# A Method of Increasing the Accuracy of Radar Distance Measurement in VTS Systems for Vessels with Very Large Dimensions

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## Abstract

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## 1. Introduction

- Ensuring a high level of safety in the waters covered by monitoring;
- Increasing the efficiency of vessel traffic;
- Protection of the marine environment.

- Coastal radar stations;
- Communication systems;
- Hydro-meteorological conditions monitoring devices;
- Vision camera systems.

## 2. The Gulf of Gdansk VTS System

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- Supervision of the work of foreign and Polish research and development vessels;
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- Supervision of specific sea tows;
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- Supervision and co-operation in the framework of actions and events affecting the protection of the safety of navigation;
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- Co-operation in the implementation of tasks related to NATO’s Naval Co-ordination and Guidance for Shipping (NCAGS).

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- In Wladyslawowo;
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- At the lighthouse in Hel;
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- On the tower of the Port of Gdynia Harbor Master’s Office;
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- On the tower of the Harbor Master’s Office, Gdansk Northern Port;
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- On the radar tower in Gorki Zachodnie;
- •
- At the lighthouse in Krynica Morska.

- •
- In Hel;
- •
- In Gdynia;
- •
- In Gdansk.

- •
- Rozewie radio beacon;
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- Hel radio beacon;
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- Tower of the Harbor Master’s Office of Gdynia;
- •
- Tower of the Harbor Master’s Office of Gdańsk;
- •
- Krynica beacon;
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- Long-range station located on the “Baltic Beta” oil rig.

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- Hel;
- •
- Gdynia;
- •
- Gdansk New Port;
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- Gdansk Northern Port;
- •
- Gorki Zachodnie.

## 3. Model for Correcting the Radar Distance Taking into Account the Shape of the Vessel

## 4. Analytical Determination of the Vessel’s Position with the Use of Redundant Observations

## 5. Experiment Validation

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- For the radar station Hel_LM:

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- For the radar station Gdynia_NW:

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- For the radar station Gdańsk_KPP:

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- For the radar station Gdańsk_GZ:

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- For $\alpha ={133.1}^{\circ}\hspace{0.17em}\mathrm{sb}$ within the range: $\alpha \in \left({090}^{\circ},{\alpha}_{G}\right)$, the correction to the measured distance from Hel_LM station is ${d}_{P\u2019-P}=17.12\hspace{0.17em}\mathrm{m}$;

- •
- For $\alpha ={009.1}^{\circ}\hspace{0.17em}\mathrm{ps}$ within the range: $\alpha \in \left({000}^{\circ},{090}^{\circ}\right)$, the correction to the measured distance from Gdynia_NW station is ${d}_{{P}^{\prime}-P}=54.82\hspace{0.17em}\mathrm{m}$;

- •
- For $\alpha ={094.1}^{\circ}\hspace{0.17em}\mathrm{ps}$ within the range: $\alpha \in \left({090}^{\circ},{\alpha}_{G}\right)$, the correction to the measured distance from Gdansk_KPP station is ${d}_{{P}^{\prime}-P}=12.53\hspace{0.17em}\mathrm{m}$;

- •
- For $\alpha ={110.6}^{\circ}\hspace{0.17em}\mathrm{ps}$ within the range: $\alpha \in \left({090}^{\circ},{\alpha}_{G}\right)$, the correction to the measured distance from Gdansk_GZ station is ${d}_{P\u2019-P}=13.35\hspace{0.17em}\mathrm{m}$.

- For the measured radar distances $\left({d}_{{R}_{i}}\right)$: $L={\left[\begin{array}{c}31.37\\ 51.21\\ 12.41\\ 15.87\end{array}\right]}_{\left[\mathrm{m}\right]}$;
- For the corrected radar distances $\left({d}_{i}\right)$: $L={\left[\begin{array}{c}14.25\\ -3.61\\ -0.12\\ 2.52\end{array}\right]}_{\left[\mathrm{m}\right]}$.

- Ship’s position determined for the measured radar distances $\left({d}_{{R}_{i}}\right)$:
- $\hat{X}={X}^{a}+{\hat{d}}_{X}=\left[\begin{array}{c}6045640.44\\ 350830.93\end{array}\right]+\left[\begin{array}{c}-2.34\\ -14.06\end{array}\right]=\left[\begin{array}{c}6045638.10\\ 350816.87\end{array}\right]=\left[\begin{array}{c}{\hat{X}}_{P}\\ {\hat{Y}}_{P}\end{array}\right]$

with the mean error of the determined ship’s position ${m}_{X}=44.14\hspace{0.17em}\left[\mathrm{m}\right]$; - Ship’s position determined for the corrected radar distances $\left({d}_{i}\right)$:
- $\hat{X}={X}^{a}+{\hat{d}}_{X}=\left[\begin{array}{c}6045640.44\\ 350830.93\end{array}\right]+\left[\begin{array}{c}1.81\\ 8.83\end{array}\right]=\left[\begin{array}{c}6045642.25\\ 350839.75\end{array}\right]=\left[\begin{array}{c}{\hat{X}}_{P}\\ {\hat{Y}}_{P}\end{array}\right]$

with the mean error of the determined ship’s position ${m}_{X}=6.40\hspace{0.17em}\left[\mathrm{m}\right]$.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Radar subsystem of the Zatoka Gdańska VTS System (satellite photo from https://www.google.pl/maps, the accessed date: 14 May 2021).

**Figure 3.**Measurement structure while determining the radar distances d

_{R}measured to the bow section of the hull.

**Figure 4.**Measurement structure for the model when the radar beam hits the side of the vessel’s hull.

**Figure 5.**Measurement structure for the model wherein the radar beam falls on the stern of the vessel.

Symbol | Lokalizacja | Geographical Co-ordinates | Rectangular Co-ordinates | ||
---|---|---|---|---|---|

ϕ | λ | X | Y | ||

Władysławowo | Port of Władysławowo | 54°47.809′ N | 018°25.281′ E | 6,075,231.55 | 334,234.35 |

Hel_LM | Hel Lighthouse | 54°36.003′ N | 018°48.771′ E | 6,052,486.06 | 358,713.75 |

HEL_F | Hel, South breakwater | 54°35.985′ N | 018°48.058′ E | 6,052,476.63 | 357,945.55 |

Gdynia_NW | Gdynia, Wenda Wharf | 54°31.739′ N | 018°33.576′ E | 6,045,119.44 | 342,083.22 |

Gdynia_KP | Gdynia, Harbor Master’s Office | 54°32.021′ N | 018°32.841′ E | 6,045,669.81 | 341,309.47 |

Gdańsk_KPP | Harbor Master’s Office, Gdansk Northern Port | 54°23.987′ N | 018°41.778′ E | 6,030,447.63 | 350,457.03 |

Gdańsk_NP | Gdansk, Nowy Port | 54°24.405′ N | 018°39.658′ E | 6,031,298.79 | 348,189.74 |

Gdańsk_GZ | Radar tower, Gorki Zach. | 54°22.229′ N | 018°46.734′ E | 6,027,017.31 | 355,714.79 |

KM | Krynica Morska, Lighthouse | 54°23.123′ N | 019°27.046′ E | 6,027,506.85 | 399,392.32 |

Baltic Beta | Oil rig | 55°28,896′ N | 018°10,962′ E | 6,151,993.05 | 321,972.12 |

Coastal Radar Stations | Radar Distances ${\mathit{d}}_{\mathit{R}}$$\left[\mathbf{m}\right]$ |
---|---|

Hel Lighthouse (Hel_LM) | 10,409 |

Gdynia, Wenda Wharf (Gdynia_NW) | 8712 |

Gdansk Northern Port (Gdansk_KPP) | 15,185 |

Gorki Zachodnie (Gdansk_GZ) | 19,237 |

Coastal Radar Stations | True Bearing ${\mathit{B}}_{\mathit{R}}^{\mathit{T}}$ |
---|---|

Hel Lighthouse (Hel_LM) | 227.1 |

Gdynia, Wenda Wharf (Gdynia_NW) | 84.6 |

Gdansk Northern Port (Gdansk_KPP) | 359.9 |

Gorki Zachodnie (Gdansk_GZ) | 343.4 |

Coastal Radar Stations | Corrected Radar Distances $\left(\mathit{d}\right)$$\left[\mathbf{m}\right]$ |
---|---|

Hel Lighthouse (Hel_LM) | 10,426.12 |

Gdynia, Wenda Wharf (Gdynia_NW) | 8766.12 |

Gdansk Northern Port (Gdansk_KPP) | 15,197.53 |

Gorki Zachodnie (Gdansk_GZ) | 19,250.35 |

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**MDPI and ACS Style**

Czaplewski, K.; Świerczyński, S.
A Method of Increasing the Accuracy of Radar Distance Measurement in VTS Systems for Vessels with Very Large Dimensions. *Remote Sens.* **2021**, *13*, 3066.
https://doi.org/10.3390/rs13163066

**AMA Style**

Czaplewski K, Świerczyński S.
A Method of Increasing the Accuracy of Radar Distance Measurement in VTS Systems for Vessels with Very Large Dimensions. *Remote Sensing*. 2021; 13(16):3066.
https://doi.org/10.3390/rs13163066

**Chicago/Turabian Style**

Czaplewski, Krzysztof, and Sławomir Świerczyński.
2021. "A Method of Increasing the Accuracy of Radar Distance Measurement in VTS Systems for Vessels with Very Large Dimensions" *Remote Sensing* 13, no. 16: 3066.
https://doi.org/10.3390/rs13163066