Space Object Collision Detection Based on Derived Bayesian Criterion

For space debris larger than 10cm in diameter, it is usually necessary to carry out an evasive protection. The traditional collision probability method has the high probability of false or missing alarms and is difficult to guide the decision-making directly. This paper proposes a decision that whether the spacecraft and the debris collide with each other with their spatial position knowledge, that is, both the center of the probability and the error distribution of the spatial position. The complex spatial position error probability distribution function 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, and the decision threshold and detection performance are given. The data of two examples of spacecraft collision events in history are used to verify the algorithm and the theoretical requirements for early warning of avoidance decisions are satisfied.