# Range-Doppler Based CFAR Ship Detection with Automatic Training Data Selection
## 6 Experimental Results and Discussion
### Clutter Model Fitting and Performance Evaluation
#### 6.1.2 False Alarm Rate Error
In contrast to the X-band, the L-band 3 dB azimuth antenna beamwidth is in the order of \(18^{\circ}\) so that the ship signal is always visible in the data as shown in Figure 31.  
Figure 31: **(a)** Circularly acquired real single-channel HH polarized RC L-band radar data. **(b)** Binary detection map shown in time-domain after applying CFAR based ship detection in range–Doppler domain. K-Rayleigh distribution was used in the near and mid ranges, and the 3 MD model was used in the far range of the data. The desired false alarm rate was set to \(P_{\text{fa}}=10^{-6}\). The detections marked by the red circles are due to the interfering signals from a ground surveillance radar located close to the test site (for visualization purposes not all of the interfering signals are marked). Figure 30: **(a)** Circularly acquired real single-channel HH polarized RC X-band radar data. **(b)** Corresponding binary detection map shown in time-domain after applying CFAR based ship detection in range–Doppler domain. K-Rayleigh distribution was used in the near and mid ranges, and the 3 MD model was used in the far range of the data. The desired false alarm rate was set to \(P_{\text{fa}}=10^{-6}\). The detections marked by the red circles are due to the interfering signals from a ground surveillance radar located close to the test site (for visualization purposes not all of the interfering signals are marked). Furthermore, experimental detection results from the linearly acquired VV polarized real X-band single-channel RC radar data are shown in Figure 32. Here, the ships are moving in directions of 45\({}^{\circ}\), 90\({}^{\circ}\) and 0\({}^{\circ}\) w.r.t. the flight direction. From Figure 32, it can be observed that the ship is well detected in the RC radar data with the proposed methodology, independent of its moving direction w.r.t. the flight path. To summarize, the performance of the proposed CFAR ship detection algorithm mainly depends on two factors: the target pre-detection threshold (cf. Section 3.1) and the accuracy of the clutter model. Inappropriate estimation of the target pre-detection threshold in time domain may prevent target cancellation, and, thus can directly impact the average Doppler spectrum (cf. Figure 16c) and degrade the performance of the clutter models. Therefore, the parameters for computing the target pre-detection threshold should be carefully selected for obtaining later a valid CFAR threshold in Doppler domain. Additionally, an appropriate selection of the clutter model also plays a key role to improve the target detection by minimizing the detection threshold amplitude and the false alarm rate errors (cf. Sections 6.1.1 and 6.1.2). In the paper, we recommend using a K-Rayleigh distribution in the near and mid ranges because of the numerous discrete sea spikes present in the data at those ranges. For the far range, where less sea spikes are observable in our experimental data, the clutter intensity is more Rayleigh distributed so we recommend using a chi-square or 3 MD model. Figure 32: RC F-SAR X-band VV polarized radar data with a ship moving at (**a**) 45\({}^{\circ}\), (**b**) 90\({}^{\circ}\) and (**c**) 0\({}^{\circ}\) w.r.t the flight track. The detection results corresponding to (**a–c**) are shown in (**d–f**) respectively. Only the K-Rayleigh distribution was used for detection because the maximum incidence angle in the data is below 50\({}^{\circ}\). The desired false alarm rate was set to \(P_{\text{fa}}=10^{-6}\). One potential third factor which may negatively influence the performance of the proposed algorithm is the sea state, although not investigated in the paper. Especially in the case of high sea state, i.e., if the pixels corresponding to the vessel have similar statistics and intensity as the surrounding clutter, it may happen that the vessel is not detectable, especially not in the time or imaging domain.