Decision-making in Space Object Collision Avoidance aiming Optimal Cost Function

For space debris larger than 10cm in diameter, it is usually necessary to carry out an evasive maneuver. The traditional collision probability method has high probability of false or missing alarms and is difficult to coach the decision-making directly. A new decision method of the collision between spacecraft and debris is introduced with their spatial knowledge and tolerability. The complex spatial position error probability distribution is given in the rotated encounter coordinate system. For the cases of cost function known and constant false alarm probability, the minimax criterion and the N-P criterion are introduced respectively. The decision threshold and detection performance are given as well. The data of two examples of spacecraft collision events in history are used to verify the algorithm and the theoretical requirement for evasive performance is satisfied.