# Probability of collision (satellites)

In collaboration with **R. Serra**, **D. Arzelier, M. Joldès, A. Rondepierre and B. Salvy ** we have provided in

**Serra R., Arzelier D., Joldes M., Lasserre J.B., Rondepierre A., Salvy B. (2016)**Fast and Accurate Computation of Orbital Collision Probability for Short-Term Encounters,*J. Guidance, Control & Dynamics 39*pp. 1--13.

an algorithm that computes the **probability of collision** between satellites in orbit. After a proper modeling, it reduces to compute the (non-centered) gaussian measure of some sphere, the scientific challenge being to provide quickly an accurate upper bound on this probability. To do so we proceed in two steps : (i) we provide an explicit expression of the Laplace transform of the probability as a function of the radius of the sphere, and then (ii) with an appropriate pre-conditionning we invert this Laplace transform to obtain a convergent series (with only positive terms) hence with arbitrary precision when increaing the number of terme in the series. This algorithm has been implemented and tested on board of the ESOC OPS-SAT 3-Units-CubeSat satellite via the ASTRIA software of the french spatial agency CNES