Comparison of Covariance Based Track Association Approaches Using Simulated Radar Data
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mparison of CovarianceBased Track Association Approaches Using Simulated Radar Data Keric Hill,1 Chris Sabol,2 and Kyle T. Alfriend3
Abstract When the Air Force Space Surveillance Network observes an object that does not correlate to an entry in the Space Object Catalog, it is called an Uncorrelated Track (UCT). Some of these UCTs arise from objects that are not in the Space Catalog. Before a new object can be added to the catalog, three or four UCTs must be associated so that a meaningful state can be estimated. Covariance matrices can be used to associate the UCTs in a more statistically valid and automated manner than the current labor-intensive process; however, the choice of parameters used to represent the orbit state have a large impact on the results. Covariance-based track association was performed in 10-day simulations of 1,000 space objects within a 20-km band of semimajor axis using many different orbit parameters and propagation methods and compared with a fixed position gate association method. It was found that Cartesian covariance with linearized propagation performed poorly, but when the covariance was propagated with the Unscented Transform the results were much better. Elliptical curvilinear coordinates also performed well, as did covariance in osculating equinoctial elements propagated with the Unscented Transform, but a covariance in mean equinoctial elements propagated with the Unscented Transform achieved the best results.
Introduction The Space Surveillance Network (SSN) is used to track Resident Space Objects (RSOs) in Earth orbit. An attempt is made to correlate all detections to an object in the Space Catalog. Examples of the types of correlation techniques in use are described by Schumacher and Cooper [1]. The fixed-gate track association technique has two modes, “Verify” and “Identify.” Verify mode is used when a track 1
Senior Scientist, Pacific Defense Solutions, LLC, 1300 N. Holopono St., Suite 116, Kihei, HI 96753. Research Aerospace Engineer, Air Force Maui Optical and Supercomputing, Air Force Research Laboratory, 535 Lipoa Parkway, Suite 200, Kihei, HI 96753. E-mail: [email protected]. 3 TEES Distinguished Research Chair Professor, Department of Aerospace Engineering, Texas A&M University, College Station, TS 77843-3141. 2
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has already been tagged to a catalog object, and that identification must be verified. First, the two orbit states must be compared at the same time, and rotated into the RSW coordinate system. For track to catalog correlation, the catalog is typically propagated to the time of the track. The R-axis points along the position vector of the spacecraft from the planet to the spacecraft. The S-axis is in the orbit plane, normal to the R-axis, and the W-axis is normal to the orbit plane. To verify the identity of a tagged track, the limits of allowable position deviations in RSW coordinates are DR DS DW
⫽ ⫽ ⫽
max(F, 0.003)a 5 DR 0.002a
(1)
where a is the semimajor axis in Earth radii. The term F is used for the intrack limit
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