Probabilistic Estimation of Rare Random Collisions in 3 Space

A study of risk assessment for artillery re randomly colliding with xed wing aircraft is presented. The research lends itself to a general study of collision models. Current models of object collisions fall under one of three categories: the historical model, the gas particle model, and the satellite model. These three vary in data requirements and mathematical representation of the impact event. The gas particle model is selected for its flexibility and robust estimation. However, current mathematical development in the literature does not include certain spatial and dynamic components necessary for a general encounter (collision) model. These are derived in this work. For the speci c application at hand Quadratic formulas estimate the ballistic arc of artillery shells to provide instantaneous relative velocities. An extended Poisson spatial process is applied over the relative volume within a collision radius during the conflict time window to provide a probability of collision. Implementation of the model for military use has been achieved via an Excel spreadsheet providing scenario study capability in real time. Results for several scenarios are presented which have been validated by experts. These results support current policy of strict deconfliction.