Keywords: 
• 物理光学法 /
• 等效电磁流法 /
• S-method /
• 逆Radon变换

Abstract: The micro-motion Doppler echo simulation and characteristic parameter extraction of the extended micro-motion target are carried out. For the extended micro-motion target, the echo from the target cannot be regarded as several points’ echo. Based on the connections between the scattering field and Doppler echo, an echo simulation method for micro-motion target (based on physical optics) and a method of equivalent current are proposed. At the moment, the micro-motion target can be taken as a static target, so the back scattering field series can be calculated by physical optics and the method of equivalent current. The back scattering field series calculated in the target coordinate system is transformed into the echo of radar coordinate system by the conversion of coordinates, and the Doppler echo is obtained. By comparing with the analytic signal model, the method is validated. The precession characteristics of a cone and warhead with fins are analyzed. Echoes come from every part of the extended micro-motion target and contain the motion characteristics of that part. So the traditional time-frequency analytical methods are not appropriate. In order to achieve better time frequency concentration and avoid the cross terms, the S-method is used to get the time-frequency distributions. The time-frequency characteristics at different radar waves’ incidence angles, target different motion states and different geometries are analyzed. From the time-frequency distribution map, the micro-motion of the cone behaves as the micro-motion of two strong scattering points at the bottom of the cone. Because of the shielding effect, the time-frequency curves are not integrated when the radar waves are incident from the cone’s bottom. The sinusoidal curve can be mapped to a point in the parameter space based on the inverse radon transform, and the target micro-motion parameters can be obtained. Results of inverse radon transform also show that the precession of the cone behaves as the precession of the two strong scattering points, and the two points’ phase difference is equal. For warhead with fins, the time frequency distribution of spin behaves as four sinusoidal curves whose phase differences are equal, implying that the micro-motion of the target behaves like the four fins’ micro-motion. However, the sinusoidal curves of precession of the warhead with fins are very different, i.e. their phase differences are not equal. This is because the precession consists of spinning and coning, and the coning has a modulation effect on the spinning. These phase information and the number of strong scattering points can be directly and easily obtained through inverse radon transform. This study combines the electromagnetic scattering with the signal procession. And some results are different from that of traditional micro-motion models through the simulation of typical ballistic targets. Results are explained and analyzed by combining scattering theory. This research has important theoretical and application values in the ballistic target detection and recognition.