# Range-Doppler Based CFAR Ship Detection with Automatic Training Data Selection
## 3 Training Data Selection
### Clutter Normalization  
With the proposed pre-detection algorithm running in time domain, potential targets are well detected and removed leaving behind the \"ocean only\" training data. These clean data can directly be used to determine a single CFAR threshold using standard sea clutter models. However, the steps of CFAR threshold computation in time domain cannot be applied one to one in Doppler domain because the training sample amplitude varies along the Doppler frequency (cf. Figures 1a and 2a). Figure 14: (**a**) RC radar data, (**b**) Google Earth image and (**c**) Pauli image corresponding to Figure 13a. Sandbanks can be clearly observed in the Google Earth image. The bright spots in the Pauli image are strong scatterers, e.g., buoys or ships. If no whitening of the Doppler spectra is performed and if it is directly used as the training data, then the CFAR threshold has to be estimated for each Doppler bin independently. Computing such a threshold for each Doppler bin comes with higher computational cost. The idea is to derive a single Doppler frequency independent threshold which is achieved by normalizing the clutter and noise power to 0 dB (cf. Figure 2b). For the normalization, let us consider a data block in Doppler domain consisting of \(R^{\prime}\) range and a number of Doppler bins. The clutter normalization is based on the estimation of the average spectra \(\hat{A}_{\mathrm{s}}(f_{\mathrm{a}})\) (cf. red curve in Figure 2a) which can be expressed [21; 22]  
\[\hat{A}_{\mathrm{s}}(f_{\mathrm{a}})=\frac{1}{R^{\prime}}\sum_{k=1}^{R^{ \prime}}\bigl{|}Z(r_{\mathrm{k}},f_{\mathrm{a}})\bigr{|}^{2}, \tag{9}\]  
where \(Z(r_{\mathrm{k}},f_{\mathrm{a}})\) is the frequency domain representation of \(z(r,n)\) and \(f_{\mathrm{a}}\) is the Doppler frequency. For simplicity we write \(\bigl{|}Z(r_{\mathrm{k}},f_{\mathrm{a}})\bigr{|}^{2}=~{}P_{\mathrm{k}}(f_{ \mathrm{a}})\) which is known as power spectral density or Doppler spectrum of the data \(Z(r_{\mathrm{k}},f_{\mathrm{a}})\). The clutter normalized data \(Z_{\mathrm{CN}}(r_{\mathrm{k}},f_{\mathrm{a}})\) can then be written as  
\[\bigl{|}Z_{\mathrm{CN}}(r_{\mathrm{k}},f_{\mathrm{a}})\bigr{|}^{2}=P_{\mathrm{ k}}(f_{\mathrm{a}})/\hat{A}_{\mathrm{s}}(f_{\mathrm{a}}), \tag{10}\]  
By estimating \(\hat{A}_{\mathrm{s}}(f_{\mathrm{a}})\) with (9) for each Doppler bin and by using (10) the clutter and noise are scaled to 0 dB. An example of clutter normalization is shown in Figure 15 (cf. also Figure 1b). The data in Figure 15b are the training data used to estimate the ocean clutter statistics. However, when the range-Doppler image additionally contains a ship signal, which may be the case if no target pre-detection is carried out, the clutter normalization causes target self-whitening. This negative and unwanted effect is shown in Figure 16b,c. Figure 15: Range-Doppler image of a target free image patch (**a**) before and (**b**) after clutter normalization. The normalized average power profiles of (**a**,**b**) are shown in (**c**). To avoid target self-whitening and a significant bias of the ocean statistics (cf. Figure 16a,b), it is essential to apply the proposed pre-detection and target cancellation algorithm before estimating the average Doppler spectrum used for clutter normalization (cf. Figure 16d,e). To show the effects of target self-whitening, the signal-to-clutter-plus-noise ratio (SCNR) is estimated and listed in Table 1. The SCNR was computed by extracting a cut along Doppler at the maximum peak value of the image in Figure 16c,e. By using a guard zone around the peak value, the SCNR is measured. \begin{table}
\begin{tabular}{c c} \hline \hline
**Range-Doppler Image** & **Target SCNR [dB]** \\ \hline Before normalization (Figure 16a) & 24.02 \\ After normalization but without pre-detection (Figure 16c) & 14.20 \\ After normalization with pre-detection and target cancellation (Figure 16e) & 23.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Measured target SCNR before and after clutter normalization.