# Range-Doppler Based CFAR Ship Detection with Automatic Training Data Selection
## 6 Experimental Results and Discussion
### Clutter Model Fitting and Performance Evaluation  
To test the clutter models fitting, the radar data are first partitioned into three regions: (a) near range (15\({}^{\circ}\)-30\({}^{\circ}\) incidence angle), (b) mid-range (30\({}^{\circ}\)-50\({}^{\circ}\)) and (c) far range (\(>\)50\({}^{\circ}\)). Since the backscatter changes over the incidence angle range (cf. Figure 7), it is important to segment the data for a detailed investigation and understanding of the chosen models. The image patches, each from the near, mid and far ranges of the linear and  
From Figures 24a,b and 25a,b, it can be observed that in near and mid-range, the K-distribution, the chi-square distribution and the 3 MD model fit only for the intensity values of up to 2.5 and 4, respectively. In contrast, the K-Rayleigh distribution is able to fit well in the near and mid-range for both linear and circular data. Due to the presence of spiky clutter, the data histogram is more skewed in the mid-range compared to the near range. The K-Rayleigh distribution is able to model this skewness by estimating an extremely low texture value of 0.04 (cf. Figure 24b), and 0.09 (cf. Figure 25b) respectively. When the K-distribution is used instead of the preferred K-Rayleigh, then the V-statistics rather than the X-statistics and the NLLSQ shall be used for parameter estimation, since it leads to the best K-distribution performance in both near and mid ranges. In the far range however, only the K-distribution parameters estimated using the NLLSQ method, the chi-square and the 3 MD model fit well. Others do not fit because the estimated parameters have negative values. This is because the NLLSQ fits the data histogram in a least square sense, whereas the MoM doesn't have optimal properties [44]. Another reason why they do not fit in far range is because, due to the long range and shallow incidence angle, the clutter power in far range is comparable to the noise power, as shown in Figure 26.  
Figure 26: Average Doppler spectrum of the linearly acquired data estimated in near, mid and far range. The ambiguities cause a variation in the average power in the noise region of the spectrum. Figure 25: Logarithmic PDFs of different distribution functions plotted for (**a**) near (**b**) mid and (**c**) far range using data acquired during the circular flight track (cf. Figure 23c). The estimated parameters corresponding to different distribution functions are shown in the legends of the plots. From Figure 26, it is clear that due to high incidence angle, the backscatter power received in far range is very low. It can also be said that in far range, the intensities are more Rayleigh distributed. This is evident from Figures 24c and 25c, where the texture value from the K-distribution estimated using the NLLSQ method in both the data is approximately 171. Such a high value implies Rayleigh distributed statistics [48]. Furthermore, the complementary cumulative distribution function (CCDF) computed from the estimated data PDF and the CCDFs computed from different clutter models are also plotted. Plotting such functions is important due to their relationship with the detection threshold. In the literature, the CCDF is also known as PFA [48]. The logarithmic CCDF plots for linearly and circularly acquired data are shown in Figures 27 and 28, respectively. Figure 27: Logarithmic CCDFs of different distribution functions plotted for (**a**) near (**b**) mid and (**c**) far range. These plots are generated from the same data used for generating the plots shown in Figure 24.  
Figure 28: Logarithmic CCDFs of different distribution functions plotted for (**a**) near (**b**) mid and (**c**) far range. These plots are generated from the same data used for generating the plots shown in Figure 25.  
It can be observed from Figure 27a,b and Figure 28a,b (near and mid ranges) that the CCDF from the K-Rayleigh distribution align very well with the estimated data CCDF.