Daniel Mulligan, Science Applications International Corporation; Michelle Stephens, Science Applications International Corporation
Keywords: Space Domain Awareness, Space Situational Awareness, Search Patterns, Leakproof, Optical, Radar, Acquisition, Tracking, Monte Carlo
Abstract:
Space domain awareness (SDA) involves detecting, tracking, identifying, and cataloging some thirty thousand known satellites or debris, a number which is only growing. Maintaining custody of each object requires tasking a sensor to look for it at its predicted position, and updating the existing state and uncertainty estimate to account for this new observation. For well-behaved, predictable objects, occasional observations are sufficient, since the objects are likely where we expect them to be. For less well-behaved, maneuverable, or potentially malicious RSOs, however, it is more likely that the objects wont be where they are expected, and a search pattern may need to be implemented. A search pattern covers some defined area or volume of space by moving the boresight and field of view (FOV) of a sensor, with the aim of observing known (or finding previously unknown) objects.
Most search patterns, like a simple raster scan, are designed to cover the uncertainty area of an object, preferably quickly and without gaps between the FOVs. However, even without gaps, a pattern is not guaranteed to find the RSO. An RSO could potentially move from an unsearched area into a previously searched area, evading detection. This could create a harmful scenario in which sensor operators believe they have confirmed that the object was not within the searched area when, in fact, it was. Leakproof search patterns prevent such scenarios. A search pattern is leakproof if it is certain, based on kinematics, that an RSO will be detected if it is within the searched area. For high priority objects, especially those with poor position estimates or high maneuverability, leakproof searches provide valuable assurance that an observation will be made.
We present a novel search pattern, the bullseye, which guarantees leakproof detection of an RSO maneuvering in any direction, provided it is within a particular angular radius when the search begins. While spiral or other circular search patterns are occasionally seen in the literature, to our knowledge, there has been no attempt to quantify the extent to which they are leakproof, or provide a precise method for determining actual sensor boresight vectors that comprise the pattern. At least one other proven leakproof pattern, the bowtie, does exist, but it is more suited to a low-earth (LEO) regime, places constraints on the RSOs heading, and requires the RSO to cross the search fence, which may take a long time depending on its angular rate. While the bullseye pattern can be used in any orbital regime, it is particularly suited to the geostationary (GEO) and super-GEO regimes, due to its geometry, the assumption that the RSO can maneuver in any direction, and the RSOs comparatively smaller angular velocities.
The bullseye search is made up of concentric rings of discrete dwells. The spacing between the rings, as well as the number of dwells in each ring, is optimized to yield the largest possible leakproof area. The bullseye will catch the RSO if it is moving in any direction, but the most stressing cases are when the RSO moves radially towards or away from the center of the bullseye. The radius of each ring is subject to constraints defined by these cases. It must overlap enough with the previous ring to capture an inward-moving RSO while also reaching out far enough to catch an outward-moving RSO. We show a method for calculating the ideal radius of each ring and the boresight vectors for each individual dwell.
We use intuitive kinematic arguments to establish the leak-proof nature of the bullseye, and derive the leakproof radius. This angular radius is determined by simple system parameters, including the expected maximum angular rate at which the RSO can move across the sensors Field of Regard (FOR), the size of the sensors FOV, and the sensors slew speed. We then show the results of a Monte Carlo (MC) simulation validating the leakproof constraints, and discuss the contexts in which implementation of the bullseye may be advantageous with a focus on the trade between detection certainty and sensor use. The bullseye can provide valuable certainty when maintaining custody of high priority RSOs.
Date of Conference: September 27-20, 2022
Track: SSA/SDA