Space target collision risk analysis algorithm based on the square Mahalanobis distance

A collision risk assessment method based on the square Mahalanobis distance was proposed to increase the reliability of collision risk prediction results in order to address the issue that probability dilution in space target collision risk prediction reduces the reliability of collision probability. Firstly, the threshold of the square Mahalanobis distance was obtained according to the $3\sigma$ rule to determine whether an event has collision risk. Then, the factors such as combined hard-body radius, position error, the aspect ratio of the error ellipse, and the rotation angle were modeled and analyzed, and the model parameters of the square Mahalanobis distance were optimized to improve the computational efficiency. Finally, a collision risk prediction and evaluation model based on the square Mahalanobis distance was developed to solve the probability dilution problem. The outcome of the simulation demonstrates that the suggested approach can successfully lower the high-risk event missed detection rate.