# Sound Source Localization Fusion Algorithm and Performance Analysis of a Three-Plane Five-Element Microphone Array

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Three-Plane Five-Element Microphone Array Model

#### 2.1. Establishment of a Three-Plane Five-Element Microphone Array Model

_{0}, ${t}_{1}$, ${t}_{2}$, ${t}_{3}$, ${t}_{4}$, ${t}_{5}$, and ${t}_{6}$, respectively. Based on the model, the relative time-delay values of six groups are set as ${\tau}_{10}={t}_{1}-{t}_{0}$, ${\tau}_{20}={t}_{2}-{t}_{0}$, ${\tau}_{30}={t}_{3}-{t}_{0}$, ${\tau}_{40}={t}_{4}-{t}_{0}$, ${\tau}_{50}={t}_{5}-{t}_{0}$, and ${\tau}_{60}={t}_{6}-{t}_{0}$. The coordinates of the sound source S are S (x, y, z) in the Cartesian coordinate system and S($r$,$\theta $,$\phi $) in the spherical coordinate system. The distance between the sound source S and M0 is $r$, the projection point of S on the X0Y plane is S′, the elevation angle S0S′ is $\theta $, and the horizontal angle X0S′ is $\phi $. The target sound source S generates sound waves propagating in the form of spherical waves with a propagation speed of c.

#### 2.2. Judgment Criteria for the Sound Source Position Quadrant

## 3. Sound Source Localization Fusion Algorithm of a Three-Plane Five-Element Microphone Array

#### 3.1. Five-Element Microphone Array Localization Algorithm in the X0Y Plane

#### 3.2. Five-Element Microphone Array Localization Algorithm in the X0Z Plane

#### 3.3. Five-Element Microphone Array Localization Algorithm in the Y0Z Plane

#### 3.4. The Three-Plane Five-Element Microphone Array Localization Fusion Algorithm

## 4. Performance Analysis of the Sound Source Localization Fusion Algorithm Based on a Three-Plane Five-Element Microphone Array

#### 4.1. Relationship between Ranging and Direction-Finding and Fusion Algorithm

#### 4.2. Performance Analysis of Direction-Finding via the Fusion Algorithm

#### 4.2.1. Analysis of the Elevation Angle Measurement Precision of the Sound Source

#### 4.2.2. Analysis of the Horizontal Angle Measurement Precision of the Sound Source

#### 4.3. Influence of Time-Delay Estimation Error on Sound Source Localization Performance

## 5. Experimental Measurement Results and Analyses

#### 5.1. Indoor Experiment

#### 5.2. Outdoor Experiment

#### 5.3. Contrast Experiment

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Man, Z.; Qian, W.; Ren, K.; Koutsonikolas, D.; Su, L.; Yanjiao, C. Dolphin: Real-Time Hidden Acoustic Signal Capture with Smartphones. IEEE Trans. Mob. Comput.
**2019**, 18, 560–573. [Google Scholar] - Jena, D.P.; Panigrahi, S.N. Automatic gear and bearing fault localization using vibration and acoustic signals. Appl. Sci.
**2015**, 98, 20–33. [Google Scholar] [CrossRef] - Chan, Y.T.; Ho, K.C. A simple and efficient estimator for hyperbolic location. IEEE Trans. Signal Process.
**1994**, 42, 1905–1915. [Google Scholar] [CrossRef] - Zilong, Z.; Yichao, R.; Jing, Z.; Longjun, D.; Lianjun, C.; Xin, C.; Ruishan, C. A New Closed-Form Solution for Acoustic Emission Source Location in the Presence of Outliers. Appl. Sci.
**2018**, 8, 949. [Google Scholar] - Trung-Kien, L.; Ho, K.C.; Trung-Hieu, L. Rank Properties for Matrices Constructed from Time Differences of Arrival. IEEE Trans. Signal Process.
**2018**, 66, 3491–3503. [Google Scholar] - Gan, R.Z.; Feng, B.; Sun, Q. Three-Dimensional Finite Element Modeling of Human Ear for Sound Transmission. Ann. Biomed. Eng.
**2004**, 32, 847–859. [Google Scholar] [CrossRef] - Vanthornhout, J.; Decruy, L.; Wouters, J.; Simon, J.Z.; Francart, T. Speech Intelligibility Predicted from Neural Entrainment of the Speech Envelope. J. Assoc. Res. Otolaryngol.
**2018**, 19, 181–191. [Google Scholar] [CrossRef] - Fleury, V.; Davy, R. Analysis of jet–airfoil interaction noise sources by using a microphone array technique. J. Sound Vib.
**2016**, 364, 44–66. [Google Scholar] [CrossRef] - Song, Y.L.; Lu, H.C.; Jin, J.M. Sound wave separation method based on spatial signals resampling with single layer microphone array. Acta Phys. Sin.
**2014**, 63, 187–196. [Google Scholar] - Tavakoli, V.M.; Jensen, J.R.; Christensen, M.G.; Benesty, J. A Framework for Speech Enhancement With Ad Hoc Microphone Arrays. IEEE-ACM Trans. Audio Speech
**2016**, 24, 1038–1051. [Google Scholar] [CrossRef] - Xu, W.; Zhang, C.; Ji, X.; Hongyan, X. Inversion of a Thunderstorm Cloud Charging Model Based on a 3D Atmospheric Electric Field. Appl. Sci.
**2018**, 8, 2642. [Google Scholar] [CrossRef] - Su, L.; Ma, L.; Song, W.; Sheng-Ming, G.; Li-Cheng, L. Influences of sound speed profile on the source localization of different depths. Acta Phys. Sin.
**2015**, 64, 024302. [Google Scholar] [CrossRef] - Yook, D.; Lee, T.; Cho, Y. Fast Sound Source Localization Using Two-Level Search Space Clustering. IEEE Trans. Cybern.
**2015**, 46, 20–26. [Google Scholar] [CrossRef] [PubMed] - Bai, M.R.; Chen, C.C. Application of convex optimization to acoustical array signal processing. J. Sound Vib.
**2013**, 332, 6596–6616. [Google Scholar] [CrossRef] - Ma, W.; Liu, X. Improving the efficiency of DAMAS for sound source localization via wavelet compression computational grid. J. Sound Vib.
**2017**, 395, 341–353. [Google Scholar] [CrossRef][Green Version] - Xing, H.; He, G.; Ji, X. Analysis on Electric Field Based on Three Dimensional Atmospheric Electric Field Apparatus. J. Electr. Eng. Technol.
**2018**, 13, 1697–1704. [Google Scholar] - Lylloff, O.; Fernandez-Grande, E.; Agerkvist, F. Improving the efficiency of deconvolution algorithms for sound source localization. J. Acoust. Soc. Am.
**2015**, 138, 172–180. [Google Scholar] [CrossRef] [PubMed] - Chen, Z.; Zhu, H.; Mao, R. Research on localization of the source of cyclostationary sound field. Acta Phys. Sin.
**2011**, 60, 104304. [Google Scholar] - Xu, W.; Feng, X.; Xing, H. Modeling and Analysis of Adaptive Temperature Compensation for Humidity Sensors. Electronics
**2019**, 8, 425. [Google Scholar] [CrossRef] - Flanagan, J. Bandwidth design for speech-seeking microphone arrays. In Proceedings of the IEEE International Conference on Acoustics, Speech, Signal Processing, Tampa, FL, USA, 26–29 April 1985. [Google Scholar]
- Brandstein, M.S.; Silverman, H.F. A practical methodology for speech source localization with microphone arrays. Comput. Speech Lang.
**1997**, 11, 91–126. [Google Scholar] [CrossRef][Green Version] - Miao, F.; Yang, D.; Wen, J.; Lian, X. Moving sound source localization based on triangulation method. J. Sound Vib.
**2016**, 385, 93–103. [Google Scholar] [CrossRef] - Liu, X.J.; Sun, C. A Sound Source Tracking Method Using Linear Prediction location. Audio Eng.
**2010**, 34, 62–66. [Google Scholar] - Qinqi, X.; Yang, P. Sound Source location Algorithm and Error Analysis Based on Tetrahedral Array. Comput. Simul.
**2013**, 30, 296–299. [Google Scholar] - Alon, D.L.; Rafaely, B. Beamforming with Optimal Aliasing Cancellation in Spherical Microphone Arrays. IEEE-ACM Trans. Audio Speech
**2016**, 24, 196–210. [Google Scholar] [CrossRef] - Su, D.; Vidal-Calleja, T.; Miro, J.V. Towards real-time 3D sound sources mapping with linear microphone arrays. In Proceedings of the IEEE International Conference on Robotics & Automation, Singapore, 29 May–3 June 2017. [Google Scholar]
- Smith, J.O.; Abel, J.S. Close-Form Least-Squares Source Location Estimation from Range-Difference Measurements. IEEE Trans. Acoust. Speech Signal Process.
**1988**, 35, 1661–1669. [Google Scholar] [CrossRef] - Alamedapineda, X.; Horaud, R.A. Geometric Approach to Sound Source Localization from Time-Delay Estimates. IEEE-ACM Trans. Audio Speech
**2014**, 22, 1082–1095. [Google Scholar] - Beck, A.; Stoica, P.; Li, J. Exact and Approximate Solutions of Source Localization Problems. IEEE Trans. Signal Process.
**2008**, 56, 1770–1778. [Google Scholar] [CrossRef] - Muravyov, S.; Zlygosteva, G.; Borikov, V. Multiplicative Method for Reduction of Bias in Indirect Digital Measurement Result. Metrol. Meas. Syst.
**2011**, 18, 481–490. [Google Scholar] [CrossRef][Green Version] - Xing, H.; Yan, Y. Detection of Low-Flying Target under the Sea Clutter Background Based on Volterra Filter. Complexity
**2018**, 2018, 1513591. [Google Scholar] [CrossRef] - Parkhill, K.L.; Gulliver, J.S. Indirect measurement of oxygen solubility. Water Res.
**1997**, 31, 2564–2572. [Google Scholar] [CrossRef] - Yang, X.; Xing, H.; Ji, X. Sound Source Omnidirectional Positioning Calibration Method Based on Microphone Observation Angle. Complexity
**2018**, 2018, 2317853. [Google Scholar] [CrossRef]

**Figure 3.**Comparison and analysis of the horizontal angle estimation error of the sound source caused by an elevation angle change.

**Figure 4.**Comparison and analysis of the horizontal angle estimation error of the sound source caused by a horizontal angle change.

**Figure 5.**Relationship between the time-delay estimation error and elevation angle measurement precision.

**Figure 6.**Relationship between the time-delay estimation error and horizontal angle measurement precision.

Basis of Judgment | Quadrant |
---|---|

${\tau}_{30}$ > ${\tau}_{10}$; ${\tau}_{40}$ > ${\tau}_{20}$; ${\tau}_{60}$ > ${\tau}_{50}$ | first quadrant |

${\tau}_{30}$ < ${\tau}_{10}$; ${\tau}_{40}$ > ${\tau}_{20}$; ${\tau}_{60}$ > ${\tau}_{50}$ | second quadrant |

${\tau}_{30}$ < ${\tau}_{10}$; ${\tau}_{40}$ < ${\tau}_{20}$; ${\tau}_{60}$ > ${\tau}_{50}$ | third quadrant |

${\tau}_{30}$ > ${\tau}_{10}$; ${\tau}_{40}$ < ${\tau}_{20}$; ${\tau}_{60}$ > ${\tau}_{50}$ | fourth quadrant |

${\tau}_{30}$ > ${\tau}_{10}$; ${\tau}_{40}$ > ${\tau}_{20}$; ${\tau}_{60}$ < ${\tau}_{50}$ | fifth quadrant |

${\tau}_{30}$ < ${\tau}_{10}$; ${\tau}_{40}$ > ${\tau}_{20}$; ${\tau}_{60}$ < ${\tau}_{50}$ | sixth quadrant |

${\tau}_{30}$ < ${\tau}_{10}$; ${\tau}_{40}$ < ${\tau}_{20}$; ${\tau}_{60}$ < ${\tau}_{50}$ | seventh quadrant |

${\tau}_{30}$ > ${\tau}_{10}$; ${\tau}_{40}$ < ${\tau}_{20}$; ${\tau}_{60}$ < ${\tau}_{50}$ | eighth quadrant |

Sound Source Spherical Coordinates | (2 m, 45°, 60°) |
---|---|

single-plane | (2.1298 m, 44.1055°, 56.7482°) |

three-plane | (2.0840 m, 44.5317°, 57.8079°) |

Sound Source Spherical Coordinates | (3 m, 15°, 45°) |
---|---|

single-plane | (3.1045 m, 14.2482°, 43.9375°) |

three-plane | (3.0729 m, 14.6057°, 44.0026°) |

Sound Source Spherical Coordinates | (4 m, 75°, 30°) |
---|---|

single-plane | (3.9104 m, 74.5260°, 28.5346°) |

three-plane | (3.9570 m, 75.1745°, 29.3421°) |

Experimental Data | Distance Error Rate/% | Elevation Angle Error Rate/% | Horizontal Angle Error Rate/% |
---|---|---|---|

first | 4.20 | 1.04 | 3.65 |

second | 2.43 | 2.63 | 2.22 |

third | 1.08 | 0.23 | 2.19 |

Data Source | Position S | Precision Compensation | Performance Analysis | Distance Error Rate/% | Angle Error Rate/% |
---|---|---|---|---|---|

fusion algorithm | Table 4 | Equation (8) | Equation (12) | 1.08 | Max 2.19 |

Xu and Yang [24] | - | - | Section 3 | Min 3.75 | - |

Su et al. [26] | Figure 8 | joint optimisation | Figure 6 | - | - |

Data Source | Sound Source Spherical Coordinates |
---|---|

fusion algorithm | (4.2 km, 24.1°, −32.7°) |

Data Source | Sound Source Spherical Coordinates |
---|---|

fusion algorithm | (1.4 km, 78.5°, 46.9°) |

Data Source | Coordinates /m | Distance Error Rate/% | Elevation Angle Error Rate/% | Horizontal Angle Error Rate/% |
---|---|---|---|---|

fusion algorithm | (1.5633, 2.6874, 1.0492) | 0.38 | 5.52 | 0.78 |

Yang et al. [33] | - | 3.89 | 7.95 | 0.66 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Xing, H.; Yang, X. Sound Source Localization Fusion Algorithm and Performance Analysis of a Three-Plane Five-Element Microphone Array. *Appl. Sci.* **2019**, *9*, 2417.
https://doi.org/10.3390/app9122417

**AMA Style**

Xing H, Yang X. Sound Source Localization Fusion Algorithm and Performance Analysis of a Three-Plane Five-Element Microphone Array. *Applied Sciences*. 2019; 9(12):2417.
https://doi.org/10.3390/app9122417

**Chicago/Turabian Style**

Xing, Hongyan, and Xu Yang. 2019. "Sound Source Localization Fusion Algorithm and Performance Analysis of a Three-Plane Five-Element Microphone Array" *Applied Sciences* 9, no. 12: 2417.
https://doi.org/10.3390/app9122417