Assessment of the vessel position dead reckoning method error

A method of the calculation of vessel dead reckoning coordinates with the accuracy assessment is proposed. It is based on previously derived formulas for the assessment of the uncertainty boundaries for vessel geodetic latitude and longitude during its motion along the ellipsoid surface. The above formulas are used as follows. At first, the latitude and its precision index are calculated. After, they are used for the calculation of the longitude and its precision index. As the result, it is possible to determine uncertainty intervals for vessel coordinates derived with dead reckoning. The implementation of this method for testing an electronic chart display and information system Navi-Sailor 4000 as to the calculation of vessel dead reckoning coordinates with it is shown. The provision of the information about vessel heading and speed through water is carried out to the system in real-time mode by means of a signal simulator. The speed and heading are remaining unchanged during one-hour time interval. During the above time interval, the data about dead reckoning coordinates are recording into a log-file, then the data are converted in a text format and used for the test. The dead reckoning coordinates, calculated by the system, are in the limits of uncertainty assessed with the proposed method. A limitation of the method is that it does not take into account the influence of errors due to rounding because of the finiteness of the computer bit grid. After the elimination of the above limitation, it seems to be possible to use a modernized version of the method as a part of a procedure for testing the navigational systems which give the information about vessel dead reckoning coordinates.

1. Kavraisky, A. V. “Algorithms for Precise Solution of the Direct and Inverse Navigation Problems.” Navigation and hydrography 14 (2002): 126–136.

2. Panteleev, N. F. V. V. Kuznetsov, A. G. Glazkov, and A. A. Vlasova. “Schislenie geodezicheskikh koordinat B, L, h dlya ob”ektov, dvizhushchikhsya po poverkhnosti Zemli.” Trudy FGUP “NPTsAP”. Sistemy i pribory upravleniya 1 (2010): 69–72.

3. Sokolov, A. U., and A. V. Motorin. “Sea currents estimation methods for the dead reckoning.” Underwater Investigations and Robotics 1(35) (2021): 41–50. DOI: 10.37102/1992-4429_2021_35_01_04.

4. Golovan, A. A., V. Y. Mishin, M. V. Chirkin, and A. V. Molchanov. “Method for analyzing the influence of the errors induced by the gyroscopic channel of a strapdown ins in the autonomous mode.” Journal of Computer and Systems Sciences International 60.4 (2021): 627–638. DOI: 10.1134/S1064230721040043.

5. Kikin, I.S. “Autonomous correction of a single-channel inertial control system.” Herald of computer and information technologies 17.11(197) (2020): 3–12. DOI: 10.14489/vkit.2020.11. pp.003-012.

6. Babichenko, A. V., A. V. Nekrasov, N. V. Borodaev, and O. A. Borodaeva. “On the issue of the accuracy ensuring of mathematical modeling of without platform inertial systems.” Avtomatizatsiya. Sovremennye tekhnologii 75.3 (2021): 126–135.

7. Skulstad, Robert, Robert Skulstad, Guoyuan Li, Thor I. Fossen, Bjornar Vik, and Houxiang Zhang. “Dead reckoning of dynamically positioned ships: Using an efficient recurrent neural network.” IEEE Robotics & Automation Magazine 26.3 (2019): 39–51. DOI: 10.1109/MRA.2019.2918125.

8. Sokolov, A., and A. Motorin. “Estimation of log dead reckoning error induced by tidal currents.” IOP Conference Series: Materials Science and Engineering. Vol. 984. No. 1. IOP Publishing, 2020. DOI: 10.1088/1757-899X/984/1/012008.

9. Qiu, Baochun, Maofa Wang, Houwei Li, Li Ma, Xiuquan Li, Zefei Zhu, and Fan Zhou. “Development of hybrid neural network and current forecasting model based dead reckoning method for accurate prediction of underwater glider position.” Ocean Engineering 285 (2023): 115486. DOI: 10.1016/j.oceaneng.2023.115486.

10. Mikhal’skii, V. A., and V. A. Katenin. Metrologiya v korablevozhdenii i reshenie zadach navigatsii. SPb.: Elmor, 2009.

11. Deryabin, Viсtor V. “The assessment of the vessel’s longitude dead reckoning method error.” Vestnik Gosudarstvennogo universiteta morskogo i rechnogo flota imeni admirala S. O. Makarova 11.3 (2019): 430–438. DOI: 10.21821/2309-5180-2019-11-3-430-438.

12. Deryabin, Viсtor V. “Assessment of a method error of dead reckoning of a vessel’s latitude.” Vestnik Gosudarstvennogo universiteta morskogo i rechnogo flota imeni admirala S. O. Makarova 9.6 (2017): 1159–1167. DOI: 10.21821/2309-5180-2017-9-6-1159-1167.

13. Bromberg, P. V. Teoriya inertsial’nykh sistem navigatsii. M.: Nauka, 1979.