Erin Griggs, Trusted Space, Inc.; Matt Schierholtz, Trusted Space, Inc; Islam Hussein, Trusted Space, Inc.; Mark Bolden, Trusted Space, Inc.; Kyle Charles, Trusted Space, Inc.; Holly Borowski, Trusted Space
Keywords: Cislunar SSA, Cislunar IOD, Cislunar OD, Passive RF Data, Data Fusion
Abstract:
The Cislunar domain is the ultimate high ground above earth; securing and protecting that domain 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 (IOD) for newly discovered objects or recovered lost objects, and for tracking objects after orbit initialization. In this paper, we look at these challenges in the context of both purely passive Radio Frequency (RF) observation scenarios and combined passive RF and optical observation scenarios.
Because of the colossal distances of the Cislunar environment, multiple observations of an object over time effectively act as a single observation as the object moves very slowly with respect to the observer. To rapidly generate an uncertain trajectory for object tracking, high-fidelity probabilistic 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, transmit frequency band) 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 multi-body gravitational dynamic 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 build on the work we presented at the 2022 AMOS Conference4. In that work we focused on the processing of optical observations in Cislunar space. Specifically, we (a) extended 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) implemented the PGMF for the processing of subsequent optical observations of the target in an integrated framework. This integrated PAR-PGMF solution was shown to be a rigorous initial orbit determination and filtering framework that is scalable, robust to modeling errors and large IOD uncertainties, and to be able to handle multi-modal uncertainties and highly nonlinear and chaotic dynamical systems.
In this paper, we shift our attention to passive RF observations. We will focus on Time Delay of Arrival (TDOA) and Doppler measurement types. Specifically, given an uncertain initial orbit using the PAR technique, we will use the PGMF to process subsequent passive RF observations of the target for orbit determination. Moreover, we will explore scenarios where optical data of the target is also available. We will study the performance of the PAR-PGMF framework under two alternative scenarios: (a) only passive RF data is used to perform PGMF orbit determination, and (b) optical and passive RF data are fused to perform PGMF orbit determination. In both of these scenarios, we will use electro-optical data to perform the PAR orbit initialization. We will compare the performances from these two scenarios against the optical-only scenario from our AMOS 2022 paper results. While we anticipate improved PAR-PGMF IOD and OD performance with the inclusion of RF data, we will also assess the degree of improvement that RF data adds to ingestion of optical data only.
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.
[4] M. Bolden, I. Hussein, H. Borowski, R. See, and E. Griggs, Probabilistic Initial Orbit Determination and Object Tracking in Cislunar Space Using Passive RF Sensors, AMOS, Maui, HI, September 2022.
Date of Conference: September 19-22, 2023
Track: Cislunar SDA