## 6 Research and Analysis of the Obtained Results  
Let us now do an experiment to software simulation of the BAUV passage along the straight section with simultaneous:  
* generating COG--measurements of INS carried out by \"VN-200\", SOG--carried out with log \"ALIZE\" and \(\Delta\)z--carried out with a hydrostatic pressure sensor \"S-20 WIKA\";
* generating by \(r\), \(\alpha\), \(\beta\) measurements--carried out by the USBL \"MicronNav System\";
* calculating the BAUV estimated coordinates of positions, parallel to the USBL system, with the method of dead reckoning and using the extended Kalman filter.  
As a measuring testing ground, we assume a sea area around the USBL transponder system (Figure 7).  
Figure 7: Measuring testing ground.  
Let the BAUV swims near the USBL transceiver system (located at a depth of 6 m) overcoming the test section with COG \(=\ 220^{\circ}\), SOG \(=\ 1\) m/s, submerged at \(z\ =\ 3\) m. Meanwhile, \(\tau=\left\langle 0\ \mathrm{s},\ 600\ \mathrm{s}\right\rangle\) simulated measurements will be carried out by the on-board BAUV and USBL system, i.e.,  
* at fixed moments \(k+1\) (every one second) COG \(\left(k+1\right)=\ \mathrm{COG}_{w}\left(k+1\right)+\Delta_{COG}\), SOG \(\left(k+1\right)=\ \mathrm{SOG}_{w}\left(k+1\right)+\Delta_{SOG}\) and \(\Delta z\left(k+1\right)=\ \Delta z_{w}\left(k+1\right)+\Delta_{\Delta z}\);
* at some moments \(k+1\) (every 5, 20 and 100 s) \(r\left(k+1\right)=\ r_{w}\left(k+1\right)\ +\ \Delta_{r}\), \(\alpha\left(k+1\right)=\alpha_{w}\left(k+1\right)+\Delta_{\alpha}\), \(\beta\left(k+1\right)=\beta_{w}\left(k+1\right)+\Delta_{\beta}\).  
Each simulated value of the measurement is obtained by adding the reference measurement and the error (e.g., simulated COG \(\left(k+1\right)=\ \mathrm{COG}_{w}\left(k+1\right)+\Delta_{COG}\)). Measurement error \(\Delta\) will be treated as a random variable with uniform distribution, the value of which will be contained within three mean errors (\(3\sigma\)) of measurements made in the device (i.e., the probability of its occurrence will be at 99%).  
Reference measurements of the USBL system \(r_{w}\left(k+1\right)\), \(\alpha_{w}\left(k+1\right)\), \(\beta_{w}\left(k+1\right)\) will be determined relative to the reference positions consecutively occupied by the BAUV, which moves with undisturbed movement. On the other hand, the BAUV reference position will be dead reckoned (DR) on the basis of reference COG\({}_{w}\left(k+1\right)\), SOG\({}_{w}\left(k+1\right)\) and \(\Delta z_{w}\left(k+1\right)\), which will be located exactly at the measuring section (see Figure 7).  
For realigning the experiment for calculating the accepted mean error values close to the actual values (provided by the manufacturer and determined on the basis of their own--selected arbitrarily):  
* \(\sigma_{\mathrm{COG}}=8^{\circ}\)--for INS \"VN-200\",
* \(\sigma_{\mathrm{SOG}}=0.5\) km--for the electromagnetic log \"ALIZE\",
* \(\sigma_{\Delta z}=0.25\) m--for the hydrostatic pressure sensor \"WIKA S-20\",
* \(\sigma_{r}=0.2\) m, \(\sigma_{\alpha}=\sigma_{\beta}=3^{\circ}\)--for the USBL \"MicronNav System\" system.  
The experiment will commence at the moment of \(k=0\) and will be completed when the BAUV swims about 600 m. The extended Kalman filter will be \"fine-tuned\" at the start of the experiment and the coordinates of the initial BAUV position will be determined with a mean error of about 3 m (it is assumed that the coordinates were determined before submergence using GNSS) [31]. In the calculations, changes of COG, SOG, and \(\Delta z\) caused by the BAUV wave motion (swinging, on a sine curve) will be omitted.