Adaptive Angular-sector Segmentation Radar Target Recognition based on Grey System

The aspect sensitivity of high-resolution range profile (HRRP) leads to the anomalous change of the HRRP statistical characteristic, which is one of inextricable problems on the target recognition based on HRRP. Aiming at the HRRP statistical characteristic, an adaptive angular-sector segmentation method is proposed through based on the grey relational mode. Comparing to the equal interval angular-sector segmentation method, the new method improves the recognition performance. And these simulation results of five kinds of aircraft targets HRRPs prove the feasibility and validity.

Then the power of HRRP used in the target recognition is: Where the symbol ' ' represents the complex conjugate.
Where nik  is the phase difference between the   , ni scatterer and the   , nk scatterer.
It can be seen that the power of HRRP is composed of two parts according to the expression (3). The first part is known as the scatterer auto-term (SAT), which is the sum of the scatterer energy in the resolution range. The second part is called the scatterer cross-term (SCT), which is the result of phase interference among the scatterers in the resolution range. When the target posture changes, the number of the scatterers will increase or decrease with the MTRC, and then the total scattering characteristics will also change. The SAT has nothing to do with the azimuth without the MTRC. And it is a stable feature of the power of HRRP, but the change of the relative distance     ,, n i n k d m d m  among these scatterers causes the change of the phase difference so that the echo amplitude happens to the fluctuation.

Equal Angular-sector Segmentation
The HRRP target posture sensitivity mainly is composed of the pitch sensitivity and azimuth sensitivity. This paper researches on the RAR method of the aircraft target. And the aircraft target is mostly flat, so changes of the pitch angle tend to be small. Therefore, the research of the posture sensitivity aims at the azimuth sensitivity. The equal angular-sector segmentation is generally divided into two steps. The first step is to divide equally the target angular sector, and the second step is to make statistical analysis of the angular partition, to extract the feature and to establish the HRRP template model in turn. Figure 1 shows respectively the results of the mutual Deng-Si degree of grey incidene (DGI) model, degree of grey slope incidence (SGI)model and type-B degree of grey incidence (BGI) model between the adjacent HRRP, which is sampled at 0.1 azimuth interval from the full azimuth turntable simulation data of five aircraft targets (Su27, F16, M2000, J8II and J6). These data all include 128 resolution ranges provided by the Target Characteristic Research Center of Nanjing University of Aeronautics and Astronautics, and they are done the normalization and alignment pretreatment so as to solve the amplitude sensitivity and shift sensitivity. The step frequency of the signal radiated by the radar is 4MHz, and then the effective bandwidth of the  Figure 1, the azimuth sensitivity is also different in some same azimuth angle intervals for these different targets. So these different targets should correspond to different segmentation intervals. And the azimuth sensitivity is different while the azimuth angle is different for each target, that is, there are some adjacent HRRPs which are poor incidence, so these HRRPs cannot be divided into the same segmentation frame. But in the positive line of sight which the azimuth angle is about 90 , these five aircraft targets also have the strong azimuth sensitivity, so these HRRPs should be considered separately. Figure 1. the mutual relational degree between the adjacent HRRP samples of full azimuth of five aircraft targets

Adaptive Angular-sector Segmentation Based on Grey System
It is seen from the upper section that it causes the mismatch between the data and the model when the equal angular-sector segmentation is adopted. So the angular-sector should be segmented according to the specific distribution of HRRP. For these strong azimuth sensitivity or easy misjudgment sector, the azimuth interval should be smaller, while for these poor azimuth sensitivity sector the interval should be bigger in order to reduce calculations and save storage spaces. For this reason, on the basis of the previous research results [15], the adaptive angular-sector segmentation based on the grey incidence analysis (GIA) model is researched. That is to say, the angular-sector is adaptively segmented according to the mutual grey incidence value of the adjacent HRRPs. The specific process is as follows: Step 1. Assume that the target A contains N HRRP training samples, calculate the mutual grey incidence value of each training sample with its adjacent HRRP sample, and get the grey incidence value array  Step 3. According to these settings of the Step 2, give the mutual grey incidence value threshold Step 4. Compare the grey incidence value array a with 1  and 2  , put the HRRP training sample where the grey incidence value is below two thresholds as the breakpoint, divide unevenly these HRRP training samples, and gain the initial angular-sector segmentations; Step 5. Calculate the azimuth interval of these segmentations obtained by the Step 4, in accordance with MTRC  separate evenly these segmentations whose azimuth interval is far greater than MTRC  , where MTRC  corresponds to the azimuth interval where MTRC does not occur.
Step 6. Delete less sample segmentations including these segmentations near 90 azimuth, because the SCT of the average HRRP cannot be weakened effectively for the segmentations whose amount of the HRRP sample is smaller; Step 7. Calculate each segmentation template according to (6), get M templates; , , Where L is the sample number of the segmentation, and 2  is the 2-norm calculation of the vector.
Step 8. If max MK  , calculate the mutual grey incidence value of each HRRP template with its adjacent HRRP template and get the mutual grey incidence value array , merge these HRRP templates which the grey incidence value is larger according to a certain proportion , such as 5% M  ; Step 9. Return to the Step 8 until max MK  , calculate the normalized average HRRP for each HRRP template.
After the target A finishes the above algorithm, the angular-sector segmentation number and their normalized average HRRP will be obtained.

Experimental Simulation 4.1. Experimental Process
These HRRP data are sampled with the 0.1 interval from the full azimuth turntable simulation data of five aircraft targets. So these data contain various azimuths. One half of them are used as the training samples, and the other half of them are used as the testing samples. After the HRRP samples preparation, the experiment is done according to the following algorithm.
Step 1. Execute the adaptive angular-sector segmentation method based on the GIA model in the above section. Some frames and their corresponding normalization average range profiles are gained. And they are matching templates. The number of frames is supposed to Step 2. Calculate the degree of grey incidence , Then the degree of grey incidence matrix which is degrees of grey incidence between x and the whole template library.   (6) In the actual segmentation, the number of frames are not necessarily equal for five aircraft targets. So the matrix cannot be formed, five degree of grey incidence arrays are obtained.
Step 3. Search the maximum degree of grey incidence for each a testing sample. The line corresponding to the maximum degree of grey incidence is the category of the testing sample x .
Step 4. Do statistics the number of the testing samples judged by the recognition decision for a certain target and divide it by the total number of the test samples extracted from the target. The recognition rate and the average rate of recognition both can be gotten. That is: Where avg is the recognition rate of a certain target, num is the number of the testing samples judged by the recognition decision for the target, total N is the total number of the test samples extracted from the target. Figure 2 shows the comparison of the recognition rate for six different methods aiming at the Su27, F16, M2000, J8II and J6 in different SNR. The six different methods are respective the DGI, SGI, BGI and three adaptive angular-sector segmentation based on three GIA models. These three adaptive methods are abbreviated as ADGI, ASGI and ABGI. Among them, the sub graph (a), (b), (c), (d) and (e) are corresponding to the Su27, F16, M2000, J8II and J6 aircraft target. And then Table 1 is the recognition rate of these methods at =20 B SNR d . In the simulation,  is the coefficient of the DGI model and is set to be 0.5 according to the principle of minimal information.

Result Analysis
As can be seen from these recognition results, these adaptive angular-sector segmentation methods are better than these equal angular-sector segmentation methods. ABGI considers the mean information, the first order changes slope information and the second order changes slope information on the basic of SGI and ASGI which consider the change rate in each a resolution range, so the recognition rate of ABGI is the best.

Conclusion
In this paper, the grey system theory is applied to the RTR based on HRRP, and an adaptive angular-sector segmentation method based on the gray incidence analysis model is proposed to solving the azimuth sensitivity of HRRP. These experiments of full azimuth angle turntable HRRP data of Su27, F16, M2000, J8II and J6 five fighter models have shown that the new method can improve the recognition performance. So the method has a practical significance in target recognition applications. At the same time it should be noted that the angular-sector segmentation number, these angular-sector regions which needs to be segmented meticulously, and these thresholds are predetermined. The determination of these parameters is the compromise between the template number, computational workload and the recognition performance.