A Determination and Reduction of Collision Probability for Satellites Using a Metalog Distribution

The increasing levels of space debris in Earth's orbit require more accurate and efficient methods for estimating satellite collision probabilities to ensure reliable operations. Monte Carlo analysis remains a widely adopted approach due to its robustness, but its high computational cost is a limiting factor. This work introduces a methodology to increase efficiency by obtaining the probability estimation from a flexible metalog distribution that has been fitted to the Monte Carlo data. By fitting the metalog distribution to Monte Carlo sampling results, a continuous representation of collision probability is generated, allowing the probability estimation to be evaluated with a significantly reduced number of iterations. With this estimation, an optimized avoidance maneuver is calculated to reduce the probability of collision by targeting a user-specified miss distance with an in-plane burn. The results of this study demonstrate a reduction in computational demands associated with Monte Carlo methods and the feasibility of decreasing the probability of satellite collisions using a fuel-optimized avoidance burn. This combination of computational efficiency and maneuver planning provides a powerful approach to mitigating collision risks in increasingly congested orbital environments.