# Method for Localization Aerial Target in AC Electric Field Based on Sensor Circular Array

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## Abstract

**:**

## 1. Introduction

## 2. Localization Principle

_{0}with a radius r is arranged in the center of the array, and the remaining n sensors g

_{1}, g

_{2}, …, g

_{n}are evenly arranged on the circumference. R is the radius of the array, and the charge amount of the air-charged target P in the air is $Q$. The distance from the geometric center of the target to the center of the array is ρ, the azimuth of the target φ is the angle between the projection OT of ρ on the OXY plane and the X axis, the elevation angle θ of the target is the angle between the Z axis and ρ, and the angle between the i sensor and the X axis is φ

_{i}.

## 3. Error Analysis

#### 3.1. Error Model

#### 3.2. Influence of Layout Parameters on Measurement Errors

#### 3.2.1. Value Range of Layout Parameters

#### 3.2.2. Simulation Analysis of the Effect of the Number of Sensors on the Localization Error

^{−6}C. The center of the detector is 10 m away from the target, the elevation angle is 30°, the azimuth angle 30°, the radius of the array is 0.1 m, the radius of the sensor is 1 cm, and the range of the number of sensors is n + 1 = [5,31].

#### 3.2.3. Simulation Analysis of the Influence of Array Radius on Localization Error

#### 3.2.4. Simulation Analysis of the Effect of Sensor Radius on Localization Error

## 4. Building an Optimization Model

#### 4.1. Determination of Constraints

^{−12}C can be used as the minimum induced charge of the sensor designed in this paper. The sensor is a circular plate capacitive sensor with a radius of 1 cm.

#### 4.2. Determination of the Objective Function

## 5. Optimization of Sensor Layout Parameters Based on Genetic Algorithm

#### 5.1. The Solution Process of Genetic Algorithm

**Step****1:**- Establish an optimization model based on the localization principle and error analysis.
**Step****2:**- Determine the encoding method. The mathematical equation of the objective function and constraints in this article is a function optimization problem, so the real number encoding is selected.
**Step****3:****Step****4:**- Initialize the population. The optimization of the layout parameters in this article belongs to a more complicated optimization problem. Therefore, the number of the initial population is set to 200, and the current generation number is g = 1.
**Step****5:**- According to Equation (27), calculate the fitness value of each individual in the contemporary population, and rank the fitness from large to small.
**Step****6:**- Judgment of termination condition. If g ≥ G = 500, the operation is terminated, and the most adaptive individual in the current population is the optimal solution; if g < G, the operation continues, and step 7 is performed.
**Step****7:**- Genetic evolution operation. Genetic evolution includes selection, crossing, and mutation. It is the most basic component of genetic algorithm [36]. After the operation is completed, a new generation of population will be generated. At this time, g = g + 1, go to Step 5.

#### 5.2. Simulation Experiments and Optimization Results

## 6. Experimental Verification

#### 6.1. Detector Hardware Design

#### 6.2. Experimental Platform Construction and Experimental Analysis

_{1}= 0.25 m above the ground and a carton with a height of h

_{2}= 0.15 m from the ground for measurement (not shown in the carton text). As shown in Figure 10b, ρ and H-h constitute the hypotenuse and right angle of a right triangle, respectively. When the hypotenuse of a triangle is constant and the value of the right angle edge of the triangle is changed, the elevation angle will change. Therefore, this experiment is carried out without changing the condition of $\rho $. Therefore, in this experiment, by changing h

_{2}to h

_{1}without changing $\rho $, different elevation angles can be measured under the condition of constant $\rho $ and $\theta $.

_{1}to h

_{2}, the measured value also decreases at the same distance. This is because the field source is closer to the ground and the electric field lines reach the detector as a non-uniform electric field. However, the localization method in this article can still be used. It should be noted that when the azimuth angles are 90° and 270°, no feasible solution can be obtained. In this case, it can only be used for the calculation of distance and elevation angle.

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Xiao, X.; Li, S. Impacts of flexible obstructive working environment on dynamic performances of inspection robot for power transmission line. J. Cent. South Univ. Technol.
**2008**, 15, 869–876. [Google Scholar] [CrossRef] - Azevedo, F.; Dias, A.; Almeida, J.; Oliveira, A.; Ferreira, A.; Santos, T.; Martins, A.; Silva, E. LiDAR-Based Real-Time Detection and Modeling of Power Lines for Unmanned Aerial Vehicles. Sensors
**2019**, 19, 1812. [Google Scholar] [CrossRef] [PubMed][Green Version] - Fan, F.; Ji, Q.; Wu, G.; Wang, M.; Ye, X.; Mei, Q. Dynamic Barrier Coverage in a Wireless Sensor Network for Smart Grids. Sensors
**2019**, 19, 41. [Google Scholar] [CrossRef] [PubMed][Green Version] - Qin, X.; Wu, G.; Lei, J.; Fan, F.; Ye, X. Detecting Inspection Objects of Power Line from Cable Inspection Robot LiDAR Data. Sensors
**2018**, 18, 1284. [Google Scholar] [CrossRef] [PubMed][Green Version] - Hu, Y. Research and Development of Live Working Technology on Transmission and Distribution Lines. High Volt. Eng.
**2006**, 32, 1–10. [Google Scholar] - Zhang, W.; Ning, Y.; Suo, C. A Method Based on Multi-Sensor Data Fusion for UAV Safety Distance Diagnosis. Electronics
**2019**, 8, 1467. [Google Scholar] [CrossRef][Green Version] - Xiao, D.; Ma, Q.; Xie, Y.; Zheng, Q.; Zhang, Z. A power electric field sensor for portable measurement. Sensor
**2018**, 18, 1053. [Google Scholar] [CrossRef][Green Version] - Liu, C.; He, W.; Wang, J. Design of Portable Power Frequency Electric Field Measurement Device. High Volt. Appar.
**2012**, 48, 57–62. [Google Scholar] - Tong, J.; Lie, Y.; Liu, G.; Wang, H.; Jing, X.; Yang, P. Power-frequency Electric Field Measurement Using a Micromachined Electric Field Sensor. J. Electron. Inf. Technol.
**2018**, 12, 3036–3041. [Google Scholar] - Ling, B.; Peng, C.; Ren, R.; Chu, Z.; Zhang, Z.; Lei, H.; Xia, S. Design, Fabrication and Characterization of a MEMS-Based Three-Dimensional Electric Field Sensor with Low Cross-Axis Coupling Interference. Sensors
**2018**, 18, 870. [Google Scholar] [CrossRef][Green Version] - Gu, Z.; Yang, P.; Peng, C. Electric field measurement safety warning system of live working based on MEMS structure. Transducer Microsyst. Technol.
**2017**, 36, 111–113. [Google Scholar] - Zhou, N.; Fang, Z.; Tang, L.; Fan, L.; Zhang, W. Design and analysis of power frequency electric field sensing unit for high voltage near-electricity early warning. Transducer Microsyst. Technol.
**2017**, 36, 111–113. [Google Scholar] - Wang, W.; Wen, G. Electric field examination and alarm display with Hall element. J. Suzhou Univ. (Nat. Sci.)
**2003**, 19, 47–50. [Google Scholar] - Zhang, W.; Yang, C.; Zhou, N. Automatic identification method of voltage level of high voltage transmission line based on SVM. Ferroelectrics
**2017**, 521, 86–93. [Google Scholar] [CrossRef] - Suo, C.; Sun, H.; Zhang, W.; Zhou, N.; Chen, W. Adaptive Safety Early Warning Device for Non-contact Measurement of HVDC Electric Field. Electronics
**2020**, 9, 329. [Google Scholar] [CrossRef][Green Version] - Hu, L.; Wang, S.; Zhang, E. Aspect-Aware Target Detection and Localization by Wireless Sensor Networks. Sensors
**2018**, 18, 2810. [Google Scholar] [CrossRef][Green Version] - Kan, Y.; Wang, P.; Zha, F.; Li, M.; Gao, W.; Song, B. Passive Acoustic Source Localization at a Low Sampling Rate Based on a Five-Element Cross Microphone Array. Sensors
**2015**, 15, 13326–13347. [Google Scholar] [CrossRef][Green Version] - Huang, S.; Wu, Z.; Misra, A. A Practical, Robust and Fast Method for Location Localization in Range-Based Systems. Sensors
**2017**, 17, 2869. [Google Scholar] [CrossRef][Green Version] - Wu, F.; Luo, L.; Jia, T.; Sun, A.; Sheng, G.; Jiang, X. RSSI-Power-Based Direction of Arrival Estimation of Partial Discharges in Substations. Energies
**2019**, 12, 3450. [Google Scholar] [CrossRef][Green Version] - Yan, J.; Qiao, R.; Tang, L.; Zheng, C.; Fan, B. A fuzzy decision based WSN localization algorithm for wise healthcare. China Commun.
**2019**, 4, 208–218. [Google Scholar] - Fan, L.; Zheng, Q.; Kang, X. Baseline optimization for scalar magnetometer array and its application in magnetic target localization. Chin. Phys. B
**2018**, 27, 215–221. [Google Scholar] [CrossRef] - Yin, J.; Xiong, C.; Wang, W. Acoustic Localization for a Moving Source Based on Cross Array Azimuth. Appl. Sci.
**2018**, 8, 1281. [Google Scholar] [CrossRef][Green Version] - Trinks, H.; Haseborg, J. Electric Field Detection and Ranging of Aircraft. IEEE Trans. Aerosp. Electron. Syst.
**1982**, AES-18, 268–274. [Google Scholar] [CrossRef] - Chen, X.; Cui, Z.; Bi, J. Modeling on Passive Ground Electrostatic Detection System with Spherical Electrode. J. Beijing Inst. Technol.
**2004**, 24, 994–997. [Google Scholar] - Li, M.; Feng, X.; Man, X. A Transformer Partial Discharge UHF Localization Method Based on TDOA and TS-PSO. Proc. CSEE
**2019**, 39, 1834–1842. [Google Scholar] - Chen, H.; Zhu, C.; Li, Y.; Xu, D. Research on Calculation and Measurement of Power Frequency Electric Field for Transmission Line. J. Electr. Eng.
**2016**, 11, 40–45. [Google Scholar] - Chen, X.; Cui, Z.; Chen, F. Analysis on the Properties of Electrostatic Target. Trans. Beijing Inst. Technol.
**2005**, 25, 159–163. [Google Scholar] - Tian, D. Design and Implementation of Electrostatic Detection System. Master’s Thesis, Beijing Institute of Technology, Beijing, China, 2007. [Google Scholar]
- Hao, X.; Xu, L.; Cui, Z.; Chen, X. Design of fuze MEMS electrostatic detection array. Opt. Precis. Eng.
**2009**, 17, 1223–1227. [Google Scholar] - Hu, Z.; He, W.; Yao, D.; Wang, J.; Wen, J.; Li, L. Research of High-voltage Power Frequency Electric Field Warning Instrument. Electr. Meas. Instrum.
**2009**, 9, 45–48. [Google Scholar] - Chen, X.; Cui, Z.; Xu, L. Optimization of Round Array Passive Electrostatic Detection System. J. Beijing Inst. Technol.
**2006**, 26, 610–613. [Google Scholar] - Chen, X.; Xu, L.; Bi, J.; Cui, Z. Location Method of Round Array Based Passive Electrostatic Detection System. J. Beijing Inst. Technol.
**2005**, 25, 159–163. [Google Scholar] - Chen, F. Research on Target Identification of Electrostatic Detection. Ph.D. Thesis, Beijing Institute of Technology, Beijing, China, 2006. [Google Scholar]
- Xiao, D.; Liu, H.; Zhou, Q.; Xie, Y.; Ma, Q. Influence and Correction from the Human Body on the Measurement of a Power-Frequency Electric Field Sensor. Sensors
**2016**, 16, 859. [Google Scholar] [CrossRef] [PubMed][Green Version] - Zhu, L.; Zhuang, Z.; Zhang, Q. An Omni-Directional Passive Locatlization Technology of Acoustic Target with Plane Circular Array. Acta Acust.
**1999**, 2, 204–209. [Google Scholar] - Chen, F.; Xu, S.; Zhao, Y.; Zhang, H. An Adaptive Genetic Algorithm of Adjusting Sensor Acquisition Frequency. Sensors
**2020**, 20, 990. [Google Scholar] [CrossRef] [PubMed][Green Version] - Misakian, M.; Fulcomer, P. Measurement of no uniform power frequency electric fields. IEEE Trans. Ind. Electron.
**1983**, 18, 657–661. [Google Scholar] [CrossRef] - Bohnert, K.; Randle, H.; Frosido, G. Field test of interferometric optical fiber high-voltage and current sensors. Proc. SPIE
**1994**, 23, 16. [Google Scholar]

**Figure 6.**Waveform change diagram: (

**a**) electric field strength is 0–31.3 V/m; (

**b**) the electric field strength is 62.5 V/m.

Voltage level (kV) | 10 | 35 | 110 | 220 |

Safe distance (m) | 0.7 | 1.0 | 1.5 | 3.0 |

9 | Numerical Value | Parameter | Numerical Value |
---|---|---|---|

$Q$ | 10^{−6}C | ${k}_{\sigma}$ | 0.4 |

${\rho}_{0}$ | 10 m | ${k}_{R}$ | 0.3 |

$\theta $ | 60° | ${k}_{r}$ | 0.2 |

${\epsilon}_{r}$ | $2.5{\epsilon}_{0}$ | ${k}_{n}$ | 0.1 |

${Q}_{\mathrm{min}}$ | 1.3 × 10^{−12}C | $r$ | 5 to 30 mm |

φ | 30° | $n$ | 4 to 108 |

${\epsilon}_{0}$ | 8.58 × 10^{−12} | ${k}_{e}$ | 0.01 |

$R$ | 0 to 20 cm |

Parameter | Meaning | Set Value |
---|---|---|

m | Initial population | 200 |

G | Maximal genetic algebra | 500 |

${P}_{c}$ | Crossover probability | 80% |

${P}_{m}$ | Mutation probability | 1% |

Serial Number | Distance Accuracy (%) | Array Radius (m) | Sensor Radius (m) | Number of Sensors | Evaluation Function Value |
---|---|---|---|---|---|

1 | 7.2 | 0.2 | 0.015 | 4 | 8.67219 |

2 | 10.8 | 0.199 | 0.015 | 4 | 8.65989 |

3 | 11.5 | 0.199 | 0.015 | 4 | 8.68891 |

4 | 8 | 0.2 | 0.015 | 4 | 8.65807 |

5 | 8.4 | 0.2 | 0.015 | 4 | 8.65588 |

6 | 12.4 | 0.2 | 0.011 | 6 | 11.1286 |

7 | 12.2 | 0.2 | 0.011 | 6 | 11.1308 |

8 | 10.6 | 0.2 | 0.011 | 6 | 11.1282 |

9 | 8.5 | 0.2 | 0.011 | 6 | 11.1253 |

10 | 11.5 | 0.2 | 0.011 | 6 | 11.1303 |

Target Coordinates $\mathit{P}$ | Target Measurement ${\mathit{P}}^{\prime}$ | Sensor0 (kV/m) | Sensor1 (kV/m) | Sensor2 (kV/m) | Sensor3 (kV/m) | Sensor4 (kV/m) | Measurement Error (${\mathit{\rho}}^{\prime},{\mathit{\theta}}^{\prime},{\mathit{\phi}}^{\prime}$) |
---|---|---|---|---|---|---|---|

(1.05,35.52,0) | (0.92,30.89,1.16) | 3.30 | 4.01 | 3.16 | 2.60 | 3.13 | (0.13,4.63,1.16) |

(1.05, 35.52,60) | (1.21,44.12,57.17) | 3.30 | 3.68 | 3.93 | 2.88 | 2.69 | (0.16,8.6,4.57) |

(1.05,42.55, 0) | (0.87,36.40, 2.29) | 2.77 | 3.58 | 2.65 | 2.10 | 2.64 | (0.18,6.15,2.29) |

(1.5,24,0) | (1.67,22.33, 5.14) | 1.34 | 1.49 | 1.30 | 1.24 | 1.28 | (0.17,1.67,5.14) |

(1.5,24,30) | (1.30,18.67,26.10) | 1.34 | 1.4.4 | 1.36 | 1.21 | 1.25 | (0.2,4.8,3.9) |

(1.5,28.25,0) | (1.31,33.05,−1.72) | 1.07 | 1.25 | 1.04 | 0.90 | 1.05 | (0.19,4.8,1.72) |

(2.25,15.73,0) | (1.78,51.2,0) | 0.45 | 0.47 | 0.43 | 0.42 | 0.43 | (0.47,35.47,0) |

(2.2.5,15.73,100) | (×,×,76.29) | 0.45 | 0.46 | 0.47 | 0.45 | 0.43 | (×,×,23.71) |

(2.25,18.39,0) | (1.11,12.1,−11.86) | 0.35 | 0.37 | 0.33 | 0.32 | 0.33 | (1.14,6.29,11.86) |

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**MDPI and ACS Style**

Zhang, W.; Li, P.; Zhou, N.; Suo, C.; Chen, W.; Wang, Y.; Zhao, J.; Li, Y.
Method for Localization Aerial Target in AC Electric Field Based on Sensor Circular Array. *Sensors* **2020**, *20*, 1585.
https://doi.org/10.3390/s20061585

**AMA Style**

Zhang W, Li P, Zhou N, Suo C, Chen W, Wang Y, Zhao J, Li Y.
Method for Localization Aerial Target in AC Electric Field Based on Sensor Circular Array. *Sensors*. 2020; 20(6):1585.
https://doi.org/10.3390/s20061585

**Chicago/Turabian Style**

Zhang, Wenbin, Peng Li, Nianrong Zhou, Chunguang Suo, Weiren Chen, Yanyun Wang, Jiawen Zhao, and Yincheng Li.
2020. "Method for Localization Aerial Target in AC Electric Field Based on Sensor Circular Array" *Sensors* 20, no. 6: 1585.
https://doi.org/10.3390/s20061585