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Attitude and Orbital Coupled Modeling and Micro-Doppler Characteristics Analysis of the Projectile with Initial Disturbances
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摘要: 基于动力学与运动学原理的雷达回波建模是炮弹目标微多普勒特征分析与参数提取的理论基础。该文首先对炮弹在直线弹道段受到的起始扰动进行分析，结合炮弹目标动力学方程，建立了以两圆运动模式为特征的炮弹角运动模型，阐明了炮弹目标自旋、章动和进动等角运动的含义；在此基础上，推导了炮弹角运动产生的微多普勒信号参数化表征，获得了炮弹目标角运动对目标回波在信号级的映射关系；然后，对高速自旋炮弹和低速自旋尾翼炮弹两种典型目标角运动受起始扰动影响的雷达回波信号进行仿真和时频分析，并基于炮弹目标实测数据对比验证了理论分析与模型的正确性。通过理论分析、建模仿真与实验验证，丰富和验证了炮弹目标的微多普勒效应理论，为炮弹目标运动特性辨识提供了理论和技术支撑。Abstract: Radar echo modeling based on dynamics and kinematics serves as the theoretical basis for micro-Doppler characteristic analysis and projectile parameter extractions. First, the initial disturbance of a projectile in the straight-line ballistic segment is analyzed. Based on the dynamic equation of the projectile, an angular motion model of the projectile characterized by two circular motion modes is established. Moreover, the motion definitions of projectile spin, nutation, and precession are explained. Subsequently, the parameterized characterization of the micro-Doppler signal produced by the angular motion of the projectile is derived. Furthermore, the mapping relationship between the angular motion of the projectile and the radar echo is obtained at the signal level. Taking high-speed spin projectile and a low-speed spin tail projectile as examples, when the angular motion of the two targets are affected by the initial disturbance, the radar echo signal model of the two targets is simulated and time-frequency analysis is carried out. The validity of the theoretical analysis and the model is verified by comparing the simulation results with the measured data of the projectile. Therefore, the micro-Doppler effect theory of projectile is enriched and verified through theoretical analysis, simulation modeling, and experimental verification. This study provides theoretical and technical support for the identification and analysis of projectile motion characteristics.
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Key words:
- Micro-motion /
- Micro-Doppler /
- Initial disturbances /
- Angular motion /
- Two circular motion
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图 1 弹道轨迹与直线弹道段示意图
Figure 1. Schematic diagram of ballistic and the straight line segment
图 2 炮弹直线段角运动空间几何关系
Figure 2. Spatial geometric relation of projectile angular motion in the straight line segment
图 3 初始时刻4种坐标系空间几何关系
Figure 3. Spatial geometric relation of the four coordinate systems as the projectile is stationary
图 4 快圆和慢圆不衰减情况(高速旋转炮弹)
Figure 4. In the case of neither the fast nor the slow circular motion decays (high-speed rotating projectile)
图 5 快圆衰减而慢圆不衰减情况(高速旋转炮弹)
Figure 5. In the case of the fast circular motion decays and the slow circular motion remains (high-speed rotating projectile)
图 6 快圆和慢圆均在衰减情况(高速旋转炮弹)
Figure 6. In the case of both the fast and the slow circular motion decays (high-speed rotating projectile)
图 7 快圆和慢圆不衰减情况(旋转尾翼炮弹)
Figure 7. In the case of neither the fast nor the slow circular motion decays (rotating tail projectile)
图 8 快圆衰减而慢圆不衰减情况(旋转尾翼炮弹)
Figure 8. In the case of the fast circular motion decays and the slow circular motion remains (rotating tail projectile)
图 9 快圆和慢圆均在衰减情况(旋转尾翼炮弹)
Figure 9. In the case of both the fast and the slow circular motion decays (rotating tail projectile)
图 10 某型炮弹直线段回波时频分析仿真结果
Figure 10. Simulated time-frequency image of projectile in the straight line segment
图 11 某型末制导炮弹时频分析仿真结果
Figure 11. Time-frequency image of terminal guided projectile in the straight line segment
图 12 某型炮弹直线段回波真实时频图像
Figure 12. Actual time-frequency image of projectile in the straight line segment
图 13 某型末制导炮弹直线段回波真实时频图像
Figure 13. Time-frequency image of terminal guided projectile in the straight line segment
表 1 仿真参数设置(高速旋转炮弹)
Table 1. Simulation parameters setting (high-speed rotating projectile)
参数 数值 点A坐标 (0.5 m, 0, 0) 点B1坐标 (–0.3 m, 0.06 m, 0) 点B2坐标 (–0.3 m, –0.06 m, 0) 自旋频率${\varOmega _{\text{s} } }$ 300π rad/s 进动频率${\varOmega _{\text{c} } }$ 4π rad/s 章动频率${\varOmega _{\text{u} } }$ 60π rad/s 章动角$\phi $ 1.2° 进动角$\psi $ 8.2° 观测时间 2.00 s 采样率 25 kHz 
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表 2 Hough变换提取的时频图像周期(高速旋转炮弹)
Table 2. Extracted period of time-frequency image with Hough Transform (high-speed rotating projectile)
蒙特卡罗
次数弹顶
微动周期均值(s)弹底边缘点
微动周期均值(s)5 0.484 0.482 10 0.488 0.485 20 0.492 0.490
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表 3 仿真参数设置(旋转尾翼炮弹)
Table 3. Simulation parameters setting (rotating tail projectile )
参数 数值 点A坐标 (1.2 m, 0, 0) 点B1坐标 (–1.8 m, 0.12 m, 0) 点B2坐标 (–1.8 m, –0.12 m, 0) 自旋频率${\varOmega _{\text{s} } }$ 10π rad/s 进动频率${\varOmega _{\text{c} } }$ π rad/s 章动频率${\varOmega _{\text{u} } }$ 4π rad/s 章动角$\phi $ 0.8° 进动角$\psi $ 8.2° 观测时间 4.00 s 采样率 5 kHz
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表 4 Hough变换提取的时频图像周期(旋转尾翼炮弹)
Table 4. Extracted period of time-frequency image with Hough Transform (rotating tail projectile)
蒙特卡罗
次数弹顶
微动周期均值(s)尾翼
微动周期均值(s)5 1.993 1.990 10 1.995 1.991 20 1.996 1.992
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