Spline reconstruction of the informativeness template in correlation-extreme navigation tasks

The problem of correlation-extreme navigation is addressed based on the reconstructed spline template of informativeness, incorporating a priori information about the safe movement of vessels in conflict navigation spaces. The paper focuses on the practical implementation of intelligent ship motion control guided by the principle of analyzing the geophysical field geometry when enabling autonomous ship movement along an electronic spline trajectory. The study substantiates terrain-based navigation principles by comparing measured navigation parameters with a pre-created virtual informative template via an extreme correlation functional for continuous vessel location updates. An analysis of alternative positioning reveals the advantages and disadvantages of various autonomous map-aided navigation methods, emphasizing their potential accuracy. The hypothesis of spatial and surface field navigation as the sole alternative to satellite systems is examined. Alternative navigation is proposed as an assistive technology to complement traditional satellite positioning, ensuring maximum noise resistance and cybersecurity in operational situational awareness. Integrity monitoring is studied as a modern criterion for validating navigation information. The application of integrity is hypothesized to improve real-time iterative coordinate calculations in alternative positioning. A new procedure is developed to optimize grid approximation point distribution by determining the effective positions of sliding nodes. Computational implementation of a wide range of correlation-extreme navigation tasks is achieved through enhanced Pascal programs. The proposed algorithm, tested with spline function methods, provides harmonized assistance to navigators, extending situational awareness horizons for watch assistants navigating challenging scenarios.

1. Berdyshev, V. I. and V. B. Kostousov. “Navigation of moving objects by geophysical fields.” Journal of Mathematical Sciences 140.6 (2007): 767–795. DOI: 10.1007/s10958-007-0017-5.

2. Stepanov O. A., V. A. Vasilev, Yu. A. Litvinenko, and A. M. Isaev. “Map- Aided Navigation Taking into Account a Priori Information on the Object Trajectory.” 2023 30st Saint Petersburg International Conference on Integrated Navigation Systems (ICINS). — IEEE, 2023. DOI: 10.23919/ICINS51816.2023.10168423.

3. Yuyukin, I. V. “Correlation- extreme navigation through geophysical fields based on the use of spline technology.” Vestnik Gosudarstvennogo universiteta morskogo i rechnogo flota imeni admirala S. O. Makarova 13.4 (2021): 266–274. DOI: 10.21821/2309-5180-2021-13-4-505-517.

4. Koneshov, V. N., P. S. Mikhailov, and V. V. Dorozhkov. “Conditions for determining the coordinates of a moving object on a geophysical landmark.” Geophysical research 24.4 (2023): 43–57. DOI: 10.21455/gr2023.4-3.

5. Yuyukin, I. V. “Correlation- extreme method based on spline functions as an alternative to satellite navigation.” AIP Conference Proceedings 2476.1 (2023): 030030. DOI: 10.1063/5.0102916.

6. Yuyukin, Igor V. “Spline synthesis of the charted reference of the field informativity in mission correlation- extreme navigation.” Vestnik Gosudarstvennogo universiteta morskogo i rechnogo flota imeni admirala S. O. Makarova 14.1 (2022): 25–39. DOI: 10.21821/2309-5180-2022-14-1-25-39.

7. Berdyshev, Vitalii Ivanovich, and Viktor Borisovich Kostousov. “Extremal problems of navigation by geophysical fields.” Eurasian Journal of Mathematical and Computer Applications 6.2 (2018): 4–18. DOI: 10.32523/2306-6172-2018-6-2-4-18.

8. Liu, Wei. “Path Planning Methods in an Environment with Obstacles (A Review).” Mathematics and Mathematical Modeling 1 (2018): 15–58. DOI: 10.24108/mathm.0118.0000098.

9. Yuyukin, Igor V. “Realization of the smoothness of spline trajectory configuration for avoidance of no-go areas in due time.” Vestnik Gosudarstvennogo universiteta morskogo i rechnogo flota imeni admirala S. O. Makarova 16.3 (2024): 421–443. DOI: 10.21821/2309-5180-2024-16-3-421-443.

10. Psiaki, Mark L., Todd E. Humphreys, and Brian Stauffer. “Attackers can spoof navigation signals without our knowledge. Here’s how to fight back GPS lies.” IEEE Spectrum 53.8 (2016): 26–53. DOI: 10.1109/MSPEC.2016.7524168.

11. Falco, Gregory. “The Vacuum of Space Cybersecurity.” 2018 AIAA SPACE and Astronautics Forum and Exposition. American Institute of Aeronautics and Astronautics, Inc., 2018. 5275–5279. DOI: 10.2514/6.2018-5275.

12. Falco, Gregory. “Cybersecurity Principles for Space Systems.” Journal of Aerospace Information Systems 16.2 (2019): 61–70. DOI: 10.2514/1.I010693.

13. Liu, Yang, Sihai Li, Qiangwen Fu, and Zhenbo Liu. “Impact Assessment of GNSS Spoofing Attacks on INS/GNSS Integrated Navigation System.” Sensors 18.5 (2018): 1433. DOI: 10.3390/s18051433.

14. Berdyshev, Vitaly I. “Methods for Tracking an Object Moving in R3 under Conditions of Its Counterac tion.” Doklady Mathematics 109.3 (2024): 291–294. DOI: 10.1134/S1064562424702168.

15. Berdyshev, Vitaly I., and Victor B. Kostousov. “A Trajectory Minimizing the Exposure of a Moving Object.” Proceedings of the Steklov Institute of Mathematics 313.S1 (2021): S21–S32. DOI: 10.1134/S0081543821030044.

16. Lavrenov, R. and F. M,. E. Matsuno. “Modified Spline- Based Navigation: Guaranteed Safety for Obstacle Avoidance.” Interactive Collaborative RoboticsSpringer International Publishing, 2017: 123–133. DOI: 10.1007/978 3-319-66471-2_14.

17. Magid, E. and R. S,. M. K,. A. Lavrenov. “Combining Voronoi Graph and Spline- Based Approaches for a Mobile Robot Path Planning.” Informatics in Control, Automation and Robotics Springer International Publishing, 2020: 475–496. DOI: 10.1007/978-3-030-11292-9_24.

18. Dzhandzhgava, G. I., G. I. Gerasimov and L. I. Avgustov. “Navigation and homing by spatial geophysical f ields.” Izvestiya Sfedu. Engineering Sciences 3(140) (2013): 74–84.

19. Fateev, V.F., D. S. Bobrov, Yu. V. Gostev, E. A. Rybakov, M. N. Karapetyan, R. A. Davlatov, A. O. Dolgodush, and Yu. V. Moskvitin. “Layout of the system on geophysical potential of the earth.” Al’manac of Modern Metrology 4 (2020): 173–184.

20. Stepanov, Oleg Andreevich, and Aleksei Sergeevich Nosov. “The Effect of Measurement Preprocessing intheGravity- Aided Navigation.” 5th Symposium on Terrestrial Gravimetry: Static and Mobile Measurements (TG SMM 2019). — International Association of Geodesy Symposia. — Springer International Publishing, 2021. DOI: 10.1007/1345_2021_131.

21. Yuyukin, Igor V. “Perspective magnetic navigation with using the method of spline functions for optimal formation of the map-aided standard.” Vestnik Gosudarstvennogo universiteta morskogo i rechnogo flota imeni admirala S. O. Makarova 14.4 (2022): 519–534. DOI: 10.21821/2309-5180-2022-14-4-519-534.

22. Toropov, Anton B. Algoritmy filtratsii v zadashah сorrektsii pokazaniy morskoy navigatsionnoy sistemy s ispol’zovaniem nelineynyh izmereniy. Abstract of PhD diss. SPb., 2013.

23. Xi, Menghan, Lin Wu, Qianqian Li, Guocheng Mao, Pengfei Wu, Bing Ji, Lifeng Bao, and Yong Wang. “Matching area selection for arctic gravity matching navigation based on adaptive all‐field extended extremum algorithm.” IET Radar, Sonar & Navigation 18.8 (2024): 1307–1317. DOI: 10.1049/rsn2.12571.

24. Yuyukin, Igor V. “The problem of implementing the concept of maximum integration of heterogeneous data in practical navigation.” Vestnik Gosudarstvennogo universiteta morskogo i rechnogo flota imeni admirala S. O. Makarova 15.6 (2023): 998–1014. DOI: 10.21821/2309-5180-2023-15-6-998-1014.

25. Safin, Ramil, Tatyana Tsoy, Roman Lavrenov, Ilya Afanasyev, and Evgeni Magid. “Modern Methods of Map Construction Using Optical Sensors Fusion.” International Conference on Artificial Life and Robotics (ICAROB 2023). — ALife Robotics Corporation Ltd., 2023. DOI: 10.5954/ICAROB.2023.OS6–6.

26. Morales, Joshua J., Joe J. Khalife, and Zaher M. Kassas. “Information fusion strategies for collaborative inertial radio SLAM.” IEEE Transactions on Intelligent Transportation Systems 23.8 (2022): 12935–12952. DOI: 10.1109/TITS.2021.3118678.

27. Dai, Yeying, and Rui Sun. “An Adaptive and Robust Strategy for GPS/IMU/VO Integrated Navigation.” China Satellite Navigation Conference (CSNC 2024) Proceedings. — Lecture Notes in Electrical Engineering. Springer Nature Singapore, 2024. DOI: 10.1007/978–981–99–6944–9_48.

28. Yan, Xin, Xiaofei Yang, Mengmeng Lou, Hui Ye, Zhengrong Xiang. “Cooperative navigation in unmanned surface vehicles with observability and trilateral positioning method.” Ocean Engineering 306 (2024): 118078. DOI:10.1016/j.oceaneng.2024.118078.

29. Fateev, Vyacheslav, Dmitrii Bobrov, Murat Murzabekov, and Ruslan Davlatov. “Problems of creating autonomous navigation systems on geophysical fields.” E3S Web of Conferences. Vol. 310. EDP Sciences, 2021. DOI: 10.1051/e3sconf/202131003008.

30. Peshekhonov, V.G. “High- Precision Navigation Independently of Global Navigation Satellite Systems Data.” Gyroskopy and Navigation 13.1 (2022): 1–6. DOI: 10.1134/S2075108722010059.

31. Kurshin, Vladimir V., and Andrej V. Molokanov. “Method for assessment of integrity of high-precision navigational sightings.” Rocket- Space Device Engineering and Information Systems 4.2 (2017): 3–10. DOI: 10.17238/issn2409-0239.2017.2.3.

32. Yuyukin, Igor V. “Generalization of the underwater relief image using the spline approximation method on a vector electronic chart.” Vestnik Gosudarstvennogo universiteta morskogo i rechnogo flota imeni admirala S. O. Makarova 16.6 (2024): 910–934. DOI: 10.21821/2309-5180-2024-16-6-910-934.

33. Stepanov, Oleg, Yulia Litvinenko, and Alexey Isaev. “Recursive Estimation Algorithms for AUV Collaborative Navigation in Case of Abnormal Outliers in Measurements.” International Conference on Interactive Collaborative Robotics. — Springer Nature Switzerland, 2024. DOI: 10.1007/978-3-031-71360-6_7.

34. Ivanov, A.V., D. V. Boykov, O. V. Trapeznikova, A. P. Pudovkin, and E. V. Trapeznikov. “Autonomous navigation data integrity monitoring of satellite radio navigation systems based on residual method.” Journal of Physics: Conference Series. Vol. 1546. No. 1. IOP Publishing, 2020. DOI: 10.1088/1742–6596/1546/1/012016.