Ryan Shepperd, Iridium; William Boyce III, Iridium
Keywords: Mean element sets, collision assessment, collision mitigation solution space
Abstract:
Mean Element sets, as an averaging of short periodic or long periodic terms, may seem ill suited for the topic of collision assessment. Afterall, the exact position of a satellite at the time of closest approach is the desired knowledge–not an average. However, certain applications of mean elements prove useful in both short- and long-term collision assessment and mitigation applications. These range from long-term assessments of constellation control boxes, covariance propagation, Monte Carlo probability of collision calculation, and prominently the efficient construction of collision mitigation solution spaces.
The Iridium constellation’s experience with mean elements dates from its inception. The constellation itself was defined as a combination of short period and long period mean elements with an epoch of June 1, 1996. The guidance targets from that epoch for each constellation slot still define the constellation today 29 years later. In that time, Iridium operations came to appreciate the many nuances of the types and flavors of mean elements, from those available for use, to the types of short period, long period, and with precession and nutation terms.
The two foremost advantages of mean elements are the visualizable description of an orbit state and the ability to analytically or efficiently propagate that state. For the first, mean elements overcome the obstacle of cartesian state vectors, for which the full shape of the orbit is mentally difficult to appreciate, or osculating elements, which instantaneously fit 6 classical or other natural elements to the true motion of a satellite perturbed by forces beyond 2-body motion. By averaging short and/or long periodicities, mean elements better describe the motion through time as a simple single snapshot in time. For the second, efficient propagation is aided by aligning non-conservative perturbing forces such as atmospheric drag and maneuvers both with specific elements as well as a description of those elements that is constant or linear without the perturbing forces.
Such efficient analytic propagation is the quintessential use in collision assessment. Iridium has long operated at an unfortunate peak in debris density and at an altitude where solar activity is slow to remove debris that accumulates. In this environment, not only is the aggregate probability of collision important but mitigation maneuvers are more likely to encounter other debris if not accounted for in the planning. Operators have traditionally built solution space plots of maneuver size as a function of collision probability. The degree of fidelity can range from first-order analytic estimates to full numeric propagation of each maneuver option within the extent of the solution space considered. The latter is expensive. Although modern hardware and data services can handle it to some extent such as the Office of Space Commerce is planning for TraCSS with candidate maneuvers, such brute force can be unnecessary and perhaps undesirable, particularly in the Iridium case of examining up to half a million possibilities for each vehicle.
Instead, Iridium builds the solution space with mean elements and only submits those maneuvers to the service provider that pass initial scrutiny. Higher fidelity is preserved by using a single numerically propagated ephemerides as a reference about which changes to the mean elements are applied and propagated. Tied to the reference, those propagated states with covariance are then efficiently brought back to cartesian states for probability of collision by methods such as Elrod’s, which balances accuracy with efficiency. This methodology has proven accurate enough to trust commanding execution of a maneuver without a blocking requirement that the screening provider finishes processing that chosen maneuver. Contrary to the perception that too many Conjunction Data Messages represent false alarms rather than data, the importance of a large unfiltered screening volume to proactively lower the aggregate probability of collision will be shown in this application of mean elements.
Iridium’s long experience of using mean elements for short-term and long-term constellation monitoring and maintenance expanded to useful applications in collision assessment. Such usage of mean elements will be explained and demonstrated along with the achievable performance.
Date of Conference: September 16-19, 2025
Track: Conjunction/RPO