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.