# Research and Analysis on the Localization of a 3-D Single Source in Lossy Medium Using Uniform Circular Array

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Model

**X**and

**N**are $M\times 1$ dimensional signal and noise matrix.

**A**is the steering vector.

**S**is $1\times K$ dimensional signal sequence at reference point with signal power of ${\sigma}_{s}^{2}$.

## 3. Proposed Method

**X**can be calculated:

#### 3.1. Phase Method

**R**to estimate the source location. We can thus obtain

#### 3.2. Amplitude Method

**R**,

#### 3.3. Synthesis Method

**R**adequately, we put the phase and amplitude information together to detect the source location in the conductive medium ($\alpha =\beta =\sqrt{\pi f\mu \sigma}$).

#### 3.4. Applicability Analysis

## 4. Numerical Results

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Root mean square errors (RMSEs) of location estimations for single-source in the lossless medium versus SNRs. $\left(r,\theta ,\phi \right)=\left(1200,\frac{\pi}{6},\frac{\pi}{3}\right)$, and the snapshot number is 1000 with 500 independent trials.

**Figure 3.**RMSEs of location estimations for single-source in the lossless medium versus snapshot. $\left(r,\theta ,\phi \right)=\left(1200,\frac{\pi}{6},\frac{\pi}{3}\right)$, and the signal-to-noise ratio (SNR) is 10 dB with 500 independent trials.

**Figure 4.**RMSEs of location estimations for single-source in the weak lossy medium versus SNRs. $\left(r,\theta ,\phi \right)=\left(1200,\frac{\pi}{6},\frac{\pi}{3}\right)$, and the snapshot number is 1000 with 500 independent trials.

**Figure 5.**RMSEs of location estimations for single-source in the weak lossy medium versus snapshot. $\left(r,\theta ,\phi \right)=\left(1200,\frac{\pi}{6},\frac{\pi}{3}\right)$, and the SNR is 10 dB with 500 independent trials.

**Figure 6.**RMSEs of location estimations for single-source in the conductive medium versus SNRs. $\left(r,\theta ,\phi \right)=\left(120,\frac{\pi}{6},\frac{\pi}{3}\right)$, and the snapshot number is 1000 with 500 independent trials.

**Figure 7.**RMSEs of location estimations for single-source in the conductive medium versus snapshot. $\left(r,\theta ,\phi \right)=\left(120,\frac{\pi}{6},\frac{\pi}{3}\right)$, and the SNR is 10 dB with 500 independent trials.

**Figure 8.**RMSEs of location estimations for single-source in the lossy medium versus snapshot. $\left(r,\theta ,\phi \right)=\left(1200,\frac{\pi}{6},\frac{\pi}{3}\right)$, $\sigma $ is unknown, the SNR is 10 dB, and the snapshot number is 1000 with 500 independent trials.

**Figure 9.**RMSEs of location estimations for single-source in the lossy medium versus snapshot. $\left(r,\theta ,\phi \right)=\left(1200,\frac{\pi}{6},\frac{\pi}{3}\right)$, $\sigma $ is known, the SNR is 10 dB, and the snapshot number is 1000 with 500 independent trials.

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**MDPI and ACS Style**

Xue, B.; Qu, X.; Fang, G.; Ji, Y.
Research and Analysis on the Localization of a 3-D Single Source in Lossy Medium Using Uniform Circular Array. *Sensors* **2017**, *17*, 1274.
https://doi.org/10.3390/s17061274

**AMA Style**

Xue B, Qu X, Fang G, Ji Y.
Research and Analysis on the Localization of a 3-D Single Source in Lossy Medium Using Uniform Circular Array. *Sensors*. 2017; 17(6):1274.
https://doi.org/10.3390/s17061274

**Chicago/Turabian Style**

Xue, Bing, Xiaodong Qu, Guangyou Fang, and Yicai Ji.
2017. "Research and Analysis on the Localization of a 3-D Single Source in Lossy Medium Using Uniform Circular Array" *Sensors* 17, no. 6: 1274.
https://doi.org/10.3390/s17061274