# Underwater Cylindrical Object Detection Using the Spectral Features of Active Sonar Signals with Logistic Regression Models

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## Abstract

**:**

## 1. Introduction

## 2. Introduction to Logistic Regression

## 3. Simulated Underwater Environment

#### 3.1. Scattering and Path Models for Target

#### 3.2. Reverberation Models for Seabed

## 4. Feature Vector Generation

## 5. Learning and Prediction

#### 5.1. 8:2 Shuffle-Split Cross-Validation

#### 5.2. Detection Performance

## 6. Application to Experimental Data

#### 6.1. Experimental Data

#### 6.2. Simulated Training Data

#### 6.3. Results

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 4.**Magnitude spectra of the target response for various rotation angles for an linearly frequency modulated (LFM) signal of 13 kHz center frequency and 14 kHz bandwidth.

**Figure 9.**One example of the ten receiver operation characteristic (ROC) curves with average AUC = 0.8983 and its standard deviation = 0.0036. AUC: area under ROC curve.

**Figure 11.**ROC curve with the learning parameter $\mathbf{\beta}$ of Figure 10 for the test data set.

**Figure 14.**2D plots of the matched filtered backscattering time series of the three objects at the orientation of 0 degrees (broadside). The dB scale is relative to the brightest pixel in each measurement group. The red lines represent the cross range from −2.5 to 2.5 m, where 400 time series are located.

**Figure 15.**One example of 1000 ROC curves with average AUC = 0.9325 and its standard deviation = 0.0038.

Predicted Class | ||||
---|---|---|---|---|

No Target | Target | Total | ||

True class | No target | 18,530 | 3640 | 22,170 |

Target | 3784 | 18,046 | 21,830 | |

Total | 22,314 | 21,686 | 44,000 |

Predicted Class | ||||
---|---|---|---|---|

No Target | Target | Total | ||

True class | No target | 4576 | 924 | 5500 |

Target | 1037 | 4463 | 5500 | |

Total | 5613 | 5387 | 11,000 |

No. | Coef. 2 | Coef.3 | Coef. 2 | Coef. 3 | Coef. 2 | Coef. 3 |
---|---|---|---|---|---|---|

1 | 0.4 | 0.4 | 0.35 | 0.4 | 0.3 | 0.4 |

2 | 0.45 | 0.45 | 0.4 | 0.45 | 0.35 | 0.45 |

3 | 0.5 | 0.5 | 0.45 | 0.5 | 0.4 | 0.5 |

4 | 0.55 | 0.55 | 0.5 | 0.55 | 0.45 | 0.55 |

5 | 0.6 | 0.6 | 0.55 | 0.6 | 0.5 | 0.6 |

6 | 0.65 | 0.65 | 0.6 | 0.65 | 0.55 | 0.65 |

7 | 0.7 | 0.7 | 0.65 | 0.7 | 0.6 | 0.7 |

8 | 0.75 | 0.75 | 0.7 | 0.75 | 0.65 | 0.75 |

9 | 0.8 | 0.8 | 0.75 | 0.8 | 0.7 | 0.8 |

10 | 0.85 | 0.85 | 0.8 | 0.85 | 0.75 | 0.85 |

11 | 0.9 | 0.9 | 0.85 | 0.9 | 0.8 | 0.9 |

**Table 4.**Classification table of the model with the test data for 1000 simulations.The numbers in parentheses indicate the standard deviation.

Predicted Class | ||||
---|---|---|---|---|

No Target | Target | Total | ||

True class | No target | 3479.773 (19.8751) | 120.227 (19.8751) | 3600 |

Target | 568.718 (29.0805) | 1951.282 (29.0805) | 2520 | |

Total | 4048.491 | 2071.509 | 6120 |

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**MDPI and ACS Style**

Seo, Y.; On, B.; Im, S.; Shim, T.; Seo, I.
Underwater Cylindrical Object Detection Using the Spectral Features of Active Sonar Signals with Logistic Regression Models. *Appl. Sci.* **2018**, *8*, 116.
https://doi.org/10.3390/app8010116

**AMA Style**

Seo Y, On B, Im S, Shim T, Seo I.
Underwater Cylindrical Object Detection Using the Spectral Features of Active Sonar Signals with Logistic Regression Models. *Applied Sciences*. 2018; 8(1):116.
https://doi.org/10.3390/app8010116

**Chicago/Turabian Style**

Seo, Yoojeong, Baeksan On, Sungbin Im, Taebo Shim, and Iksu Seo.
2018. "Underwater Cylindrical Object Detection Using the Spectral Features of Active Sonar Signals with Logistic Regression Models" *Applied Sciences* 8, no. 1: 116.
https://doi.org/10.3390/app8010116