# A New Hybrid Algorithm to Image Lightning Channels Combining the Time Difference of Arrival Technique and Electromagnetic Time Reversal Technique

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## Abstract

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## 1. Introduction

## 2. Data and Methods

#### 2.1. Instruments and Data

#### 2.2. Procedure of TDOA-EMTR Method

- (1)
- For one positioning window, select the VHF electromagnetic signals in the time domain (denoted by ET) and perform a fast Fourier transform (FFT) on them. The obtained signals in the frequency domain are denoted by EF. In this study, the length of one positioning window is set to be 512 sample points (1024 $ns$) and the sliding step for neighboring windows is 128 sample points (256 $ns$).
- (2)
- Conjugate EF (equal to reversing ET in the time domain) and obtain the reversed signal (EF_TR).
- (3)
- Grid the two-dimensional space domain (azimuth and elevation) and calculate the delay vector (A).
- (4)
- Multiply EF_TR by A (EF_TR$\times A$) and obtain the refocused signal (Y) on each grid point in the space.
- (5)
- Calculate the signal power (P) on each grid point using Y. Then the location of the radiation source is determined by searching the grid point with a maximum power P. For a given positioning window, if the location result can pass the thresholds of some filtering metrics, this location result is deemed to be a radiation source on a lightning channel.

#### 2.3. Filtering Noise Events

## 3. Imaging Capacity and Improvement of TDOA and TDOA-EMTR Method

## 4. Detailed Imaging Result of the Natural CG Lightning Flash

## 5. Summary

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of the VHF interferometer configuration and the EMTR method. (

**a**) The three VHF interferometer antennas during the field experiment for this study were configured as a scalene-triangle shape in a horizontal plane, and their locations in Cartesian coordinates are shown in the bracket. A schematic of the received signal waveforms emitted by radiation sources are shown as blue wavy lines on the left side of the antennas. (

**b**) By using the EMTR technique, the signal is reversed and then back-propagated in the space. The reversed signal would focus on the location of the radiation source.

**Figure 2.**An example showing how the domain of the EMTR method for each positioning window can be determined by the result of the TDOA method. (

**a**) The mapping result for the whole negative CG flash provided by the TDOA method. (

**b**) Imaging result of three radiation sources from three consecutive positioning windows. The inset shows the expanded view. Gray dots depict previous lightning radiation sources. (

**c**) For a positioning window that the TDOA method cannot locate any radiation sources, the domain used for the TDOA-EMTR method is determined according to the mapping result of the whole lightning flash by the TDOA method, and is marked by a gray rectangle (0$\xb0$–100$\xb0$ for azimuth and 0$\xb0$–60$\xb0$ for elevation). (

**d**) For a positioning window where the TDOA method can locate at least one source, the domain used for the EMTR method is determined as a spatial range that centers on the TDOA result and extends outward 3°. The initial domain in (

**c**) and (

**d**) ranges from 0$\xb0$–360$\xb0$ for azimuth and 0$\xb0$–90$\xb0$ for elevation, respectively.

**Figure 3.**An example showing the removing of low-power frequency points and its effect on the EMTR imaging result. (

**a**) One segment of recorded VHF signals lasting for 1024 nanoseconds (512 sampling points). (

**b**) The FFT result of the VHF signals. (

**c**) The power P calculated using all of the FFT signals ranging from 28–70 MHz. (

**d**) Same with (

**c**) but the FFT signals ranging from 28–70 MHz with power lower than FFTbase are not included in the calculation. In (

**b**), the frequency points from 20–28 MHz and 70–80 MHz (NoiseSpectrum) are marked by solid black circles and the FFTbase is shown by a dashed gray line. Frequency points with a power smaller than the FFTbase are marked by a black rectangle.

**Figure 5.**Composite high-speed video image (

**a**), imaging result of a negative CG by the TDOA method (

**b**) and the EMTR method with CR and ER as filtering metrics (

**c**,

**d**), where Q is selected to be 10. The numbers of solutions are labeled at the bottom-right corner in panels (

**b**–

**d**).

**Figure 6.**Same as Figure 5

**b**–

**d**, but for the IC lightning flash without the composite high-speed video image. The black rectangle in the left-bottom corner in (

**a**,

**c**) marks the region of the negative leader branches.

**Figure 7.**Imaging results by the TDOA-EMTR method, which are filtered with different thresholds of CR (

**a**–

**c**), and further filtered with SNR (

**d**–

**f**). Note that the imaging result in (

**a**) is the same as that in Figure 5d. The window number Q for CR is 10, 6, and 4 for the left panel, middle panel and right panel, respectively. In all panels, ER is larger than 0.85.

**Figure 8.**Same as Figure 7, but for the IC lightning flash.

**Figure 9.**Statistical result of the received signal amplitude by the TDOA method and the TDOA-EMTR method (with Q = 4 and CR $\ge $ 0.75) for the negative CG (

**a**) and the IC lightning flash (

**b**). In the left y axis, counts of solutions for each signal amplitude are shown; in the right y axis, the ratio of the counts of solutions by the TDOA-EMTR method to that by the TDOA method is shown.

**Figure 10.**The VHF signal and the imaging result by the TDOA method (

**a**–

**b**) and by the EMTR method with different window number Q (

**c**–

**h**) for a breakdown process on the tip of a negative leader. The VHF signal and the variation of elevation with time are shown in the left panel. The azimuth-elevation of the process is shown in the right panel, with the number of radiation sources shown in the upper-right corner. The gray dots depict the sources occurring before this time. Black arrows show the direction of the negative leader.

**Figure 11.**Same as Figure 10, but for scattered discharges on a positive leader channel. In the left panel, the red rectangle marks the weak positive discharge processes imaged by different methods. The gray dots depict the scattered sources from positive discharge processes occurring before this time.

**Figure 12.**Same as Figure 10 but for a leader process (labeled as A) and a K leader on a previous positive leader channel. The three branches of the K leader which occurred simultaneously are labeled as B1, B2 and B3, respectively.

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## Share and Cite

**MDPI and ACS Style**

Li, F.; Sun, Z.; Liu, M.; Yuan, S.; Wei, L.; Sun, C.; Lyu, H.; Zhu, K.; Tang, G.
A New Hybrid Algorithm to Image Lightning Channels Combining the Time Difference of Arrival Technique and Electromagnetic Time Reversal Technique. *Remote Sens.* **2021**, *13*, 4658.
https://doi.org/10.3390/rs13224658

**AMA Style**

Li F, Sun Z, Liu M, Yuan S, Wei L, Sun C, Lyu H, Zhu K, Tang G.
A New Hybrid Algorithm to Image Lightning Channels Combining the Time Difference of Arrival Technique and Electromagnetic Time Reversal Technique. *Remote Sensing*. 2021; 13(22):4658.
https://doi.org/10.3390/rs13224658

**Chicago/Turabian Style**

Li, Fengquan, Zhuling Sun, Mingyuan Liu, Shanfeng Yuan, Lei Wei, Chunfa Sun, Huimin Lyu, Kexin Zhu, and Guoying Tang.
2021. "A New Hybrid Algorithm to Image Lightning Channels Combining the Time Difference of Arrival Technique and Electromagnetic Time Reversal Technique" *Remote Sensing* 13, no. 22: 4658.
https://doi.org/10.3390/rs13224658