Report

Determining & Evaluating High Risk Conjunction Events Improving Space Operations Workshop Boulder, CO 5 – 6 April 2011 Introduction • • • • • • • Conjunction Assessment Process Collision Probability Sigma Level Analysis Alignment of Radial Vectors Collision Probability Sensitivity Maximum Collision Probability High Risk Events Conjunction Assessment Process (1/2) • Conjunction assessment is performed based on state and state uncertainty data generated and disseminated by the JSpOC. • Close approach predictions are generated based on a 5-day screening span. • Results are sent out daily, or more frequently for high risk conjunction events. • Predictions are made using data from the JSpOC highaccuracy space object catalog. Conjunction Assessment Process (2/2) • The typical conjunction assessment process for a satellite program is to receive Orbital Conjunction Messages (OCMs) for secondary objects that are predicted to violate a designated screening volume around the primary satellite. • OCMs contain sufficient data to calculate a Pc value; i.e., state vector and state uncertainty data. • The screening volume must be large enough to capture close approaches with objects with a wide range of covariance sizes—this can result in large amounts of data and many conjunction events that are not a threat. Collision Probability (1/2) • Collision probability (Pc) is a measure of the overlap of the error distribution of the two objects, where the error distribution is given by the covariance matrix. • When the covariances of the objects are combined, Pc can be thought of as the relationship of the miss vector to the combined covariance. Primary & Secondary object with covariance ellipsoids Combined covariance with keep-out region positioned by miss vector Collision Probability (2/2) • Pc is used as the primary measure of risk since it captures the miss distance, the relative geometry, and the associated uncertainty of the close approach. • A conjunction assessment process based on miss distance alone does not account for the uncertainty inherent in the problem. • Miss distance is used as the basis of the screening process, leading to the receipt of many OCMs for conjunction events with zero Pc values. • This approach can lead to large amounts of data; especially for satellites in LEO. Sigma Level Analysis (1/2) • The miss vector and the state uncertainty of the two objects can be used for a streamlined screening process. • The sigma level can be calculated using the Radial, Intrack, and Crosstrack (RIC) directions of the primary. = + − = where ≡ 2 + + 2 = + and ≡ • OCMs are not required for these calculations. Sigma Level Analysis (2/2) • The two semi-major axes equal the largest possible in-plane uncertainty component, + ; and the semi-minor axis equals the sum of the radial uncertainties, + . • A high sigma level from either calculation should result in a near zero Pc value, but a low sigma level does not necessarily lead to a high Pc value. • A sigma level > 4 is recommended. Sigma Level Analysis Results • Sample report of data required: Predicted Miss Distances Primary Error at TCA Secondary Error at TCA Total Radial Intrack Crosstrack Radial Intrack Crosstrack Radial Intrack Crosstrack • Sample results with corresponding collision probability: Case Radial Sigma Level In-plane Sigma Level Collision Probability 1 2.29 0.35 7.78e-5 2 1.13 3.42 5.18e-9 3 -9.29 0.05 0 4 0.84 0.36 1.18e-3 5 4.17 0.09 4.74e-012 Alignment of Radial Vectors = 2 + 2 Since ≫ for tangible conjunction events, is small and the two Radial unit vectors can be considered collinear for the purposes of this analysis. ≡ & = arc ≡ • The Radial unit vectors of the two objects nearly align for conjunction events, therefore, the Radial direction can be decoupled from the Intrack and Crosstrack directions. Earth center Collision Probability Sensitivity log Pc • Covariance size can be scaled to determine the sensitivity of the Pc value. • Since covariance is propagated from OD epoch to Time of Close Approach (TCA), a Collision Probability Sensitivity -4 reduction in covariance size gives an indication of how -5 the Pc will evolve. -6 • This calculation is -7 performed with a static -8 miss distance. -9 -10 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Normalized Covariance Size 0.9 1 Maximum Collision Probability Normalized Covariance Size 12 10 8 6 4 2 0 4 Sigma Level log Pc • The Pc sensitivity curve allows evaluation of the Pc max condition. • Pc max tends to occur when the miss vector lies on the 1-sigma uncertainty ellipsoid. Collision Probability Sensitivity -2 • Most conjunction events -3 evolve to the left of the -4 Pc max condition. Pc . -5 Radial Sigma Level • Those that don’t tend to -6 In-plane Sigma Level be of concern … -7 • Notice that in this example -8 the covariance was enlarged -9 to show Pc max. -10 0 0.5 1 1.5 2 2.5 3 3.5 log Pc • Some conjunction events show little change in Pc as the covariance is contracted. • This occurs when the miss vector is within the 1 or 2-sigma of the combined covariance Collision Probability Sensitivity -2.5 2.5 ellipsoid. 2 • This condition can be a sign Pc . Radial Sigma Level that the conjunction event -3 In-plane Sigma Level 1.5 will remain a threat as the TCA approaches. 1 -3.5 0.5 -4 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Normalized Covariance Size 0.9 0 1 Sigma Level High Risk Events