# Modeling and Analysis of Sea-Surface Vehicle System for Underwater Mapping Using Single-Beam Echosounder

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## Abstract

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## 1. Introduction

- In previous studies, bathymetric data measured using a single-beam sonar were analyzed for cases in which the seafloor was inclined in only one axis. In contrast, two axes’ seafloor slope angles are proposed and discussed here for a 3D seafloor.
- The measured bathymetric data are corrected when the seafloor angles are inclined in two axes after the seafloor angles are estimated using the proposed approach.
- To avoid missing the bathymetric measurement of any point in the mapped area, we successfully selected a grid range value on the basis of its geometry.
- The effects of the sonar beam angle, external disturbance, draft of the sonar on the measured bathymetric data and the underwater map, the seafloor slope, and grid range were analyzed in detail.

## 2. Single-Beam Echosounder Model

## 3. Definition of the Effects of Underwater Map Accuracy

#### 3.1. Seafloor Slope Effect

**Definition 1.**

**Definition 2.**

**Lemma 1.**

**Proof.**

#### 3.2. Grid Range Effect

**Lemma 2.**

#### 3.3. Beam Angle of Echosounder Effect

#### 3.4. External Disturbance Effect

**Definition 3.**

#### 3.5. Echosounder Position Effect

**Definition 4.**

## 4. Underwater Mapping Simulator

- the seafloor slope angle;
- the beam angle of the echosounder;
- the grid range in the mapped area;
- the position of the sonar’s transducer;
- the external disturbances to the motion of the sea-surface vehicle in order to show the single-beam echosounder performance.

#### 4.1. Topographical Settings

#### 4.2. Analysis of Underwater Mapping Accuracy

#### 4.2.1. Analysis of the Sea-Bottom Slope Effect

#### 4.2.2. Analysis of the Grid Range and Beam Angle Effect

#### 4.3. Analysis of the Sonar Position Draft/Bias Effect

#### 4.4. Analysis of the External Disturbances Effect

## 5. Underwater Mapping Experiment

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Sea-bottom coverage for a flat seafloor. In this situation, ${h}_{m}=h$. (

**b**) Theta angle ($\theta $) related to the seafloor slope is inside the insonified (conical) area for inclined seafloor. In this situation, ${h}_{m}\ne h$. (

**c**) Theta angle related to the seafloor slope is outside the insonified (conical) area for an inclined seafloor. In this situation, ${h}_{m}\ne h$.

**Figure 3.**(

**a**) Depth measurement without external disturbances and draft of echosounder at the inclined seafloor. (

**b**) Depth measurement with a draft of the echosounder at inclined seafloor. In this situation, the echosounder is below the sea surface by an amount of ${h}_{d}$. (

**c**) Depth measurement with external disturbances in the x and y axes (${\delta}_{x}$ and ${\delta}_{y}$) at the inclined seafloor.

**Figure 6.**Underwater map with measured depth level and underwater map with estimated depth level. Estimated sea-bottom slope angles in the x ($\alpha $) and y ($\beta $) axes.

**Figure 8.**Variation in the absolute and RMS total measured errors (blue lines), and the absolute and RMS total estimated errors (red lines) for different beam angles at a constant grid range without external disturbances.

**Figure 9.**Variation in the absolute and RMS total measured errors (blue lines), and the absolute and RMS total estimated errors (red lines) for different grid ranges at a constant beam angle without external disturbances.

**Figure 10.**Absolute and RMS total meaured errors (blue lines), and absolute and RMS total estimated errors (red lines) related to the draft (or bias) of the echosounder from sea-surface level at a constant grid range and beam angle.

**Figure 11.**Absolute and RMS total measured errors (blue lines), and absolute and RMS total estimated errors (red lines) related to the external-disturbance effect to the oscillation of the sea-surface vehicle at constant grid range and beam angle.

**Figure 15.**Sea-surface vehicle integrated with measurement devices used in the experiment, and the measurement of the acoustic sound velocity in the sea before the experiment (

**right**side).

**Figure 16.**Estimated sea-bottom slope angles in the x ($\alpha $) and y ($\beta $) axes in the experimental area based on experimental data.

**Figure 17.**Underwater map with (

**top**) measured and (

**bottom**) estimated depth levels based on experimental data.

**Figure 19.**(

**top**) Bottom topography model based on the measured map. (

**bottom**) Corrected map model based on the slope of the bottom topography.

Frequency | 24 kHz–210 kHz |

Depth | 5–5000 m |

Acoustic velocity | 1300–1800 m/s |

Accuracy | at—0–100 m, 1 cm |

Beam spread | ±4 minimal degrees |

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**MDPI and ACS Style**

Kartal, S.K.; Hacıoğlu, R.; Görmüş, K.S.; Kutoğlu, Ş.H.; Leblebicioğlu, M.K.
Modeling and Analysis of Sea-Surface Vehicle System for Underwater Mapping Using Single-Beam Echosounder. *J. Mar. Sci. Eng.* **2022**, *10*, 1349.
https://doi.org/10.3390/jmse10101349

**AMA Style**

Kartal SK, Hacıoğlu R, Görmüş KS, Kutoğlu ŞH, Leblebicioğlu MK.
Modeling and Analysis of Sea-Surface Vehicle System for Underwater Mapping Using Single-Beam Echosounder. *Journal of Marine Science and Engineering*. 2022; 10(10):1349.
https://doi.org/10.3390/jmse10101349

**Chicago/Turabian Style**

Kartal, Seda Karadeniz, Rıfat Hacıoğlu, K. Sedar Görmüş, Ş. Hakan Kutoğlu, and M. Kemal Leblebicioğlu.
2022. "Modeling and Analysis of Sea-Surface Vehicle System for Underwater Mapping Using Single-Beam Echosounder" *Journal of Marine Science and Engineering* 10, no. 10: 1349.
https://doi.org/10.3390/jmse10101349