*3.3. Simulation of Frequency Diversity Based on Three Hydrophones*

Assuming three hydrophones, the positions of which are not in a straight line, the coordinates are: (0,0), (−325 m, 141 m), (−253 m, −213 m). The radius of the circle is determined to be 202 m, according

to the position of the three points. The target signal is 50–1000 Hz band-limited white noise, and the incident angle is 40◦. Using Equation (23) to calculate *f* <sup>m</sup> according to *f* 1, wherein the sampling point *M* is set to 512, the azimuth estimate can be obtained according to Equation (24). The result is shown in Figure 8.

**Figure 8.** DOA estimation results under different SNR: (**a**) SNR = 0 dB (**b**) SNR = −10 dB.

From Figure 8, it can be seen that, when three hydrophones are used, an azimuth estimation result of −180◦ to 180◦ can be obtained, and there is no problem with port and starboard ambiguity. When the position of the three hydrophones changes, the radius of the virtual circle changes. The simulations compared the azimuth estimation results under the three apertures, with radii of 20 m, 202 m, and 2019 m, as can be seen in Figure 9:

**Figure 9.** The relationship between the azimuth resolution and the virtual radii of three hydrophones.

As can be seen, in Figure 9, the increase in the radius of the virtual circle is beneficial to the resolution. The farther the distance is placed in the three hydrophones, the better the azimuth estimation performance.
