According to the spin and precession characteristics of ballistic missile midcourse flight, we established the model of micromotion target and echoes, analyzed two motion modes of spin and precession. The mathematical formula of micro Doppler frequency produced by fretting is deduced. obtained twodimensional timefrequency graph verifies the correctness of the model. In view of the small Doppler ambiguity which may be produced by the low Pulse repetition frequency, use the compressed sensing to reconstruct the signal micro Doppler, and solve the fuzzy problem. The radar signal pressure is reduced. And on this basis Obtained Spin and precession of periodic motion .Experimental results show the effectiveness of the proposed method in target recognition.