# Establishment of a Pressure Variation Model for the State Estimation of an Underwater Vehicle
## 2 Methodology and Results
### Numerical Results  
Figures 7-12 illustrate the pressure for each motion condition obtained through the numerical analysis to find the PVM coefficients. The pressure values used for the regression analysis were obtained by subtracting the hydrostatic pressure from the gauge pressure, which was considered sufficiently converged at a physical time of 2.5 s. We summarized the results for sensors 2 to 7, selected based on the coefficient of determination and MAE among pressure sensors 1 to 11. Sensors 8 to 11 on the parallel body part exhibited pressure characteristics similar to seshinsor 7; hence, we excluded their results. Figure 7 presents the calculated pressure results at the positions of each sensor of the AUV during straight motion. For straight motion, the pressure characteristics of only the left sensor concerning velocity are shown since the pressures for all sensors are equal. The pressure differences among sensors are approximately 500 Pa across all velocity conditions, demonstrating a distinct pressure characteristic concerning velocity. Furthermore, it can be observed that the pressure clearly varies in proportion to the square of the velocity.  
Figure 6: Numerical simulation domain.  
Figure 7: Pressure on the array of sensors during straight motion.  
Figure 8 shows the pressure characteristics of the top, bottom, left, and right sensors concerning velocity and angular velocity during turning motion. In this case, only right turns were considered, resulting in pressure differences between the left and right sensors, while the pressure between the top and bottom sensors remained consistent. The disparity in pressure between the left and right sensors notably appears more pronounced in the front sensors, with substantial changes in the AUV's shape. Then, it seems logical to estimate the drift angle using the pressure data from front-positioned sensors. Figure 9 shows the pressure characteristics of sensors located on the AUV's top, bottom, left, and right sides concerning drift angles during gliding motion at a design speed of 3 knots. Uniform pressures are confirmed at the left and right sensors, and differences are noticeable between the top and bottom sensors, with these differences becoming more pronounced as  
Figure 8: Pressure on the array of sensors during turning motion.  
the sensors are positioned towards the front. The pressure values calculated from the upper sensors are higher than those from the lower sensors due to the negative angle of attack.  
Figure 10 shows the pressure characteristics of the top, bottom, left, and right sensors concerning velocity and angular velocity during turning motion with drift angle. As the drift angle increases, the pressure difference between the left and right sensors becomes more significant, while higher angular velocities are associated with more minor pressure differences.  
Figure 9: Pressure on the array of sensors during gliding motion.  
Figure 11 presents the pressure characteristics of the sensors concerning the drift angles during gliding motion with drift angle at a design speed of 3 knots. As drift angles increase, the pressure differences also increase. Moreover, as in the previous cases, it is noticeable that the pressure difference is more pronounced in the sensors located towards the front. Figure 12 shows the pressure characteristics of sensors concerning the angle of attack and angular velocities during spiral motion at a design speed of 3 knots. As the angle of attack and angular velocity increase, the pressure differences also increase.  
Figure 10: Pressure on the array of sensors during turning motion with drift angle.  
Figure 11: Pressure on the array of sensors during gliding motion with drift angle.