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In the boost phase, it is important to early detect and classify an enemy ballistic missile for a swift defense response. These tasks can be typically achieved by search radar which is generally operated at a low data gathering rate of 6 and 12rpm. Moreover, detection altitude is limited by the elevation angle of an antenna. For these reasons, the number of radar measurement is about only 10 to 20 until the ballistic missile in the ascent phase reaches to the maximum detection altitude of the search radar. Such a low data update rate makes detection and classification of a ballistic missile difficult. But, fortunately, a ballistic missile has special features that make it distinguish from other aerial vehicles. In this paper, contrary to general algorithm using the characteristics of the radar signal, we suggest an algorithm using the dynamic characteristics of a ballistic missile for a detection and classification of a ballistic missile in ascent phase.