# Underwater Wireless Sensor Network-Based Localization Method under Mixed Line-of-Sight/Non-Line-of-Sight Conditions

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## Abstract

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## 1. Introduction

- Proposing a practical TDOA-based algebraic solution for underwater source localization in shallow seas, which addresses the challenges arising from sensor position errors and multipath effects;
- Exploiting the SNLOS link to introduce virtual sensors, providing additional TDOA measurement information;
- Employing the weighted least squares method to obtain an initial estimate of the source position, followed by direct estimation and correction of bias to refine the solution;
- Avoiding the introduction of intermediate parameters, allowing precise localization using only four sensors even when only the LOS link is considered;
- Deriving the CRLB and providing theoretical analysis showing the proposed solution can achieve CRLB accuracy under low noise conditions.

## 2. Related Work

## 3. Scenario and Measurement Model

## 4. The Proposed Algebraic Localization Algorithm

## 5. CRLB and Performance Analysis

#### 5.1. Derivation of CRLB

#### 5.2. Performance Analysis of the Proposed Algorithm

## 6. Simulation Results

#### 6.1. The Impact of the Distance between Source and Sensor Nodes

#### 6.2. The Impact of Using Only Four Sensor Nodes

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Sensor No. | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

${x}_{i}$ | 238 | −640 | 160 | −314 | 560 | 890 |

${y}_{i}$ | −127 | 457 | −200 | 85 | −439 | 232 |

${z}_{i}$ | 330 | 176 | 372 | 157 | 349 | 88 |

Solution | Posed Solution | MP Solution | SDP-MLE |
---|---|---|---|

Time(s) | 3.62 | 5.87 | 2639.7 |

Rel. Time | 1 | 1.62 | 729.20 |

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## Share and Cite

**MDPI and ACS Style**

Liu, Y.; Wang, Y.; Chen, C.; Liu, C.
Underwater Wireless Sensor Network-Based Localization Method under Mixed Line-of-Sight/Non-Line-of-Sight Conditions. *J. Mar. Sci. Eng.* **2023**, *11*, 1642.
https://doi.org/10.3390/jmse11091642

**AMA Style**

Liu Y, Wang Y, Chen C, Liu C.
Underwater Wireless Sensor Network-Based Localization Method under Mixed Line-of-Sight/Non-Line-of-Sight Conditions. *Journal of Marine Science and Engineering*. 2023; 11(9):1642.
https://doi.org/10.3390/jmse11091642

**Chicago/Turabian Style**

Liu, Ying, Yingmin Wang, Cheng Chen, and Chenxi Liu.
2023. "Underwater Wireless Sensor Network-Based Localization Method under Mixed Line-of-Sight/Non-Line-of-Sight Conditions" *Journal of Marine Science and Engineering* 11, no. 9: 1642.
https://doi.org/10.3390/jmse11091642