Inkwan Park, LeoLabs; Matthew Stevenson, LeoLabs; Michael Nicolls, LeoLabs; Edward Lu, LeoLabs; Nathan Griffith, LeoLabs, Inc.; Chris Rosner, LeoLabs, Inc.;
Keywords: Covariance Realism, Reliability, Overlap Analysis, Low Earth Orbit Object, Reliability
Abstract:
As low-Earth orbit (LEO) becomes increasingly congested, more accurate and reliable information is required to protect space objects from potential threats, such as satellite-satellite or satellite-debris collisions. In particular, state covariance information is needed as the basis for satellite operators to make decisions regarding whether to maneuver space assets to avoid potential collisions. For that reason, the accuracy of the covariance and its propagation, called covariance realism, becomes a critical factor.
In this work, we verify LeoLabs’ covariance realism and investigate applicable approaches to improve reliability. To confirm the accuracy of the propagated covariance, we compare the distance between propagated states with different estimation epochs in a so-called overlap analysis, checking to see if the new states are consistent with the covariance determined at a previous time. Mahalanobis distance is introduced to assess if the new states are successfully captured by the propagated covariance. We also investigate applicable metrics by analyzing data accumulated from LeoLabs database for monitoring covariance realism, enabling us to recognize inconsistencies in calculated data.
We address the question “How consistently does the propagated covariance capture a new estimated state?” Due to the time gap between observations, it is necessary to propagate covariance until new measurements are obtained. To verify the consistency, we analyze if newly estimated states are located inside an anticipated region based on the Mahalanobis distance; if the states are consistent, the collected distances will be bounded throughout a propagation interval. We calculate the distances between the propagated trajectories of all overlapping states within a specific time window, using a 7-day propagation time to match the typical time period of Conjunction Data Messages prior to closest approach.
In this study, we demonstrate the results from the overlap test to show the consistency with which LeoLabs propagates covariance. The performance of LeoLabs current covariance propagation is demonstrated with case studies and a containment analysis which shows what proportion of the results from the overlap test exist within a predicted region. Then, to increase reliability, we focus on defining applicable metrics to monitor inconsistency. A two-step approach is introduced: 1) investigate the overlap test results to see if they follow a specific distribution of random variables, and 2) characterize the distribution of the test results. Throughout these steps, we search for useful statistical metrics to capture inconsistent events.
In summary, we present the covariance realism of LeoLabs data and some approaches to improve its reliability. The verification of this covariance realism is carried out by confirming how well the distribution of the Mahalanobis distances from the overlap test is bounded. To improve the reliability of data, we characterize LeoLabs covariance propagation algorithm and define statistical metrics for monitoring inconsistency in propagated covariance.
Date of Conference: September 17-20, 2019
Track: Astrodynamics