## 6 Research and Analysis of the Obtained Results
### Test No. 2  
The test depended on carrying out three, followed by a hundred passages in the test section. COG, SOG and \(\Delta\)z were measured every one second. \(r\), \(\alpha\), \(\beta\) were measured every 20 s.  
The statistical parameters of the positioning errors using EKF, DR methods and the USBL system for single passage are presented in Table 5 (for first passage) in Table 6 (for second passage) and in Table 7 (for third passage).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Positioning Method**} & **Minimum Distance** & **Maximum Distance** & **Average Distance from the** \\  & **from the Reference** & **from the Reference** & **Reference Position (m)** \\  & **Position (m)** & **Position (m)** & **Average Distance from the** \\ \hline EKF & 0.6 & 3.3 & 2.2 \\ DR & 0.6 & 20.1 & 10.6 \\ USBL & 1.3 & 57.0 & 23.4 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The statistical parameters of the positioning errors using EKF, DR methods and the USBL system (one hundred passages).  
Figure 20: Histogram of the reference position distance from the position estimated by EKF and DR methods and determined by the USBL system (one hundred passages).  
Third Passage  
The analysis of Figures 21-23 shows that the accuracy of the estimated position coordinates using EKF method improves almost every 20 s, when measurements from the USBL system are included in the calculations. Even if the position determined by the USBL system is significantly distant from the reference position, the accuracy of the estimated position using EKF method increases. This may be due to the fact that EKF suppresses the significant and obviously erroneous measurement direction of \(\alpha\left(k+1\right)\), \(\beta\left(k+1\right)\) and reinforces the accurate measurement of the distance of \(r\left(k+1\right)\).  
On the basis of analysis of the graphs in Figures 21-23, and the statistical parameters from Tables 6 and 7, it can be concluded that the accuracy of the estimated position coordinates using EKF method is greater than the estimated ones using DR method and determined by USBL system. The maximum reference position distance from the estimated ones using EKF method does not exceed 8 m. However, as in test No. 1, it can be seen on the graphs that there were intervals in which the reference position is more distant from the estimated position by the EKF method, compared to the estimated position by the DR method or that determined by the USBL system.  
Figure 24 presents determined routs during one hundred passages using different methods of positioning. Graph of the reference position distance is presented in Figure 25.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Positioning Method**} & **Minimum Distance to the** & **Maximum Distance to the** & **Average Distance to the** \\  & **Reference Position (m)** & **Reference Position (m)** & **Reference Position (m)** \\ \hline EKF & 0.3 & 6.1 & 2.2 \\ DR & 0.3 & 15.3 & 6.2 \\ USBL & 1.3 & 72.6 & 21.1 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Statistical parameters of positioning errors using EKF and DR methods and the USBL system (single passage).  
Figure 24: Determined route (one hundred passages).  
Figure 23: Graph of the reference position distance from the position estimated by EKF and DR methods and determined by the USBL system (single passage).  
Generalizing the results of Test No. 2, they are similar to Test No. 1 based on the indicators presented in Figure 26 and Table 8.