# Research on Passive Ranging Technology of Moving Ship Based on Vertical Hydrophone Array
## 4 Experimental Analysis
### Results Analysis  
The top hydrophone is chosen as the reference element for the below discussion, and the other 15 elements are processed in the same way. Then, the range estimation results of 16 hydrophones are fused to improve the estimation accuracy. We choose a piece of data with a length of 900 s for processing. Figure 12 shows the time domain diagram and time-frequency domain diagram of the received signal for the reference element. From Figure 12a, we can see that the received signal has a low-frequency envelope. Figure 12b validates that the ship-radiated noise contains multiple frequency components. In addition, adjacent spectrum components are prone to aliasing, and the low-frequency line spectrum components directly extracted from the spectrum are unstable. Therefore, the DEMON spectrum analysis method is employed to extract the stable low-frequency line spectrum. As shown in Figure 13a, the signal frequency after the DEMON analysis is 14 Hz. The time interval between two points ranges from 1 s to 200 s, and the corresponding interference fringes of the sound intensity of the pressure difference is shown in Figure 13b. The period of the interference oscillations is calculated through Fourier transform and is then applied to calculate the radial velocity. The estimated radial velocity changing over time is shown in Figure 13c. From this figure, we can find that the estimated radial velocity is about 4.6 m/s. Then, when the MSE between the estimated value and true value reaches the minimum, the corresponding range and time of the CPA point can be obtained. Through the above processing, the range and time of the CPA point are 190 m and 115 s, respectively. Based on the above analysis, the range versus time is estimated by  
Figure 11: Measured sound speed profile. Figure 12: Received signal of the reference element: (**a**) in the time domain; (**b**) in the time-frequency domain. Equation (17). Then, the estimated range and the range recorded by the GPS data are compared in Figure 13d. The two curves have similar trends, but there is a slight difference in the range \(r\) at the same time \(t\). One can see that the range estimation result of a single hydrophone is inaccurate. Our experiment adopts a 16-element vertical hydrophone line array, and all of the elements are processed separately by the proposed method. Figure 14 shows the range estimation results of the 16 elements and the data fusion result. Figure 14: Range estimation results for all elements and the data fusion result. Figure 13: Experimental results of the reference element. (**a**) DEMON spectrum output; (**b**) Interference fringes of the sound intensity of the pressure difference; (**c**) Estimated radial velocity; (**d**) Comparison of the estimated range and true range. (The solid red line represents the estimation result for the reference element, and the dotted blue line represents the real-time range recorded by the GPS module.). From this figure, we can see that the estimation results of most elements are close to the GPS true value and that there are three obvious curves with large deviations. When performing WLS fusion, we assign smaller weights to the estimation results with larger range deviations, and larger weights to the elements with smaller deviations. Therefore, the fusion result is in good agreement with the actual curve. To further measure the performance of this range localization method, we calculate the parameter of the relative mean square error (RMSE), defining RMSE as:  
\[{\sigma_{i}}^{2}=\sum_{j=1}^{M}\left(\frac{r_{i}\big{(}t_{j}\big{)}-R\big{(}t_ {j}\big{)}}{R\big{(}t_{j}\big{)}}\right)^{2}\quad i=1,2\cdots N \tag{28}\]  
where \(r_{i}\big{(}t_{j}\big{)}\) represents the estimated range at the \(j\)-th second by the \(i\)-th element. \(R\big{(}t_{j}\big{)}\) is the real range at the \(j\)-th second. \({\sigma_{i}}^{2}\) is the RMSE of the \(i\)-th element. \(M\) and \(N\) are the length of time and the total number of elements.