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In this paper, a multiple hypotheses tracking (MHT) algorithm is developed to successfully track multiple ballistic missiles. A framework is developed for the MHT, which includes a linear assignment problem approach used to search the measurement-to-contact association matrix for the set of exact i-best feasible hypotheses. A hypothetical scenario in which multiple ballistic missiles have been launched and threaten the North American continent is considered as a test case for this MHT algorithm. To aid in the interception and destruction of the threat far from their intended targets, the research focuses on the boost-phase portion of the missile-flight. The near-simultaneous attacks are detected by a network of radar sensors positioned near the missile launch sites. Each sensor provides position reports or track files for the MHT routine to process. The results show that this new algorithm works well in a realistic-environment where complex interactions of missile staging, non-linear thrust profiles and sensor noise can significantly degrade the track algorithm performance especially in multiple target scenarios.