PROBABILITY OF COLLISION ERROR ANALYSIS KYLE T. ALFRIEND 1 , MARUTHI R. AKELLA 2 , JOSEPH FRISBEE 3 , JAMES L. FOSTER 4 , DEOK-JIN LEE 2 AND MATTHEW WILKINS 2 1 Professor and Head, Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141, USA (E-mail: alfriend@aero.tamu.edu); 2 Assistant Professor, Department of Aerospace Engineering, University of Texas Austin, Austin, TX 78712, USA; 3 United Space Alliance, 600 Gemini, Houston, TX 77058-2783, USA; 4 Barrios Corporation, 1331 Gemini, Houston, TX 77058-2711, USA (Received 2 October 1998; Accepted 12 May 1999) Abstract. The decision for the International Space Station (ISS) to maneuver to avoid a potential collision with another space object will be based on the probability of collision, P C . The calculation of P C requires the covariance of both objects at conjunction. It is well known that the covariance computed by US Space Command is optimistic (too small), especially at altitudes where atmospheric drag is the dominant perturba- tion, because its computation assumes there are no dynamic model errors. In this paper the effect of errors in the covariance on P C and the sensitivity of P C to the encounter geometry are investigated. Keywords: covariance, probability of collision, collision avoidance Nomenclature Subscripts s – refers to the ISS d – refers to another space object, debris o – refers to values at estimated conjunction Variables P C – probability of collision P – covariance A – matrix of partial derivatives of the measurements with respect to the initial state  r,  v – position and velocity  v r – relative velocity,  v d − v s  ρ – relative position vector,  r d − r s  s – relative position vector in the conjunction plane  e – uncertainty vector β – angle between ISS and debris orbit planes d – horizontal plane separation distance at conjunction h – radial separation distance at conjunction L – ISS distance from orbit plane intersection at conjunction R – radius of the sphere around the ISS that defines collision, called collision sphere Space Debris 1, 21–35, 1999. © 2000 Kluwer Academic Publishers. Printed in the Netherlands.