Abstract
A method for the computation of the probability of collision between two space object is pre- sent.ed. The method is based on the Taylor expansion of the time of close approach (TCA) and distance of close approach (DCA) of the two orbiting objects. These quantities are computed during the conjunction detection phase by means of a global optimizer based on Differential Al-gebra, which is implemented in the language COSY-lnfinity. When a close approach is identified, TCA and DC A nominal values are computed. Subsequently, analytical expansions with respect to uncertainties in the initial states are obtained by means of Differential Algebra. The collision probability is then computed via Monte Carlo simulation, sampling values of initial position and velocity according to their estimated uncertainties. The newr value of DCA for the couple of virtual objects is computed evaluating its Taylor polynomial, using the sampled deviations from the nominal initial state. The minimum distance is then compared with the collision threshold, that is the diameter of the sphere that envelopes the two spacecraft. To improve the efficiency and accuracy of the method advanced Monte Carlo Markov Chain techniques are employed. The presented test cases considers conjunctions occurring in LEO, MEO and GEO. For each test case the collision probabilities are computed with both standard and advanced Monte Carlo methods. The computed probabilities and the associated computational times are then compared. The method is suitable for a wide range of orbits since no simplifications of the conjunction event are made, hence it can be applied to geosynchronous orbits, where relative velocity is lower. The effects of main orbital perturbations are accounted for in the computation of the relative distance.