# Locating Ships Using Time Reversal and Matrix Pencil Method by Their Underwater Acoustic Signals

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## Abstract

**:**

## 1. Introduction

## 2. Background

#### 2.1. Matrix Pencil Method

#### 2.2. Time Reversal Method

## 3. Proposed Method

#### 3.1. Matrix Pencil Method

#### 3.1.1. Signal Test

#### 3.1.2. Definition of M

#### 3.2. Time Reversal Method

## 4. Method Validation

#### 4.1. Data Reduction Produced by MPM

#### 4.2. Location Simulation Process

#### 4.2.1. Simulation Analysis Derived by the Change in the Distribution of the Sensors

#### 4.2.2. Simulation Analysis Derived by the Change in Signal of Interest

#### 4.2.3. Simulation Analysis of the Signals Treated with MPM

#### 4.2.4. Simulation Analysis of Signals Treated with MPM, Including Noise Levels

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Processing time and correlation coefficient as a function of M, in a bulk carrier ship signal with a sample rate of 2.2 kHz.

**Figure 5.**Processing time and correlation coefficient as a function of M, in a bulk carrier ship signal with a sample rate of 4.4 kHz.

**Figure 6.**Contour plot of TR calculation accuracy in a rhombus-shaped array in an area of 1 km${}^{2}$ for a landing ship signal. Red triangles are sensor positions and the color scale is a function of the difference between the expected and calculated location.

**Figure 7.**Contour plot of the accuracy in TRM array in an area of 0.72 km${}^{2}$ for a landing ship signal. Red triangles are sensor positions and the color scale is a function of the difference between expected and calculated location.

**Figure 8.**Contour plot of TR calculation accuracy in a TRM in an area of 1 km${}^{2}$ to the Bulk carrier signal. Red triangles are sensor positions and the color scale is a function of the difference between expected and calculated location.

**Figure 9.**Contour plot of the accuracy in the TRM array in an area of 1 km${}^{2}$ to a bulk carrier signal previously treated with MPM (M = 860). Red triangles are the positions of the sensor and the color scale is a function of the difference between the expected and calculated location.

**Figure 10.**Contour plot of TR calculation accuracy in a TRM in an area of 1 km${}^{2}$ to a bulk carrier signal previously treated with MPM (M = 860), and adding random noise in the propagation of the waves. Red triangles are the positions of the sensor and the color scale is a function of the difference between the expected and calculated location.

M | Compression Percentage (%) | Correlation Coefficient (${\mathit{R}}^{2}$) |
---|---|---|

10 | 99.09 | 0.25 |

50 | 97.72 | 0.39 |

80 | 96.36 | 0.441 |

100 | 95.45 | 0.4715 |

200 | 90.909 | 0.5638 |

300 | 86.363 | 0.6318 |

400 | 81.81 | 0.6922 |

500 | 77.305 | 0.756 |

600 | 72.727 | 0.803 |

700 | 68.182 | 0.842 |

800 | 63.687 | 0.8812 |

900 | 59.14 | 0.9312 |

1000 | 54.54 | 0.955 |

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**MDPI and ACS Style**

Chaparro-Arce, D.; Gutierrez, S.; Gallego, A.; Pedraza, C.; Vega, F.; Gutierrez, C.
Locating Ships Using Time Reversal and Matrix Pencil Method by Their Underwater Acoustic Signals. *Sensors* **2021**, *21*, 5065.
https://doi.org/10.3390/s21155065

**AMA Style**

Chaparro-Arce D, Gutierrez S, Gallego A, Pedraza C, Vega F, Gutierrez C.
Locating Ships Using Time Reversal and Matrix Pencil Method by Their Underwater Acoustic Signals. *Sensors*. 2021; 21(15):5065.
https://doi.org/10.3390/s21155065

**Chicago/Turabian Style**

Chaparro-Arce, Daniel, Sergio Gutierrez, Andres Gallego, Cesar Pedraza, Felix Vega, and Carlos Gutierrez.
2021. "Locating Ships Using Time Reversal and Matrix Pencil Method by Their Underwater Acoustic Signals" *Sensors* 21, no. 15: 5065.
https://doi.org/10.3390/s21155065