Quaternion based micro-Doppler simulation of ballistic targets

As a key issue of ballistic target micro-Doppler feature research, the micro-motion kinetics modeling technique usually bases on Euler angles, Euler-Rodrigue formula and homogeneous coordinates those have some problems such as “Gimbal lock” and singularity which don´t happen with quaternion. Quaternion is more intuitive and provides for easier rotation than matrices. It allows us use 4 values instead of the 9 of the corresponding matrix. Consequently, the Quaternion based precession and wobbling micro-Doppler frequency expressions of ballistic targets are derived for the sake of simplifying the calculation of target micro-Doppler and reduce matrix operations. The simulation results prove that the micro-Doppler signature based on quaternion is valid. Furthermore, the warhead has different micro-Doppler signature with that of the decoy. By means of different micromotion producing different micro-Doppler signature, the corresponding micro-Doppler signature can make ballistic targets recognition possible under the assumption that decoys motion without attitude control module.