A method for determining the maneuver required by a space vehicle to reduce its collision probability with another tracked object below a predefined threshold was developed. The methodology employs efficient computational schemes for computing collision probability, propagating space vehicles, and three-dimensional root finding. The collision probability calculation was improved by reducing a two-dimensional integral to a one-dimensional integral, thereby realizing a significant reduction in computational effort. In addition, a method to circumvent high-fidelity propagation of the space objects from the time of the maneuver to the time of closest approach was found. The method essentially replaces high-fidelity propagation. with simple two-body Keplerian propagation. A gradient technique is used to,find the maneuver direction. The maneuver magnitude is found using a one-dimensional root finding scheme that takes advantage of the linear relationship between the maneuver velocity and resulting displacement. The method was applied to an actual case involving two geostationary satellites whose collision probability was unacceptably high. For various times before closest approach, the maneuver required to reduce the collision probability below a required threshold was found and provided to satellite operators. X maneuver time was selected and the associated maneuver was executed by satellite operators. Postmaneuver tracking of the satellites indicated that the maneuver worked as planned and reduced the collision probability to the desired level. References: 12
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