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A fast multi-target tracking algorithm is presented for T-RN (one transmitter and N receivers) radar system in which only range-sum and velocity-sum can be observed. After preprocessing to initialize one-dimensional local track for each target, a novel hypothesis testing with velocity-sum is employed to eliminate false tracks caused by localization procedure. Then, the fusion center realizes multi-target tracking by using local track association technique instead of complex data association of "measurements-to-measurements" and "measurements-to-track". Compared with centralized tracking methods, this algorithm is much easier and simpler to apply in engineering, so is suitable for real-time applications.