# Three-Dimensional Wind Measurement Based on Ultrasonic Sensor Array and Multiple Signal Classification

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## Abstract

**:**

## 1. Introduction

## 2. 3D Wind Measurement

#### 2.1. The Ultrasonic Sensor Array

#### 2.2. Measuring Principle

#### 2.2.1. Premise Assumptions

#### 2.2.2. Signal Model

#### 2.3. Wind Measurement Based on MUSIC Algorithm

^{H}denotes the conjugate transpose. ${\mathrm{R}}_{S}$ and ${\mathrm{R}}_{N}$ are the correlation matrices of signal and noise, respectively. ${\sigma}^{2}$ is the variance of noise, and $I$ is the unit matrix.

## 3. Simulations and Results

#### 3.1. Simulations

#### 3.2. Comparison with State-Of-The-Art Method

- The trends of RMSEs and MAEs are consistent, which all decrease with higher SNR.
- Accordingly, the biggest RMSE and MAE of wind speed and direction occur at SNR of 0 dB. The biggest wind speed RMSE of the proposed method is slightly bigger than that of WSDM2D, while the biggest direction RMSE is smaller.
- The speed and direction RMSEs of proposed method tend to zeros as SNR of 5 dB, outperforming the WSDM2D method, which converges to zero since SNR$=\text{}$15 dB. Wind speed and direction MAEs of two methods have similar patterns with those of RMSEs.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Result of the spectral peak searching: (

**a**) result of peak searching, (

**b**) the slice result in the direction of wind speed, (

**c**) the slice result in the direction of wind azimuth angle, and (

**d**) the slice result in the direction of wind pitch angle.

**Figure 4.**The type A evaluation of standard uncertainty of the results under different SNRs: (

**a**) Measurement uncertainty of the wind speed, (

**b**) measurement uncertainty of the wind pitch angle, and (

**c**) measurement uncertainty of the wind azimuth angle.

**Figure 5.**Results of Root Mean Square Error (RMSE) under different SNRs: (

**a**) RMSE of the wind speed, (

**b**) RMSE of the wind pitch angle, and (

**c**) RMSE of the wind azimuth angle.

**Figure 6.**Results of mean absolute error (MAE) under different SNRs: (

**a**) MAE of the wind speed, (

**b**) MAE of the wind pitch angle, and (

**c**) MAE of the wind azimuth angle.

SNR (dB) | RMSE | MAE | ||||||
---|---|---|---|---|---|---|---|---|

Speed | Direction | Speed | Direction | |||||

Proposed | WSD M2D | Proposed | WSDM2D | Proposed | WSDM2D | Proposed | WSDM2D | |

0 | 6.023 | 3.150 | 4.970 | 13.506 | 0.824 | 0.337 | 0.820 | 1.420 |

5 | 0 | 0.020 | 0 | 0.141 | 0 | 0.004 | 0 | 0.020 |

10 | 0 | 0.010 | 0 | 0.100 | 0 | 0.001 | 0 | 0.010 |

15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

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**MDPI and ACS Style**

Ma, B.; Teng, J.; Zhu, H.; Zhou, R.; Ju, Y.; Liu, S.
Three-Dimensional Wind Measurement Based on Ultrasonic Sensor Array and Multiple Signal Classification. *Sensors* **2020**, *20*, 523.
https://doi.org/10.3390/s20020523

**AMA Style**

Ma B, Teng J, Zhu H, Zhou R, Ju Y, Liu S.
Three-Dimensional Wind Measurement Based on Ultrasonic Sensor Array and Multiple Signal Classification. *Sensors*. 2020; 20(2):523.
https://doi.org/10.3390/s20020523

**Chicago/Turabian Style**

Ma, Bian, Jing Teng, Huixian Zhu, Rong Zhou, Yun Ju, and Shi Liu.
2020. "Three-Dimensional Wind Measurement Based on Ultrasonic Sensor Array and Multiple Signal Classification" *Sensors* 20, no. 2: 523.
https://doi.org/10.3390/s20020523