Matthew Stevenson, LeoLabs; Michael Nicolls, LeoLabs; Chris Rosner, LeoLabs, Inc.
Keywords: Attitude Stability, Low Earth Orbit, Radar Cross Section, Statistical Analysis, Leolabs, Data Service
Abstract:
We present a new method for estimating the attitude stability of low-Earth resident space objects (RSOs) using radar cross-section (RCS) statistics from LeoLabs global radar network. We show that, assuming a non-isotropic object shape, an Earth-oriented RSO will have an elevation-angle dependent RCS when viewed from a ground-based radar. We describe our algorithm for automatically classifying the attitude stability states of RSOs and the method used to tune this algorithm (with particular focus on the resulting false-positive and false-negative rates). We provide several illustrative examples using data from LeoLabs’ Midland Space Radar.
This method has applications for interpreting the stability of RSOs, and its outputs can be used for advanced object and mission classification. Examples of applications include: determining if an individual RSO is attitude stabilized and detecting changes in that attitude stabilization; measuring the attitude stability characteristics of satellite constellations; identifying individual RSOs that do not conform to the attitude stability characteristics of their constellation; categorizing unlabeled RSOs into groups with similar attitude dynamics properties; studying the attitude stability characteristics of uncontrolled RSOs, such as retired satellites, rocket upper stages, and debris.
The method requires the construction of a metric that quantifies the difference between the average RCS of an RSO when viewed at high elevation vs. low elevation. The RCS of a complex, spatially unresolved object is highly sensitive to viewing angle, so we treat the RCS measurements as values drawn from a probability distribution. The metric is designed to isolate differences in the probability distributions at different viewing elevations. We present statistical analysis validating this approach using historical data from the LeoLabs data archive.
The underlying algorithm involves comparing the metric to significance thresholds, and those thresholds are carefully tuned. In the absence of a sufficiently large ground-truth data set, we use Monte Carlo simulations to tune these parameters. The Monte Carlo simulations are built on statistical analysis of the LeoLabs data archive, and they account for both the inherent RCS distributions of the RSOs and the measurement uncertainty of LeoLabs’ radar facilities. The results of these Monte Carlo simulations are robust thresholds for our RCS metric with well-understood false-positive and false-negative rates.
The algorithm also makes use of hysteresis in order to suppress spurious detections of changes in attitude stability due to the probabilistic nature of the metric. The hysteresis is achieved by requiring the metric to cross the Monte Carlo-tuned thresholds for a specified period of time before declaring a change in the RSO stability state. The hysteresis time is similarly tuned via additional Monte Carlo simulations. This tuning is constrained by the desired false-positive rate of the system, and it allows us to characterize the expected time latency in detecting significant changes in an RSOs stability state.
It is thus possible to measure and automatically characterize the stabilization properties of RSOs and satellite constellations using RCS statistics. We demonstrate this technique on several satellites using measurements from LeoLabs’ Midland Space Radar, and we note that this metric will continue to increase in sensitivity as LeoLabs expands its global radar network.
Date of Conference: September 17-20, 2019
Track: Non-Resolved Object Characterization