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An effective collision avoidance system for unmanned aircraft will enable them to fly in civil airspace and greatly expand their applications. One promising approach is to model aircraft collision avoidance as a partially observable Markov decision process (POMDP) and automatically generate the threat resolution logic for the collision avoidance system by solving the POMDP model. However, existing discrete-state POMDP algorithms cannot cope with the high-dimensional state space in collision avoidance POMDPs. Using a recently developed algorithm called Monte Carlo Value Iteration (MCVI), we constructed several continuous-state POMDP models and solved them directly, without discretizing the state space. Simulation results show that our 3-D continuous-state models reduce the collision risk by up to 70 times, compared with earlier 2-D discrete-state POMDP models. The success demonstrates both the benefits of continuous-state POMDP models for collision avoidance systems and the latest algorithmic progress in solving these complex models.