Patrick B. Miga, University of Colorado Boulder; Marcus J. Holzinger, University of Colorado Boulder
Keywords: Cislunar, Space, Situational, Domain, Awareness, SSA, SDA, Astrodynamics, Information
Abstract:
An analytical approach for finding instantaneous information gain is found in a general form but applied to cislunar space domain awareness (SDA). Optimal information gain is equivalent to optimal uncertainty reduction and is a fundamental performance driver of initial orbit determination, catalog quality, and architecture design, particularly for the cislunar regime. Recently, there has been massive interest in the cislunar regime because of plans to return to the moon. The goal of this research effort is to inform the best utilization of observer satellites in cislunar orbit by providing a methodology for the selection of the observer satellite orbit as well as governing which target satellite to observe at a given time. In the future, when there are many satellites in the cislunar regime, a precise understanding of these satellites’ states will be necessary for national security and space traffic management reasons. This research effort seeks to understand the optimal way of doing this with minimal resources.The Fisher Information Matrix is investigated over the course of a measurement sequence, or two measurements with some time horizon between them. This matrix is expanded into an analytical expression that is a function of the magnitude of relative position, the magnitude of relative velocity, the angle between relative position and velocity, observation length, time between observations, and measurement uncertainty. Simplifying assumptions are made that are still applicable to a variety of scenarios, an argument is made to justify that only the trace is needed, and this expression is reduced into two simplified equations: the position information trace and the velocity information trace. Because the covariance matrix is the inverse of the information matrix, when these trace equations are maximized, uncertainties are minimized. These equations show that maximizing relative velocity and minimizing relative position, among other things, will lead to a reduction in uncertainty. Additionally, these equations are derived independently of dynamics, and are not just applicable to cislunar space, but any situation in which there is a target and observer in a situation that follows the assumptions made.Final simulations to verify these equations show agreement with information gain, position and velocity uncertainties, and relative geometry. These equations can help inform selection of orbits for mission design relevant to cislunar SDA. An expected outcome of future work is to provide an understanding of which cislunar periodic orbits are an ideal orbit to place observer satellites as well as providing some fundamental truths as to when to focus the observing satellite’s attention on a specific target satellite.
Date of Conference: September 27-20, 2022
Track: Cislunar SSA