# A Pretreatment Method for the Velocity of DVL Based on the Motion Constraint for the Integrated SINS/DVL

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## Abstract

**:**

## 1. Introduction

## 2. Integrated Navigation System of SINS/DVL/MCP/PS

#### 2.1. Error Propagation Model of SINS

#### 2.2. Error Propagation Model of DVL

#### 2.3. Error Propagation Models of MCP and PS

## 3. Data Fusion in the Integration of SINS/DVL/MCP/PS

#### 3.1. Data Fusion with the Subsystems

#### 3.1.1. Standard Kalman Filter

#### 3.1.2. System and Measurement Equations of SINS/DVL

#### 3.1.3. System and Measurement Equations of SINS/MCP and SINS/PS

_{PS}are the heights in SINS and PS, respectively. The variance matrix

**R**corresponding to measurement noise $\mathit{V}$ in Equation (12) is set according to the random noise in h

_{PS}.

#### 3.2. Data Fusion of SINS/DVL/MCP/PS

## 4. Velocity Tracing Method for DVL Based on Motion Constraint

#### 4.1. Analysis of the Relationship between the DVL Error and SINS Navigation Accuracy

#### 4.2. Velocity Tracing Algorithm for DVL Based on AUV Motion Constraints

## 5. Simulations

#### 5.1. Simulation Setting

#### 5.2. Simulation Results and Analysis

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Paull, L.; Saeedi, S.; Seto, M.; Li, H. AUV navigation and localization: A review. IEEE J. Ocean. Eng.
**2014**, 39, 131–149. [Google Scholar] [CrossRef] - Brown, H.; Kim, A.; Eustice, R.M. An overview of autonomous underwater vehicle research and testbed at PeRL. Mar. Technol. Soc. J.
**2009**, 43, 37–47. [Google Scholar] [CrossRef] - Stutters, L.; Liu, H.; Tiltman, C.; Brown, D.J. Navigation technologies for autonomous underwater vehicles. IEEE Trans. Syst. Man Cybern.
**2008**, 38, 581–589. [Google Scholar] [CrossRef] - Titterton, D.H.; Weston, J.L. Strapdown Inertial Navigation Technology, 2nd ed.; Lavenham Press Ltd.: London, UK, 2004; pp. 263–274. [Google Scholar]
- Jalving, B.; Gade, K.; Hagen, O.K. A toolbox of aiding techniques for the HUGIN AUV integrated inertial navigation system. Model. Identif. Control
**2004**, 25, 173–190. [Google Scholar] [CrossRef] - Jalving, B.; Gade, K.; Hagen, O.K. DVL velocity aiding in the HUGIN 1000 integrated inertial navigation system. Model. Identif. Control
**2004**, 25, 223–235. [Google Scholar] [CrossRef] - Lee, P.M.; Jun, B.H. Pseudo long base line navigation algorithm for underwater vehicles with inertial sensors and two acoustic range measurements. Ocean Eng.
**2007**, 34, 416–425. [Google Scholar] [CrossRef] - Lee, P.M.; Jun, B.H.; Kim, K.; Lee, J.; Aoki, T.; Hyakudome, T. Simulation of an inertial acoustic navigation system with range aiding for an autonomous underwater vehicle. IEEE J. Ocean Eng.
**2007**, 32, 327–345. [Google Scholar] [CrossRef] - Geng, Y.R.; Martins, R.; Sousa, J. Accuracy analysis of DVL/IMU/Magnetometer integrated navigation system using different IMUs in AUV. In Proceedings of the 2010 8th IEEE International Conference on Control and Automation, Xiamen, China, 9–11 June 2010; pp. 516–512.
- Lv, Z.P.; Tang, K.H.; Wu, M.P. Online estimation of DVL misalignment angle in SINS/DVL integrated navigation system. In Proceedings of the Tenth International Conference on Electronic Measurement & Instruments, Chengdu, China, 16–19 August 2011; pp. 336–339.
- Kinsey, J.C.; Whitcomb, L.L. In situ alignment calibration of attitude and doppler sensors for precision underwater vehicle navigation: Theory and experiment. IEEE J. Ocean Eng.
**2007**, 32, 286–299. [Google Scholar] [CrossRef] - Liu, X.; Xu, X.; Liu, Y.; Wang, L. Kalman filter for cross-noise in the integration of SINS and DVL. Math. Probl. Eng.
**2014**, 2014. [Google Scholar] [CrossRef] - Ben, Y.Y.; Zhu, Z.J.; Li, Q.; Wu, X. Aided fine alignment for marine SINS. In Proceedings of the 2011 IEEE International Conference on Mechatronics and Automation, Beijing, China, 7–10 August 2011; pp. 1630–1635.
- Li, W.; Wang, J.; Lu, L.; Wu, W. A novel scheme for DVL-aided SINS in-motion alignment using UKF techniques. Sensors
**2013**, 13, 1046–1063. [Google Scholar] [CrossRef] [PubMed] - Tang, K.H.; Wang, J.L.; Li, W.L.; Wu, W.Q. A novel INS and Doppler sensors calibration method for long range underwater vehicle navigation. Sensor
**2013**, 13, 14583–14600. [Google Scholar] [CrossRef] [PubMed] - Xu, X.; Li, P.; Liu, J. A fault-tolerant filtering algorithm for SINS/DVL/MCP integrated navigation system. Math. Probl. Eng.
**2015**, 2015. [Google Scholar] [CrossRef] - Øyvind, H.; Oddvar, H. Model-aided INS with sea current estimation for robust underwater navigation. IEEE Ocean. Eng.
**2011**, 36, 316–337. [Google Scholar] - Xu, W.M.; Liu, Y.C. Algorithm of multi-rate integrating multiple model for underwater target tracking. J. Electron. Inf. Technol.
**2008**, 30, 581–584. [Google Scholar] [CrossRef] - Xu, W.M.; Liu, Y.C.; Yin, X.D. Method for underwater target tracking based on integrating multiple model. Geomat. Inf. Sci. Wuhan Univ.
**2007**, 32, 782–785. [Google Scholar]

**Figure 1.**Integrated navigation scheme of Strapdown Inertial Navigation System/Doppler Velocity Log/Magnetic Compass/Press Sensor (SINS/DVL/MCP/PS).

**Figure 5.**DVL velocity in the navigation frame: (

**a**) East velocity; (

**b**) North velocity; (

**c**) Up velocity.

Axes | Gyro Bias (°/h) | Acce Bias (ug) | ||
---|---|---|---|---|

Constant | Random (White Noise) | Constant | Random (White Noise) | |

x-axis | 0.01 | 0.01 | 50 | 50 |

y-axis | 0.01 | 0.01 | 50 | 50 |

z-axis | 0.01 | 0.01 | 50 | 50 |

Parameters | Pitch | Roll | Yaw |
---|---|---|---|

Amplitude (°) | 1.5 | 1.5 | 1.0 |

Cycle (s) | 8 | 7.5 | 6 |

Initial Phase (°) | 0 | 0 | 0 |

Swinging center (°) | 0 | 0 | 0 |

Statistical Items | Velocity along the y-axis | East Velocity | North Velocity | Upward Velocity | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Sch. 1 | Sch. 2 | Ideal | Sch. 1 | Sch. 2 | Ideal | Sch. 1 | Sch. 2 | Ideal | Sch. 1 | Sch. 2 | Ideal | |

Mean | 5.0002 | 5.0033 | 5 | 0.0005 | 0 | 0 | 5.0009 | 5.0005 | 5.0008 | 0.0004 | 0 | 0 |

Std | 0.4975 | 0.0220 | 0 | 0.4996 | 0.0617 | 0.0618 | 0.5001 | 0.0020 | 0.0220 | 0.5153 | 0.0926 | 0.0925 |

Statistical Items | Pitch | Roll | Yaw | East Velocity | East Velocity | East Velocity | Height | |
---|---|---|---|---|---|---|---|---|

Scheme 1 | Mean | −0.2208 | 0.0935 | −0.3450 | 0 | 0.0015 | −0.0012 | −0.4873 |

Std | 1.0416 | 1.0835 | 3.9327 | 0.0406 | 0.0418 | 0.0073 | 0.2589 | |

Scheme 2 | Mean | −0.2232 | 0.1092 | −0.3507 | 0 | 0.0020 | −0.0015 | −0.4907 |

Std | 0.6773 | 0.5885 | 4.0719 | 0.0056 | 0.0231 | 0.0061 | 0.2540 |

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## Share and Cite

**MDPI and ACS Style**

Zhao, L.-Y.; Liu, X.-J.; Wang, L.; Zhu, Y.-H.; Liu, X.-X.
A Pretreatment Method for the Velocity of DVL Based on the Motion Constraint for the Integrated SINS/DVL. *Appl. Sci.* **2016**, *6*, 79.
https://doi.org/10.3390/app6030079

**AMA Style**

Zhao L-Y, Liu X-J, Wang L, Zhu Y-H, Liu X-X.
A Pretreatment Method for the Velocity of DVL Based on the Motion Constraint for the Integrated SINS/DVL. *Applied Sciences*. 2016; 6(3):79.
https://doi.org/10.3390/app6030079

**Chicago/Turabian Style**

Zhao, Li-Ye, Xian-Jun Liu, Lei Wang, Yan-Hua Zhu, and Xi-Xiang Liu.
2016. "A Pretreatment Method for the Velocity of DVL Based on the Motion Constraint for the Integrated SINS/DVL" *Applied Sciences* 6, no. 3: 79.
https://doi.org/10.3390/app6030079