Abstract: In midcourse, the micro-motion difference between warhead and decoy is an effective feature for target recognition. However, the parameter extraction of target micro-motion is generally constrained by the factors of target translation compensation precision, radar equipment operating state and environment which lead to the decline of target recognition rate. At first, the quaternion based micro-motion models of warhead and decoy are established in this paper. Then the target micro-Doppler time-frequency image is regarded as a color image and described by quaternion matrix. According to the stability and rotation invariance properties of singular value vector, the micro-Doppler feature extraction and classification method of ballistic targets is presented based on QMSVD and SVM. Simulation results show that the QMSVD based feature vector is more effective than that of Hu moment based. To improve the SNR is benefit to improve the target recognition rate of classifier. With the increasing of the estimation error of target radial velocity, the target recognition rate of the classifier will decrease. Moreover, the target recognition rate will increase obviously along with the increasing of the radar PRF.