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In this paper, a predictive guidance algorithm is developed for a spin-stabilized hit-to-kill guided projectile. The projectile is used as an interceptor against rockets, mortar, and artillery. Guidance is based on a new rapid trajectory prediction algorithm for projectiles fired at high quadrant elevations. The interceptor uses lateral pulse jets located near the mass center for control. High spin rates require additional guidance compensation for gyroscopic effects when compared to a fin-stabilized projectile. The probability of kill (PK) is evaluated based on typical gun pointing errors, roll angle uncertainty, and target acquisition errors. It is shown that guided interceptors can achieve a 90% PK by using as few as 5 projectiles in the presence of roll, gun pointing, and target errors. It is also shown that, despite sensitivity to errors in gun pointing and target errors, the predictive guidance system is able to achieve an acceptable PK. For a spin-stabilized interceptor, estimated-roll orientation errors may become large. Simulations are performed for errors in the estimated roll, and it is demonstrated that roll does not need to be precisely known for a successful interception.