field, tidal forces and relativistic corrections. And there may be additional factors not covered in this list. While estimates can be made for some of these factors, many change with time. Modeling these forces for a numerical propagator would require a model for all points in space which can be extremely difficult to produce. Also, modeling these forces can be dependent on the characteristics of the spacecraft that may not be known such as its shape, orientation, mass, and magnetic properties. As one attempts to improve the performance of numerical propagation, the computational load continues to increase.
The second methodology is semi-analytical propagation. These use a combination of analytical techniques and some numerical methods to provide a balance between accuracy and computational efficiency. SGP4 falls into this category because it uses analytical expressions derived from perturbation theory, with simplifications that make it computationally efficient. SGP4 is widely used for orbit determination of Earth-orbiting objects, particularly with Two-Line Element sets (TLEs). It provides a practical and computationally efficient way to predict satellite positions with reasonable accuracy.
The goal of this research was to demonstrate a novel approach that uses a neural network, trained on recent history, to substantially improve the performance of the base propagator (either numerical or semi-analytical). Regardless of the force models used in the base propagator, recent history for a specific satellite can be used to produce a “local” model of the forces on that specific satellite that were not available to the base propagator. Since the recent history of observations available for a specific satellite is limited, the machine learning methodology applied requires making the neural network as small as possible to achieve the desired result. This learning is specific to the object from which the observations are being made. The goal of the learning is to correct the output of the base propagator in order to improve the accuracy of the propagated position and velocity.
The neural enhanced propagation (NEP) described in this paper can be run on a fast platform, such as DF&NN’s Alert Management System (AMS), used by customers such as the Air Force Research Laboratory’s DRAGON Army, automated neural network training and retraining can take place as often as necessary to ensure the neural network enhanced propagation is as accurate as possible. A custom spacecraft-specific propagator approach simplifies what the neural network must learn. DF&NN has implemented this approach on the whole catalog of satellites it monitors.
The outcome expected from using the neural enhanced propagation is to lower the uncertainty of where the spacecraft is at a future point in time. Because the neural enhanced propagation is applied as a learned correction to the base propagator, its performance should always be better than the base propagator it is correcting. The importance of this capability for the SSA and SDA communities should be more accurate detection of maneuvers, proximity analyses, and computation of collision probabilities.
Date of Conference: September 17-20, 2024
Track: Machine Learning for SDA Applications