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The basic "current" statistical model and adaptive Kalman filter algorithm can not track a weakly maneuvering target precisely, though it has good estimate accuracy for strongly maneuvering target. In order to solve this problem, a novel nonlinear fuzzy membership function was presented to adjust the upper and lower limit of target acceleration adaptive-ly, and then the validity of the new algorithm for feeblish maneuvering target was proved in theory. At last, the computer simulation experiments indicated that the new algorithm has a great advantage over the basic "current" statistical model and adaptive algorithm.