**4. Experimental Data Verification**

The algorithm is first verified with Swell 96 horizontal south array data [21], using the 14th to 28th array elements. The SWellEx-96 Experiment was conducted between May 10 and 18, 1996, approximately 12 km from the tip of Point Loma near San Diego, California. Acoustic sources, towed from the R/V Sproul, transmitted various broadband and multi-tone signals at frequencies between 50 and 400 Hz.

In order to further compare the performance of the two hydrophone algorithms, conventional array processing is used to obtain the azimuth estimation result as a reference, because the array gain of the processing of multiple array elements leads to a clear trajectory. The processing frequency bandwidth is 20–1000 Hz. The azimuth history diagram is shown in Figure 10a. It can be seen, from the figure, that within this time period (1–3500 s), there are mainly two targets, one with a large span in the azimuth, and one mainly at around 40◦.

**Figure 10.** (**a**) Azimuth history diagram of Swell 96 data. (**b**) Signal spectrum of the 14th and 28th sensors.

The 14th array element and the 28th array element are selected as the two hydrophones, and the distance between them is 106 m. Figure 10b is the signal spectrum of the 14th and 28th elements, and the Fourier transform time is from 1000 s to 1001 s. The results of the cross-correlation method and the frequency diversity algorithm are shown in Figure 11. The sampling frequency *f* s is 3277 Hz, the number of samples is 3277, and Δ*f*= 1 Hz. The processing bandwidth *M*Δ*f* is set to 980 Hz, according to the processing bandwidth of 20–1000 Hz.

**Figure 11.** Azimuth history diagram of the two hydrophones: (**a**) The cross–correlation method and (**b**) frequency diversity algorithm.

From the comparison in Figure 11, it can be found that, using the same processing time, the same hydrophone, the target trajectory, estimated by the frequency diversity algorithm, is obviously clearer than that obtained by the cross-correlation algorithm. The algorithm is further verified by the South Sea data. Similarly, the conventional array processing is performed first, and a relatively accurate orientation estimation result is obtained. Then, we compare the cross-correlation method based on the passive two-hydrophone and the frequency diversity algorithm. In the array processing, 64 array elements are selected, with an interval of 4 m, and the processing method uses CBF. The processing frequency band is 20–400 Hz, and the sampling frequency is 2048 Hz. The azimuth estimation results are in Figure 12.

**Figure 12.** Azimuth history diagram of the 64-element array.

The data are processed using two hydrophones, as shown in Figure 13, and the number of samples is 2048, Δ*f*= 1 Hz, and *M*Δ*f* is set to 380 Hz.

**Figure 13.** Azimuth history diagram of the two hydrophones: (**a**) the cross-correlation method and (**b**) frequency diversity algorithm.

In Figure 13a, only a little blurred outline can be seen, and the trajectory of the target can hardly be observed. In Figure 13b, the trajectories of target 1, target 2, and target 3 can be clearly observed. The trajectory of target 4 is not clear. It can be explained that the performance of the two-hydrophone algorithm based on frequency diversity technology is significantly higher than that of the cross-correlation algorithm. Moreover, we found, in the experiment, that the frequency diversity algorithm has a higher processing gain, which is easily seen before taking the beam energy by 10 lg. Before taking 10 lg, the beam energy is shown in Figure 14.

**Figure 14.** Azimuth history diagram of the two hydrophones: (**a**) The conventional 64-element processing; (**b**) two hydrophones, cross-correlation algorithm; and (**c**) two hydrophones, frequency diversity algorithm.

Comparing Figure 14b with Figure 14c, it is found that the frequency diversity algorithm is better than the cross-correlation algorithm, regardless of whether the log is taken or not. Furthermore, comparing Figure 14c with Figure 14a, it can be found the energy of target 2 and target 3 is significantly improved when the frequency diversity algorithm is used. To further reflect this feature, we take the azimuth estimation result at 4500 s as an example. At this time, target 2 and target 3 are located at 3◦ and −17◦, respectively, and it is apparent, from the comparison of Figure 15, that the energy of target 2 and target 3 is enhanced.

**Figure 15.** DOA results at 4500s: (**top**): 64-element array processing, and (**bottom**): the two-hydrophone frequency diversity algorithm.

The reason for this phenomenon is that the frequency diversity algorithm of the two hydrophones mainly uses the frequency domain information of the signal. Therefore, rich frequency domain information and uniform frequency domain energy distribution are beneficial for the energy of the beamforming output. The spectrums of Target 1 and Target 4 are shown in Figure 16a, and the spectra of target 2 and target 3 are shown in Figure 16b. From the comparison of Figure 16a,b, the spectrums of target 2 and target 3 are significantly richer than that of target 1 and target 4, and the energy distributions are more uniform. Therefore, in the estimation results of the two hydrophones, the energy of targets 2 and 3 is strengthened. Among them, the spectrum energy distribution of target 4 is the most concentrated so, in the two-hydrophone azimuth estimation, target 4 can hardly be observed.

**Figure 16.** Frequency spectrum of the four targets. (**a**) The upper picture is target 1, and the lower picture is target 4; and (**b**) the upper picture is target 2, and the lower picture is target 3.
