An Underwater Source Localization Method Using Bearing Measurements
Abstract
:1. Introduction
2. System Model
3. Localization Method
3.1. Initial Solution
3.2. Bias Compensation Method Based on Taylor Expansion
Algorithm 1: The AOA-based localization method based on bias compensation |
Step 1: Set as an identity matrix and solve the optimization problem using (10). A rough value can be obtained. |
Step 2: Reformulate the weighting matrix W with the rough value |
Step 3: Construct constraints based on the (13)–(15). |
Step 4: Get the closed-form of the localization problem using (16) based on the SDP method. |
Step 5: Based on the closed-form solution, construct a constrained optimization equation based on the Taylor expansion as (25) shows. |
Step 6: Use Lagrange multiplier technology to get the bias as (27) shows. |
Step 7: Revise the result using (29) and an improved result can be obtained. |
3.3. CRLB Analysis
4. Simulation and Field Test
4.1. Simulation Test
4.1.1. Simulation 1—Analysis under Different AOA Noises
4.1.2. Simulation 2—Analysis under Different Sensor Numbers
4.1.3. Simulation 3—Analysis of the Algorithms’ Computational Efficiency
4.2. Field Test
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
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Algorithm | WLS (s) | SDP (s) | Proposed (s) |
---|---|---|---|
Running Time | 0.02 | 3.97 | 3.99 |
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Li, P.; Liu, Y.; Yan, T.; Yang, S.; Li, R. An Underwater Source Localization Method Using Bearing Measurements. Sensors 2024, 24, 1627. https://doi.org/10.3390/s24051627
Li P, Liu Y, Yan T, Yang S, Li R. An Underwater Source Localization Method Using Bearing Measurements. Sensors. 2024; 24(5):1627. https://doi.org/10.3390/s24051627
Chicago/Turabian StyleLi, Peijuan, Yiting Liu, Tingwu Yan, Shutao Yang, and Rui Li. 2024. "An Underwater Source Localization Method Using Bearing Measurements" Sensors 24, no. 5: 1627. https://doi.org/10.3390/s24051627
APA StyleLi, P., Liu, Y., Yan, T., Yang, S., & Li, R. (2024). An Underwater Source Localization Method Using Bearing Measurements. Sensors, 24(5), 1627. https://doi.org/10.3390/s24051627