# Navigation of Underwater Drones and Integration of Acoustic Sensing with Onboard Inertial Navigation System

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## Abstract

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## 1. Introduction

## 2. Baseline Positioning Systems

#### 2.1. Long Baseline Systems

#### 2.2. Ultra-Short Baseline Systems

#### 2.3. Short Baseline Systems

#### 2.4. GPS Intelligent Buoys

#### 2.5. Comparison of Acoustical Positioning Methods

#### 2.6. Positioning Systems Based on Absolute Velocity Measurements

## 3. Various Approaches to Underwater GPS

#### 3.1. Positioning Based on the Bio-Inspired Sensing

#### 3.2. Positioning with GPS and Dual Acoustic Device with USBL and Forward-Looking Sonar Combination

#### 3.3. Positioning Systems Based on Orthogonal Waveforms

#### 3.4. Positioning System Based on GPS Surface Nodes and Encoded Acoustic Signals

#### 3.5. Positioning with Long Baseline (LBL)

#### 3.6. Positioning with Long Baseline (LBL) under Ice

#### 3.7. Synchronous-Clock, One-Way-Travel-Time Acoustic Navigation

#### 3.8. Comparison of Various Approaches to Underwater Positioning

## 4. Doppler Effect-Based Acoustic Navigation

## 5. Navigation with the Aid of Position Estimation Algorithms Based on Acoustic Seabed Sensing and Angle Measurements

#### 5.1. Sonars

#### 5.2. Design and Performance of Sonars

## 6. Position Estimation with Seabed Sensing

- at time instant ${t}_{k+1}$, measure the seabed distances ${L}_{k+1}^{ij}$ using the acoustic sensors $i,j=1,\dots ,M$ and obtain the increments $\Delta {L}_{k+1}^{ij}={L}_{k+1}^{ij}-{L}_{k}^{ij}$;
- considering the direction angles’ values on the current step $({\gamma}_{k+1},{\theta}_{k+1})$ and the previous one $({\gamma}_{k},{\theta}_{k})$, calculate the increments ${(\Delta {e}_{k+1}^{X},\Delta {e}_{k+1}^{Y},\Delta {e}_{k+1}^{Z})}^{T}$ using ${\mathbf{e}}_{k}={({e}_{k}^{X},{e}_{k}^{Y},{e}_{k}^{Z})}^{T}=(cos({\gamma}_{k}+{\gamma}^{i})cos({\theta}_{k}+{\theta}^{j})$, $cos({\gamma}_{k}+{\gamma}^{i})sin({\theta}_{k}+{\theta}^{j})$, $sin({\gamma}_{k}+{\gamma}^{i}){)}^{T}$;
- evaluate the slope estimates $\widehat{\frac{\delta \psi}{\delta x}}\left({\mathbf{x}}_{k}^{ij}\right)$, $\widehat{\frac{\delta \psi}{\delta y}}\left({\mathbf{x}}_{k}^{ij}\right)$, $\widehat{\frac{\delta \psi}{\delta z}}\left({\mathbf{x}}_{k}^{ij}\right)$;

## 7. DOA Measurement Position Estimation

#### 7.1. Pseudo-Measurement Filter

#### 7.2. Conditionally Minimax Nonlinear Filter (CMNF)

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

ADCP | acoustic Doppler current profilers |

AUV | autonomous underwater vehicle |

BL | baseline |

CMNF | conditionally minimax nonlinear filter |

DGPS | differential GPS |

DOA | direction of arrival |

DVL | Doppler velocity logs |

EKF | extended Kalman filter |

FLS | forward looking sonar |

GIB | GPS intelligent buoy |

GPS | Global Positioning System |

INS | inertial navigation system |

KF | Kalman filter |

LBL | long baseline |

MS | mother ship |

OWTT | one-way-travel time |

ROV | remotely operated vehicle |

SAS | synthetic aperture sonars |

SBL | short baseline |

SINS | strap-down inertial navigation system |

SSBL | super-short baseline |

SV | surface vessel |

UAV | unmanned aerial vehicle |

UAPS | underwater acoustic positioning system |

USBL | ultra-short baseline |

WGS84 | World Geodetic System 1984 |

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Method | Position of Beacons/Transponders | Accuracy | Note |
---|---|---|---|

LBL | Sea floor/surface | 0.1–1 m | operation ranges limited (up to 5 km) |

USBL | SV (surface vessel) | $>>$ 1 m | only limited by SV |

SBL | SV/fixed platform | up to 0.1 m | |

GIBs | Sea surface | up to 1 m (as LBL) | easy installation |

Method | Additional Means | Accuracy | Operation Range | Multiple AUV |
---|---|---|---|---|

USBL + FLS | SV (surface vessel) | 1.2 m | Close to SV | No |

Orthogonal waveform | High | Yes | ||

GPS surface beacon | Encoded signals | High | Close to beacon | Yes |

LBL + OWTT | SV (surface vessel) | 1 m (as LBL) | Close to SV | Yes |

**Table 3.**Relative errors of measurement channels and errors of the orientation angles [50].

Scale factor | $1.0\times {10}^{-3}$ | $3.3\times {10}^{-4}$ | $3.3\times {10}^{-4}$ |

Pitch | $9.0\times {10}^{-2}$ | $1.0\times {10}^{-2}$ | $1.0\times {10}^{-2}$ |

Roll | $8.9\times {10}^{-2}$ | $7.2\times {10}^{-4}$ | $5.6\times {10}^{-4}$ |

Yaw | $8.1\times {10}^{-3}$ | $4.2\times {10}^{-3}$ | $3.8\times {10}^{-4}$ |

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**MDPI and ACS Style**

Miller, A.; Miller, B.; Miller, G. Navigation of Underwater Drones and Integration of Acoustic Sensing with Onboard Inertial Navigation System. *Drones* **2021**, *5*, 83.
https://doi.org/10.3390/drones5030083

**AMA Style**

Miller A, Miller B, Miller G. Navigation of Underwater Drones and Integration of Acoustic Sensing with Onboard Inertial Navigation System. *Drones*. 2021; 5(3):83.
https://doi.org/10.3390/drones5030083

**Chicago/Turabian Style**

Miller, Alexander, Boris Miller, and Gregory Miller. 2021. "Navigation of Underwater Drones and Integration of Acoustic Sensing with Onboard Inertial Navigation System" *Drones* 5, no. 3: 83.
https://doi.org/10.3390/drones5030083