Jonathan Kadan,Virginia Polytechnic Institute and State University; Dylan Thomas, Virginia Polytechnic Institute and State University; Amit Bala, Virginia Polytechnic Institute and State University; Kevin Schroeder, Virginia Polytechnic Institute and State University; Jonathan Black, Virginia Polytechnic Institute and State University
Keywords: UKF, SDA, filtering, orbital dynamics, AST, estimation
Abstract:
A well known issue in Space Domain Awareness (SDA) is that orbit propagation of an Earth Centered Inertial (ECI) state is inherently non-linear. Standard and Extended Kalman Filters (EKF) do not approximate nonlinear state transition matrices well which leads to numerical errors. The Unscented Kalman Filter (UKF) overcomes this problem in SDA because it can handle the nonlinear dynamics of Resident Space Objects (RSO) orbit propagation by creating 13 sigma points with the unscented transformation. However, this statistical approximation of estimate covariances are less gaussian than what a more accurate estimator like the particle filtering technique would produce. This is because estimate covariances stretch much further in the in-track direction compared to cross-track and radial directions (RIC coordinates). The center of the UKF gaussian is, on average, at a slightly lower orbit than the true center of the RSO being estimated. In orbital dynamics, this means that the estimate will be at a lower altitude than it should be and therefore have less energy. Over this time, the error compounds itself leading to degrading orbital radius and estimate divergence. There are multiple ways to overcome this issue, for example: decreasing timestep and lowering filter noise magnitude. However, these techniques diminish the advantage of using the UKF, which is its lower computational cost compared to the particle filtering technique. With the future of SDA having to account for the massive increase in RSO in the coming years due to upcoming proliferated LEO (p-LEO) constellations, e.g. Starlink, the need for quickly resolved tasking solutions and accurate estimates has never been higher. If the UKF was applied to a linear coordinate system, the results would be gaussian and closer to the correct altitude.
Luckily, such a technique already exists, the Adapted STructural Unscented Kalman Filter (AST-UKF) was developed for this very purpose. The AST coordinate system is a derivation of the equinoctial coordinate system and is more gaussian compared to standard ECI coordinates. This is because the AST coordinate system is derived in such a way that all RSO have an initial inclination of 0 degrees in their relative orbital frame. This results in no issue with retrograde orbits, a known problem in propagating in the equinoctial frame.
This work will aim to compare the AST-UKF to the standard ECI-UKF on a scale necessary for modern SDA. This work will operate on multi-day scenarios with hundreds of RSO across multiple orbital regimes (LEO, MEO and GEO) and a representative Space Surveillance Network (SSN) based on open source information that incorporates optical (2D), radar (3D) and advanced radar (4D) observations. A sub-optimal partially observed Markov decision process (POMDP) will be implemented to autonomously task this diverse, distributed sensor network to track possibly maneuvering, non-uniform RSO. This tool has the capability to simulate weeks of sensor tasking solutions for hundreds of RSO and will be used as the simulator for evaluating the ECI-UKF and AST-UKF algorithms. Multiple evaluation metrics will be used including: filter residuals, mahalanobis distance, normalized estimation error squared (NEES) and normalized innovations squared (NIS) tests.
This work expands upon the previous by combining 2D, 3D, and 4D observations into the AST-UKF filtering solution for the first time. The value in this research is the potential foundation for rapid SDA based on large scale simulation of a more accurate estimation algorithm across multiple orbital regimes.
Date of Conference: September 14-17, 2021
Track: Astrodynamics