Sean O’Neil, MITRE
Keywords: Cislunar SSA, Target Custody, Data Fusion, Performance Predicition
Abstract:
One of the primary goals of space surveillance is the establishment and maintenance of custody on resident space objects (RSOs) in orbit. For an RSO, custody at any point in time can be defined as a combination of two attributeslocalization of an object with sufficient accuracy and compactness that additional metric data could be gathered on it with minimal ambiguity with the sensors the user has at their disposal, along with a sufficient degree of confidence in the unique label, such as a catalog or track number, that was applied to that RSO when its orbit was first estimated. Degradation of either metric accuracy or confidence in the label results in loss of custody.
Given the importance of the goal of custody, it would be useful to be able to predict the ability of a given set of sensors to maintain said custody against various types of space objects, and in varying regimes. While there is not yet a well-established method of doing this, we propose an approach to try and fill this need, at least partially. Our approach is based on using a recently-proposed modification of the Mori et al. [1] formula for the probability of correct association (Pca) when tracking an object with a fixed-revisit sensor. The modification provides two key extensions to the formula given in [1]it provides a more realistic and more dynamic estimate of the Pca for specific scenario realizations, and it explicitly provides for updating of the label confidence on an object. This latter capability includes an ability to predict the impact not only of the cadence/quality/gaps of metric obs on label confidence, but also the impact of so-called feature (i.e. non-kinematic) data, such as apparent brightness, fluctuations, spectral information, RF emissions, or other measurements of the object that arent directly dependent on position or velocity on said label confidence.
We applied this approach to a problem of interest, maintaining custody on an object in a cislunar orbit. For simplicity, we assumed we are operating in a Circular Restricted 3-Body environment, meaning the Earth and Moon are treated as point masses with circular orbits about their center of mass. Similarly, inasmuch as orbits in the cislunar domain may come from a bewildering variety of periodic, quasi-periodic, and chaotic classes, so we chose a small set of periodic/quasi-periodic orbits to examine. In addition, we restraicted our sensor network to consist of a constellation of identical space-based telescopes in a Lyapunov-type Earth-Moon planar orbit around L1, L2, or L3, and choose planar and non-planar RSO orbits around those same Lagrange points to analyze custody performance.
Our first pass of analysis examined, for a given constellation type and RSO orbit, the impact of a) the number of sensors, b) their metric accuracy, c) their FOV and revisit rate, as well as external environmental factors such as d) the predictability of the orbit, and e) the density of potential confusing RSOs. This was to establish basic custody performance when only metric obs are available. In general, we find that while custody performance improves as a), b), and c) improve, the largest impacts are readily seen from changes in d) (orbit predictability), and e) the density of potential confusing RSOs. A potentially useful finding is that the view angle of telescopes relative to the cislunar population can matter quite a bit depending on certain assumptions. In general, and under certain sensitivity assumptions, custody performance can improve quite significantly if the cislunar objects are being viewed such that other RSO populations (i.e. LEO/MEO/GEO) are not present in the viewing cone. This factor seems to account for much of the difference between proposed telescope constellations.
Our second pass of analysis added a hypothetical multi-spectral capability to add feature information, which we parameterize through a confusion matrix against a generic set of objects. We find that, in general, such feature information can dramatically improve custody performance, primarily since it allows for the regaining of lost custody by increasing the confidence of a given target label, something that is not possible with metric obs alone.
We conclude by noting that while this analysis is only preliminary, the main intention is to establish a methodology for estimating custody performance for space situational awareness, and we note several avenues for future work to improve and refine these results.
[1] S. Mori,K.-C. Chang, C.-Y. Chong, and K.-P. Dunn, “Prediction of Track Purity and Tkack Accuracy in Dense Target Environments”, IEEE Trans On Automatic Control, Vol.40, no. 5, May 1995, pp. 953-959
Date of Conference: September 19-22, 2023
Track: Cislunar SDA