General method for calculating satellite collision probability

A method of calculating the collision probability between two orbiting objects given the respective state vectors and error covariance matrices is developed. The methodology is valid for the general case and does not require simplifying assumptions. It is computationally efficient and applicable to satellites of irregular shape. Analytical techniques are used to reduce the problem to that of integrating a two-dimensional symmetric probability density over a region representing the combined hard body of the colliding objects. The symmetric form of the probability density enables the two-dimensional integral to be reduced to a one-dimensional path integral that permits easy numerical implementation and reduces computational effort. Test case results are in good agreement with those generated by other collision probability tools.