Mark Bolden, Trusted Space, Inc.; Islam Hussein, Trusted Space, Inc.; Holly Borowski, Trusted Space, Inc.; Robert See, Trusted Space, Inc.; Erin Griggs, Trusted Space, Inc.
Keywords: Cislunar Space Domain Awareness, Initial Orbit Determination, Orbit Determination, Non-Linear Filtering, Optical Sensors, Radiometric Observations
Abstract:
The cislunar domain is the ultimate high ground above earth and securing and protecting that position is one of the five core competencies identified in United States Space Force Spacepower Doctrine1. Cislunar domain awareness presents unique challenges compared to common satellite regimes like Geosynchronous (GEO) and Low Earth Orbit (LEO). These challenges include initial orbit determination for newly discovered objects or recovered lost objects, as well as for tracking objects after orbit initialization.
Observations of an object in cislunar space are usually short-arced because of the colossal distances of the environment, causing multiple observations to effectively act as a single observation point. To rapidly generate an uncertain trajectory for object tracking, high-fidelity probabilistic initial orbit determination (IOD) techniques, such as the Probabilistic Admissible Region (PAR)2 approach, are needed. Such techniques need to complement the single observation with other hypothesized information (e.g., target albedo-area product) to generate a probabilistic representation of the objects orbit. A primary challenge to generating an initial track for an object is that cislunar trajectories cannot be easily described by parameters we currently use to describe near-earth orbits, such as classical orbital elements. For near-earth orbits, these parameters are often estimated using available extraneous information such as the natural distribution of space objects in Earth orbit. Such information is currently unavailable for the cislunar environment.
Once an orbit is initialized, subsequent tracking of a cislunar object also presents us with additional unique challenges. We first note that, as is the case with IOD in Earth orbit, the resulting initialized orbit is typically multi-modal2. Any subsequent object tracking technique must therefore be able to handle multi-modal object state uncertainties. On top of that, the cislunar environment is subject to highly nonlinear, possibly chaotic dynamical behavior. It is therefore desired to develop and implement high-fidelity nonlinear filters that can accommodate multi-modal probability distributions, chaotic bifurcations, and that are robust to modeling errors. Such algorithms need to be light-weight for onboard implementation given that communications with on-orbit cislunar sensing assets might be limited. One advanced algorithm that is capable of handling all of these challenges is the Particle Gaussian Mixture Filter (PGMF)3.
In this paper we propose to (a) extend the use of PAR that was developed for near-Earth IOD to the cislunar environment using possibly only a single short arc optical measurement, and (b) implement the PGMF for the processing of subsequent optical observations of the target in an integrated framework. This integrated PAR-PGMF solution is a rigorous initial orbit determination and filtering framework that is scalable, robust to modeling errors and large IOD uncertainties, and can handle multi-modal uncertainties and highly nonlinear and chaotic dynamical systems.
In this paper we describe in detail how the PAR and the PGMF will be used for cislunar object detection and tracking. We will demonstrate the power of this technique on multiple use cases.
References:
[1] United States Space Force. Spacepower: Doctrine for Space Forces. Nimble Books, 2020.
[2] I. Hussein, et al., Probabilistic Admissible Region for Multi-Hypothesis Filter Initialization, J. Guidance, Control and Dynamics, Vol. 41, No. 3, 2017.
[3] D. Raihan and S. Chakravorty, Particle Gaussian Mixture Filters II, Automatica, V. 98, pp. 341-348, 2018.
Date of Conference: September 27-20, 2022
Track: Cislunar SSA