A Novel Positional Calibration Method for an Underwater Acoustic Beacon Array Based on the Equivalent Virtual Long Baseline Positioning Model
Abstract
:1. Introduction
2. Model of EVLBL
2.1. Analysis of LBL Positioning Errors Caused by AUV Motion
2.2. EVLBL Positioning Model Based on Dead Reckoning
3. Overall Calibration Method for Acoustic Beacon Array
3.1. Calibration Method Based on Trajectory Deviations
3.2. Implementation of Beacon Calibration Method Based on PSO
Algorithm 1 Calibration method of acoustic beacon array based on PSO. |
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4. Simulation
4.1. Conditions for the Simulation
- The distribution of the underwater acoustic beacons within the array is depicted in Figure 5. The green stars represent the release positions of the beacons, indicating the coordinates where the beacons were deployed on the water surface. The blue stars indicate the anchored positions of the beacons, representing their actual locations on the seabed after being influenced by factors such as water currents. The specific positions are detailed in Table 1.
- The simulated trajectory of the AUV is illustrated in Figure 5. The trajectory began from and then underwent a continuous spiral descent motion lasting for 1200 s at a constant speed. Throughout the entire process, the AUV completed a clockwise rotation of 360.0 degrees to simulate the motion state in a real ocean environment.
- The AUV travelled in a clockwise direction, with the heading angle increasing from 30.0 degrees at a constant angular velocity, completing one full rotation. The pitch angle decreased uniformly from 0 to around −1.5 degrees during the spiral descent process and remained constant, uniformly returning to 0 before the end of the trajectory. The roll angle fluctuated near 0 throughout. The specific attitude angle data are shown in Figure 6a.
- The forward velocity of the AUV maintained a constant speed of 4.00 m/s, while the right velocity and upward velocity remained near 0. Specific data are shown in Figure 6b.
- The measurement noise for each attitude angle of the compass was white noise with a standard deviation of 0.30°.
- The measurement noise for the velocity in each direction of the DVL was white noise with a standard deviation of 0.01 m/s.
- The ranging error of the underwater acoustic beacon was specified as 0.1% of the slant range, which was compounded with white noise with a standard deviation of 0.1 m.
4.2. Results and Discussion of the Simulation
5. Conclusions
- As the trajectory of the AUV diverged further from the center of the beacon array and its velocity increased, the errors in the conventional LBL positioning model correspondingly enlarged. The EVLBL positioning model introduced in this study mitigated the positional discrepancies that arose from AUV motion, thereby notably enhancing the accuracy of the localization.
- Compared with the conventional LS method based on individual beacon data calibration, the proposed overall calibration method for beacon arrays based on the LBL trajectory overlap demonstrated significant advantages in terms of the calibration accuracy and stability. In the simulation experiments, the LS method exhibited large calibration errors for beacons distant from the AUV trajectory (up to 6.40 m). In contrast, the PSO algorithm demonstrated balanced calibration errors across all beacons, with the average error controlled around 3.00 m. This not only enhanced the calibration accuracy but also significantly improved the efficiency of the beacon calibration.
- When comparing the performances of various algorithms, the EVPSO algorithm exhibited a higher precision in the beacon array calibration, which was attributable to its comprehensive consideration of both the AUV’s motion and beacon position errors. The simulation experiments revealed that the calibration errors of the EVPSO algorithm for individual beacons were contained within 1.00 m, marking a notable enhancement in calibration accuracy compared with the PSO, which averaged around 3.00 m.
- By comparing the RMSE of the LBL system after the beacon array was calibrated using various methods, it became evident that the EVPSO algorithm, with an RMSE of approximately 1.00 m, significantly outperformed both the PSO algorithm (RMSE ≈ 1.50 m) and the LS algorithm (RMSE > 5.00 m). This outcome reinforced the validity and precision of the overall calibration method for underwater beacon arrays proposed in this paper, which was based on the EVLBL positioning model.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Position | Beacon 1 | Beacon 2 | Beacon 3 |
---|---|---|---|
Release point | (0.00, 0.00, 0.00) | (3239.81, 868.11, 0.00) | (868.11, 3239.81, 0.00) |
Anchored point | (79.36, −91.52, −1018.97) | (3223.05, 867.79, −1000.26) | (817.26, 3156.09, −1008.66) |
Algorithm | (m) | (m) | (m) | (m) | (m) | (m) |
---|---|---|---|---|---|---|
Setpoint | 79.36/0.00 | −91.52/0.00 | 3223.05/0.00 | 867.79/−0.00 | 817.22/0.00 | 3156.09/0.00 |
LS | 80.01/0.66 | −91.43/0.09 | 3216.65/−6.40 | 867.77/−0.02 | 820.15/2.93 | 3156.98/0.89 |
PSO | 76.52/−2.84 | −89.32/2.20 | 3223.49/0.45 | 870.29/2.50 | 813.60/−3.61 | 3156.09/0.01 |
EVPSO | 79.66/0.30 | −92.22/−0.71 | 3223.42/0.38 | 866.94/−0.86 | 816.88/−0.34 | 3156.29/0.20 |
Algorithm | (m) | (m) |
---|---|---|
Uncalibrated | 17.81 | 67.83 |
LS | 5.71 | 2.61 |
PSO | 1.65 | 1.46 |
EVPSO | 1.14 | 1.04 |
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Zhang, G.; Yi, G.; Wei, Z.; Xie, Y.; Qi, Z. A Novel Positional Calibration Method for an Underwater Acoustic Beacon Array Based on the Equivalent Virtual Long Baseline Positioning Model. J. Mar. Sci. Eng. 2024, 12, 825. https://doi.org/10.3390/jmse12050825
Zhang G, Yi G, Wei Z, Xie Y, Qi Z. A Novel Positional Calibration Method for an Underwater Acoustic Beacon Array Based on the Equivalent Virtual Long Baseline Positioning Model. Journal of Marine Science and Engineering. 2024; 12(5):825. https://doi.org/10.3390/jmse12050825
Chicago/Turabian StyleZhang, Ge, Guoxing Yi, Zhennan Wei, Yangguang Xie, and Ziyang Qi. 2024. "A Novel Positional Calibration Method for an Underwater Acoustic Beacon Array Based on the Equivalent Virtual Long Baseline Positioning Model" Journal of Marine Science and Engineering 12, no. 5: 825. https://doi.org/10.3390/jmse12050825