# Underwater Target Localization Using Opportunistic Ship Noise Recorded on a Compact Hydrophone Array

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

#### 2.1. The Lloyd–Mirror Pattern (LMP)

#### 2.2. The Image Model

#### 2.3. The Normal-Mode Model in an Isovelocity Environment

- (1)
- A pressure release at the surface ($z=0$);
- (2)
- A perfectly rigid bottom with lossless reflection at the sea bottom, i.e., when $z=D$. Note that, on a first order approximation, this assumption is valid for the test conditions in this work since the bottom is rocky [9].

#### 2.4. Scattering Field from Targets in a Waveguide

## 3. Methods and Material

#### 3.1. Proposed Localization Algorithm for MFP

#### 3.2. Experimental Setup and Data Collection

## 4. Simulation Results

#### Simulation Using the Synthetic Data

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Transmission loss for the experimental conditions obtained using Legendre–Galerkin with 140 modes.

**Figure 5.**The far-field scattering function from the types of target by different frequencies of the source.

**Figure 8.**The far-field scattered acoustic pressure in the waveguide for six different scenarios. (

**a**) The transmitter and receiver are located at $(x=300\phantom{\rule{0.166667em}{0ex}}\mathrm{m},y=0,d=0.5\phantom{\rule{0.166667em}{0ex}}\mathrm{m})$, and $(x=0,y=0,d=70\phantom{\rule{0.166667em}{0ex}}\mathrm{m})$, respectively. The depth of water, depth of target, the radius of target, and the average frequency of the propagated signal of source are 70 m, 25 m, 2 m, and 2500 Hz, respectively. (

**b**) same parameters as (

**a**) with the exception that the depth of the target is 0.5 m; (

**c**) same parameters as (

**a**) with the exception that the radius of target is 1 m; (

**d**) same parameters as (

**a**) with the exception that the radius of target is 10 m; (

**e**), same parameters as (

**a**) with the exception that the location of transmitter is $(x=1000\phantom{\rule{0.166667em}{0ex}}\mathrm{m},y=0,d=0.5\phantom{\rule{0.166667em}{0ex}}\mathrm{m})$; (

**f**), same parameters as (

**a**) with the exception that the location of transmitter and the radius of target are $(x=1000\phantom{\rule{0.166667em}{0ex}}\mathrm{m},y=0,d=0.5\phantom{\rule{0.166667em}{0ex}}\mathrm{m})$ and 0.5 m, respectively.

**Figure 10.**Ambiguity surface of MFP using the proposed estimator and different propagation models. The boxed area shows the maximum scattering energy at a depth of 24.8 m. (

**a**) Ambiguity surface of MFP with Normal-mode model. (

**b**) Ambiguity surface of MFP with image model. (

**c**) Ambiguity surface of MFP with Lloyd–mirror pattern.

**Figure 12.**The ambiguity surface to locate the target based on the Cartesian coordinate system using the proposed estimator and different propagation models at a depth of 24.2 m. (

**a**) Ambiguity surface of MFP with normal-mode model. (

**b**) Ambiguity surface of MFP with image model. (

**c**) Ambiguity surface of MFP with Lloyd–mirror pattern.

Parameters | Values |
---|---|

The sound speed | $c=1490.35$ m/s |

Depth of water | $D=71$ m |

Depth of source | $z\_s=1.3$ m |

Depth of Receiver | $z\_r=70$ m |

The average source frequency | $f=1500$ Hz |

Latitude | Longitude | Depth | |
---|---|---|---|

Target | 44.480366 | −63.51195 | 25 m |

Hydrophone array | 44.4803 | −63.513115 | 70 m |

Parameters | Values |
---|---|

Target diameter | 1.6 m |

The actual range of the target from the array | 93 m |

Depth of the target position from the ocean surface | 25 m |

Type of the target | Rigid |

Depth of ocean | 71.625 m |

Maximum number of polynomials in Legendre function | 15 |

Number of normal modes | 80 |

Number of paths used in the image model | 4 paths |

Sound speed in ocean | 1490 m/s |

Sound speed on seabed | 1600 m/s |

Desired frequency range | 500–2000 Hz |

Density of water | $1000\phantom{\rule{0.166667em}{0ex}}\mathrm{kg}/{\mathrm{m}}^{3}$ |

**Table 4.**The estimated location of the target by the proposed estimator with different models for JASCO’s ship noise.

Propagation Model | Estimated Target Location (x, y, z) | The Horizontal Range Relative Error | The Radial Range Relative Error |
---|---|---|---|

Normal-mode | (89 m, 29 m, 24.8 m) | 0.68% | 0.63% |

Image | (91 m, 9 m, 24.8 m) | 1.64% | 1.24% |

Lloyd-mirror | (116 m, 5 m, 24.8 m) | 24.88% | 20.62% |

**Table 5.**The estimated location of the target by the proposed estimator with different models for the CMA CGM BRAZIL ship noise.

Propagation Model | Estimated Target Location (x, y, z) | The Horizontal Range Relative Error | The Radial Range Relative Error |
---|---|---|---|

Normal-mode ${}^{\left(\mathrm{F}\right)}$ | (88 m, 4 m, 24.2 m) | 5.2786% | 3.8774% |

Image ${}^{\left(\mathrm{F}\right)}$ | (0 m, 0 m, 24.2 m) | 100% | 55.65% |

Lloyd-mirror ${}^{\left(\mathrm{F}\right)}$ | (0 m, 0 m, 24.2 m) | 100% | 55.65% |

Normal-mode ${}^{\left(\mathrm{S}\right)}$ | (85 m, 19 m, 24.2 m) | 6.3467% | 4.7295% |

Image ${}^{\left(\mathrm{S}\right)}$ | (91 m, 6 m, 24.2 m) | 1.90% | 1.19% |

Lloyd-mirror ${}^{\left(\mathrm{S}\right)}$ | (91 m, 6 m, 24.2 m) | 1.90% | 1.19% |

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## Share and Cite

**MDPI and ACS Style**

Mirzaei Hotkani, M.; Bousquet, J.-F.; Seyedin, S.A.; Martin, B.; Malekshahi, E.
Underwater Target Localization Using Opportunistic Ship Noise Recorded on a Compact Hydrophone Array. *Acoustics* **2021**, *3*, 611-629.
https://doi.org/10.3390/acoustics3040039

**AMA Style**

Mirzaei Hotkani M, Bousquet J-F, Seyedin SA, Martin B, Malekshahi E.
Underwater Target Localization Using Opportunistic Ship Noise Recorded on a Compact Hydrophone Array. *Acoustics*. 2021; 3(4):611-629.
https://doi.org/10.3390/acoustics3040039

**Chicago/Turabian Style**

Mirzaei Hotkani, Mojgan, Jean-Francois Bousquet, Seyed Alireza Seyedin, Bruce Martin, and Ehsan Malekshahi.
2021. "Underwater Target Localization Using Opportunistic Ship Noise Recorded on a Compact Hydrophone Array" *Acoustics* 3, no. 4: 611-629.
https://doi.org/10.3390/acoustics3040039