# Positioning Combination Method of USBL Using Four-Element Stereo Array

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## Abstract

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## 1. Introduction

- (1)
- In view of the poor positioning accuracy of the plane array under a high incident angle, two new arrays were designed, and a vector projection algorithm based on the new array is given. The appropriate formation parameters are found through simulation.
- (2)
- Aiming at the problem of poor positioning accuracy of regular triangular pyramid array at a low incident angle, a virtual quaternion plane array algorithm is proposed.
- (3)
- The three arrays adopt the combination algorithm of vector projection method and cross-array method, which can not only solve the localization problem of signal at a high incident angle, but also ensure that the positioning accuracy of a signal at a low incident angle is not reduced.

## 2. Three Arrays and Algorithm Principle

## 3. Simulation Analysis of Algorithm Performance

## 4. Simulation of Combined Localization Performance

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

USBL | Ultra-short Baseline |

LFM | Linear Frequency Modulation |

AD | Analog to Digital |

FFT | Fast Fourier Transform |

IFFT | Inverse Fast Fourier Transform |

DOA | Direction of Arrival |

## References

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**Figure 9.**Positioning accuracy of stereo array 1. (

**a**) parallel wave algorithm. (

**b**) vector projection algorithm.

**Figure 10.**Positioning accuracy of stereo array 2. (

**a**) parallel wave algorithm. (

**b**) vector projection algorithm.

**Figure 11.**Positioning accuracy of stereo array 3. (

**a**) parallel wave algorithm. (

**b**) vector projection algorithm.

**Figure 15.**Positioning accuracy of stereo array 1. (

**a**) combination algorithm. (

**b**) literature 18 algorithm.

**Figure 16.**Positioning accuracy of stereo array 2. (

**a**) combination algorithm. (

**b**) literature 18 algorithm.

**Figure 18.**Positioning accuracy of planar array. (

**a**) the orthogonal 8-element array. (

**b**) the non-equidistant quaternary array. (

**c**) the orthogonal quaternary array.

**Figure 21.**Comparison between combination algorithm and precombination algorithm for stereo array 3.

Array | Stereo Array 1 | Stereo Array 2 | Stereo Array 3 | Literature 18 | Orthogonal 8-Element Array | Non-Equidistant Quaternary Array | Orthogonal Quaternary Array |
---|---|---|---|---|---|---|---|

Localization time(s) | 0.0939 | 0.0880 | 0.0946 | 0.0937 | 0.0970 | 0.0520 | 0.0628 |

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**MDPI and ACS Style**

Wang, W.; Zhu, M.; Yang, B.
Positioning Combination Method of USBL Using Four-Element Stereo Array. *Sensors* **2021**, *21*, 7722.
https://doi.org/10.3390/s21227722

**AMA Style**

Wang W, Zhu M, Yang B.
Positioning Combination Method of USBL Using Four-Element Stereo Array. *Sensors*. 2021; 21(22):7722.
https://doi.org/10.3390/s21227722

**Chicago/Turabian Style**

Wang, Wei, Min Zhu, and Bo Yang.
2021. "Positioning Combination Method of USBL Using Four-Element Stereo Array" *Sensors* 21, no. 22: 7722.
https://doi.org/10.3390/s21227722