# Improved Velocity Estimation Method for Doppler Sonar Based on Accuracy Evaluation and Selection

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Autocorrelation Function of Sonar Echo

#### 2.1.1. Narrowband Case

_{0}is the distance between the scatterer and the Doppler sonar at t = 0. Assuming the transmitted signal of Doppler sonar is the continuous wave pulse x(t), and its expression is:

_{c}is the carrier frequency, scatterer echo y(t) can be expressed as a time delay function of the transmitted signal:

_{d}= 4πv/λ, and represents the Doppler shift caused by the relative movement between the scatterers and the sonar. Equation (7) demonstrates that the complex autocorrelation function of narrowband echo is only related to the correlation delay τ and the Doppler shift ω

_{d}, and is independent of the carrier frequency ω

_{c}and the initial phase of the echo.

#### 2.1.2. Broadband Case

_{n}(t) represents the nth chip, which can be expressed as:

_{n}is the initial carrier phase of the nth symbol, w

_{n}(t) = u(t − nT

_{c}) − u(t − nT

_{c}− T

_{c}) is the time window function, T

_{c}is the chip width, and u(t) is the unit step function. Equations (8) and (9) can be substituted into Equation (3) in order to obtain the expression of the broadband echo signal:

_{c}represents the pulse width, and ω

_{d}represents the Doppler shift caused by the scatterers’ movement. When the chips are the same, and thus the signal is not encoded, the result of Equation (12) is the same as that of the narrowband case. For the phase-encoded signal, the integral terms of Equation (12) represent the autocorrelation of the code, and the integral result is only related to the chip width T

_{c}and the correlation delay τ. Taking 4-times-repeated 7-bit Barker code as an example, the relationship between the integral term values in Equation (12) and the correlation delay τ is shown in Table 1. It should be noted that the correlation delay in the complex autocorrelation algorithm is generally an integer multiple of the code width.

#### 2.2. Accuracy Selection Method

^{2}can be obtained. Substituting this equation into Equation (29), the following result is obtained:

## 3. Prototype Experiment

#### 3.1. Experiment Implementation

#### 3.2. Water Tank Experiment

#### 3.3. Static Ship Experiment

#### 3.4. Moving Ship Experiment

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Velasco, D.W.; Ogle, M.; Leung, P. Long range current measurement from a surface buoy in the Gulf of Mexico. In Proceedings of the OCEANS 2019 MTS/IEEE SEATTLE, Seattle, WA, USA, 27–31 October 2019; pp. 1–10. [Google Scholar]
- Sirabahenda, Z.; St-Hilaire, A.; Courtenay, S.C.; Van Den Heuvel, M.R. Comparison of acoustic to optical backscatter continuous measurements of suspended sediment concentrations and their characterization in an agriculturally impacted river. Water
**2019**, 11, 981. [Google Scholar] [CrossRef] [Green Version] - Thomas, L.P.; Marino, B.M.; Szupiany, R.N. Application of the two-ADCP technique in estuaries to characterize the suspended particulate matter transport. In Proceedings of the 2017 IEEE/OES Acoustics in Underwater Geosciences Symposium (RIO Acoustics), Rio de Janeiro, Brazil, 25–27 July 2017; pp. 1–5. [Google Scholar]
- Cusi, S.; Rodriguez, P.; Pujol, N.; Pairaud, I.; Nogueras, M.; Antonijuan, J. Evaluation of AUV-borne ADCP measurements in different navigation modes. In Proceedings of the OCEANS 2017–Aberdeen, Aberdeen, UK, 19–22 June 2017; pp. 1–8. [Google Scholar]
- Theriault, K. Incoherent multibeam Doppler current profiler performance: Part I—Estimate variance. IEEE J. Ocean. Eng.
**1986**, 11, 7–15. [Google Scholar] [CrossRef] - Zedel, L. Modeling pulse-to-pulse coherent Doppler sonar. J. Atmos. Ocean. Technol.
**2008**, 25, 1834–1844. [Google Scholar] [CrossRef] - Ivić, I.R. Effects of phase coding on Doppler spectra in PPAR weather radar. IEEE Trans. Geosci. Remote Sens.
**2018**, 56, 2043–2065. [Google Scholar] [CrossRef] - Dillon, J.; Zedel, L.; Hay, A.E. On the distribution of velocity measurements from pulse-to-pulse coherent Doppler sonar. IEEE J. Ocean. Eng.
**2012**, 37, 613–625. [Google Scholar] [CrossRef] - Chi, C.; Vishnu, H.; Beng, K.T.; Chitre, M. Robust resolution of velocity ambiguity for multifrequency pulse-to-pulse coherent Doppler sonars. IEEE J. Ocean. Eng.
**2019**, 45, 1506–1515. [Google Scholar] [CrossRef] - Brumley, B.H.; Cabrera, R.G.; Deines, K.L.; Terray, E.A. Performance of a broad-band acoustic Doppler current profiler. IEEE J. Ocean. Eng.
**1991**, 16, 402–407. [Google Scholar] [CrossRef] - Pinkel, R.; Smith, J.A. Repeat-sequence coding for improved precision of Doppler sonar and sodar. J. Atmos. Ocean. Technol.
**1992**, 9, 149–163. [Google Scholar] [CrossRef] [Green Version] - Tong, J.; Xu, X.; Zhang, T.; Zhang, L.; Li, Y. Study on installation error analysis and calibration of acoustic transceiver array based on SINS/USBL integrated system. IEEE Access
**2018**, 6, 66923–66939. [Google Scholar] - Sun, J.; Wang, J.; Shi, Y.; Hu, F.; Wang, X.; Yu, J.; Zhang, A. Self-noise spectrum analysis and joint noise filtering for the sea-wing underwater glider based on experimental data. IEEE Access
**2020**, 8, 42960–42970. [Google Scholar] [CrossRef] - Koyama, S.; Okubo, K.; Tagawa, N. Performance comparison of signal coding method in acoustic sensing for occlusion area using super-directional sound source. In Proceedings of the 2019 IEEE International Ultrasonics Symposium (IUS), Glasgow, UK, 6–9 October 2019; pp. 603–606. [Google Scholar]
- Wang, Z.; Huang, S.; Wang, S.; Wang, Q.; Zhao, W. Design of electromagnetic acoustic transducer for helical Lamb wave with concentrated beam. IEEE Sens. J.
**2020**, 12, 6305–6313. [Google Scholar] [CrossRef] - Chi, C.; Vishnu, H.; Beng, K.T.; Chitre, M. Utilizing orthogonal coprime signals for improving broadband acoustic Doppler current profilers. IEEE J. Ocean. Eng.
**2019**, 45, 1516–1526. [Google Scholar] [CrossRef] - Jia, T.; Ho, K.C.; Wang, H.; Shen, X. Localization of a moving object with sensors in motion by time delays and Doppler shifts. IEEE Trans. Signal Process.
**2020**, 68, 5824–5841. [Google Scholar] [CrossRef] - Huang, H. Estimating the calibration error-caused bias limit of moving-boat ADCP streamflow measurements. J. Hydraul. Eng. ASCE
**2020**, 146, 06020006. [Google Scholar] [CrossRef] - Despax, A.; Le Coz, J.; Hauet, A.; Mueller, D.S.; Engel, F.L.; Blanquart, B.; Oberg, K.A. Decomposition of uncertainty sources in acoustic Doppler current profiler streamflow measurements using repeated measures experiments. Water Resour. Res.
**2019**, 55, 7520–7540. [Google Scholar] [CrossRef] - Velasco, D.W.; Wilson, W.D.; Nylund, S.; Heitsenrether, R. Enhancing the accuracy of current profiles from surface buoy-mounted systems. In Proceedings of the 2018 OCEANS–MTS/IEEE Kobe Techno–Oceans (OTO), Kobe, Japan, 28–31 May 2018; pp. 1–6. [Google Scholar]
- Velasco, D.W.; Nylund, S. Performance improvement for ADCPs on surface buoys. In Proceedings of the 2019 IEEE/OES Twelfth Current, Waves and Turbulence Measurement (CWTM), San Diego, CA, USA, 10–13 March 2019; pp. 1–6. [Google Scholar]
- Cui, J.; Li, Z.; Li, Q. Strong scattering targets separation based on fractional Fourier transformation in pulse-to-pulse coherent acoustical Doppler current profilers. IEEE J. Ocean. Eng.
**2018**, 44, 466–481. [Google Scholar] [CrossRef] - Prieur, F.; Hansen, R.E. Theoretical improvements when using the second harmonic signal in acoustic Doppler current profilers. IEEE J. Ocean. Eng.
**2012**, 38, 275–284. [Google Scholar] [CrossRef] - Chi, C.; Li, Z.; Li, Q. Design of optimal multiple phase-coded signals for broadband acoustical Doppler current profiler. IEEE J. Ocean. Eng.
**2015**, 41, 302–317. [Google Scholar] - Lin, Y.; Yuan, F.; Cheng, E. Using orthogonal combined signals in broadband ADCP for improving velocity measurement. J. Mar. Sci. Eng.
**2020**, 8, 450. [Google Scholar] [CrossRef] - Murray, J.J. On the Doppler bias of hyperbolic frequency modulation matched filter time of arrival estimates. IEEE J. Ocean. Eng.
**2018**, 44, 446–450. [Google Scholar] [CrossRef]

**Figure 3.**Implementation of the anechoic tank experiment: (

**a**) the top view of the anechoic tank; (

**b**) the installation and fixation of the sonar prototype.

**Figure 4.**(

**a**) Map of the experimental river section and (

**b**) photo of the field experiment implementation.

**Figure 5.**One-beam echo of the sonar prototype in the water tank experiment: (

**a**) a pair of orthogonal down-conversion echoes; (

**b**) the enlarged bottom echoes.

**Figure 7.**One-beam echo of the sonar prototype in the static ship experiment: (

**a**) a pair of orthogonal down-conversion echoes; (

**b**) the enlarged bottom echoes.

**Figure 8.**Bottom velocity estimation results of the three methods in the static ship experiment: (

**a**) beam 1; (

**b**) beam 2; (

**c**) beam 3; (

**d**) beam 4.

**Figure 10.**One-beam echo of the sonar prototype in the moving ship experiment: (

**a**) a pair of orthogonal down-conversion echoes; (

**b**) the enlarged bottom echoes.

**Figure 11.**Bottom velocity estimation results of the three methods in the moving ship experiment: (

**a**) beam 1; (

**b**) beam 2; (

**c**) beam 3; (

**d**) beam 4.

**Table 1.**Relationship between the autocorrelation function amplitude and correlation delay of the broadband echo (Taking 4-times-repeated 7-bit Barker code as an example).

Correlation Delay τ | Integral Term | Amplitude of R(τ) | |
---|---|---|---|

1 | 7T_{c} | 21T_{c} | A^{2}/4 |

2 | 14T_{c} | 14T_{c} | A^{2}/4 |

3 | 21T_{c} | 7T_{c} | A^{2}/4 |

Serial Number | Parameters | Values |
---|---|---|

1 | Carrier frequency | 600 kHz |

2 | System bandwidth | 50 kHz |

3 | Minimum layer thickness | 0.1 m |

4 | Velocity estimation resolution | 0.5 mm/s |

5 | Number of beam | 4 |

6 | Beam spreading | 3 degrees |

7 | Beam angle | 30 degrees |

8 | Velocity measurement range | ±5 m/s |

9 | Maximum profiling distance | 60 m |

10 | Maximum depth | 100 m |

MF Method | WT Method | Proposed Method | |
---|---|---|---|

Mean velocity (m/s) | −0.007 | −0.032 | 0.001 |

Velocity standard deviation (m/s) | 0.011 | 0.009 | 0.001 |

Beam | MF Method | WT Method | Proposed Method | |
---|---|---|---|---|

Mean velocity (m/s) | 1 | 0.053 | 0.034 | 0.027 |

2 | 0.021 | 0.019 | 0.027 | |

3 | 0.037 | 0.045 | 0.053 | |

4 | 0.063 | 0.047 | 0.044 | |

Velocity standard deviation (m/s) | 1 | 0.109 | 0.049 | 0.044 |

2 | 0.154 | 0.108 | 0.084 | |

3 | 0.142 | 0.093 | 0.074 | |

4 | 0.082 | 0.059 | 0.043 | |

Calculation time (ms) | 0.47 | 2.20 | 3.26 |

Beam | MF Method | WT Method | Proposed Method | |
---|---|---|---|---|

Mean velocity (m/s) | 1 | 0.735 | 0.815 | 0.903 |

2 | 0.203 | 0.194 | 0.201 | |

3 | −1.012 | −1.006 | −1.006 | |

4 | −0.162 | −0.151 | −0.137 | |

Velocity standard deviation (m/s) | 1 | 0.363 | 0.281 | 0.120 |

2 | 0.105 | 0.078 | 0.071 | |

3 | 0.133 | 0.101 | 0.066 | |

4 | 0.146 | 0.131 | 0.090 | |

Calculation time (ms) | 0.47 | 0.96 | 3.29 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yang, Y.; Fang, S.
Improved Velocity Estimation Method for Doppler Sonar Based on Accuracy Evaluation and Selection. *J. Mar. Sci. Eng.* **2021**, *9*, 576.
https://doi.org/10.3390/jmse9060576

**AMA Style**

Yang Y, Fang S.
Improved Velocity Estimation Method for Doppler Sonar Based on Accuracy Evaluation and Selection. *Journal of Marine Science and Engineering*. 2021; 9(6):576.
https://doi.org/10.3390/jmse9060576

**Chicago/Turabian Style**

Yang, Yongshou, and Shiliang Fang.
2021. "Improved Velocity Estimation Method for Doppler Sonar Based on Accuracy Evaluation and Selection" *Journal of Marine Science and Engineering* 9, no. 6: 576.
https://doi.org/10.3390/jmse9060576