基于四元数的弹道目标微多普勒仿真

Quaternion Based Micro-Doppler Simulation of Ballistic Targets

微动建模是研究弹道目标微多普勒特征的关键和基础。目前基于Euler角、Euler-Rodrigue公式和齐次坐标的建模方法存在"万向节死锁"、奇异、计算复杂等问题。四元数方法采用4个参数代替矩阵方法的9个参数,能够直观表示三维空间内任意旋转,并克服现有方法的缺陷。经过推导,给出了基于四元数的弹道目标进动和摆动微多普勒数学模型表达式。由于减少了矩阵运算,使得目标微多普勒频率的计算更加简单。仿真结果表明,基于四元数旋转的微动建模方法是合理的,为弹道目标的微多普勒特征提取和识别提供了科学依据。

Micromotion kinetics modeling is a key and fundamental issue of ballistic target microDoppler feature research.At presentthe modeling techniques based on Euler anglesEulerRodrigue formula and homogeneous coordinates have some problems such as “gimbal lock”singularity and computational complexity.Quaternion method can express arbitrary rotation in 3D space intuitively and overcome shortcomings of the existing methods by using 4 values instead of the 9 of the corresponding matrix.The quaternion based precession and wobbling microDoppler frequency expressions of ballistic targets are presented after derivation.It simplifies the calculation of target microDoppler in that reducing matrix operations.The simulation results prove that the quaternion based micromotion modeling method is valid and provides a scientific basis for microDoppler extraction and recognition of ballistic targets.