Skip to main content
SpringerLink
Log in

Multiple Model Algorithm for Single-Beacon Navigation of Autonomous Underwater Vehicle without Its A Priori Position. Part 1. Mathematical Formulation

  • Published:
Gyroscopy and Navigation Aims and scope Submit manuscript

Abstract—

The article considers a problem of autonomous underwater vehicle (AUV) positioning with acoustic measurements of range and possibly radial velocity relative to a single beacon, velocity components and coordinate increments from an inertial navigation system, and the data from a water-speed log or a ground log. Interruptions in acoustic measurements reception are acceptable. Availability of a priori information on relative position of AUV and the beacon is not assumed. In order to solve the problem, the author proposes a multiple model algorithm based on a bank of extended Kalman filters which independently estimate the initial horizontal range and errors of the used data under different hypotheses about a value of AUV initial azimuth relative to the beacon. Current coordinates of AUV are determined by the outputs of filters, taking into account the a posteriori probabilities of the corresponding hypotheses. The algorithm is rather simple for programming and does not require much computational power.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.

Similar content being viewed by others

REFERENCES

  1. Scherbatyuk, A.P., The AUV positioning using ranges from one transponder LBL, Proceedings of OCEANS ‘95 MTS/IEEE, Oct. 9-12,1995. San Diego, CA, USA, 1995, pp. 1620–1623.

  2. Paull, L., Saeedi, S., Seto, M., and Li, H., AUV navigation and localization: A review, IEEE Journal of oceanic engineering, 2014, vol. 39, no. 1, pp. 131–149.

    Article  Google Scholar 

  3. Kebkal, K.G., Mashoshin, A.I., AUV acoustic positioning methods, Gyroscopy and navigation, 2017, vol. 8, no. 1, pp. 80–89.

    Article  Google Scholar 

  4. Boreiko, A.A., Vaulin, Yu.V., Dubrovin, F.S., and Scherbatyuk, A.F., Modern approaches to navigation management for marine robotic systems operation. Proc. 13th Russian National Meeting on Control Issues VSPU-2019, 2019, Moscow, pp. 420-432.

  5. Dubrovin, F.S. and Scherbatyuk, A.F., Studying some algorithms for AUV navigation using a single beacon: The results of simulation and sea trials, Gyroscopy and Navigation, 2016, vol. 7, no. 2, pp. 189–196.

    Article  Google Scholar 

  6. Webster, S.E., Eustice, R.M., Singh, H., and Whitcomb, L.L., Advances in single-beacon one-way-travel-time acoustic navigation for underwater vehicles, The International Journal of Robotics Research, 2012, vol. 31, no 8, pp. 935–950.

    Article  Google Scholar 

  7. Mashoshin, A.I., Studying the accuracy of AUV single-beacon navigation, Podvodnye issledovaniya i robototekhnika, 2017, no. 2, pp. 20–27.

  8. Ferreira, B., Matos, A., and Cruz, N., Single beacon navigation: Localization and control of the MARES AUV, Proceedings of OCEANS ‘10 MTS/IEEE, September 20-23,2010. Seattle, WA, USA, 2010. https://doi.org/10.1109/OCEANS.2010.5664518

  9. Vaulin, Yu.V., Dubrovin, F.S., and Scherbatyuk, A.F., Some algorithms for determining an unknown initial position of AUV using information from a single beacon navigation system, Gyroscopy and Navigation, 2017, vol. 8, no. 3, pp. 64–77.

    Article  Google Scholar 

  10. Pelevin, A.E., Determining an AUV location by the information on the range and its change rate in the case of single-beacon navigation, Proc. 31st Conference in Memory of N.N. Ostryakov, 2–4 October, 2018, St. Petersburg, 2018, pp. 155–162.

  11. Stepanov, O.A., Vasil’ev, V.A., Toropov, A.B., Loparev, A.V., and Basin, M.V., Comparative analysis of filtering algorithms in the problems of polynomial navigation measurements processing, Proc. 31st Conference in Memory of N.N. Ostryakov, 2–4 October,2018, St. Petersburg, 2018, pp. 146–154.

  12. Stepanov, O.A., Vasiliev, V.A., Toropov, A.B., Loparev, A.V., and Basin M.V., Efficiency analysis of a filtering algorithm for discrete-time linear stochastic systems with polynomial measurements, Journal of the Franklin Institute, 2019, vol. 356, no. 10, pp. 5573–5591.

    Article  MathSciNet  Google Scholar 

  13. Palomeras, N., Ridao, P., Ribas, D., and Vallicrosa, G., Autonomous I-AUV docking for fixed-base manipulation, Proceedings of the 19th IFAC World Congress, Aug. 24-29,2014, Cape Town, South Africa, 2014, pp. 12160–12165.

  14. Vallicrosa, G., Ridao, P., Ribas, D., and Palomeras, N., Active range-only beacon localization for AUV homing, Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Sep. 14−18,2014. Chicago, IL, USA, 2014, pp. 2286–2291.

  15. Vallicrosa, G., Ridao, P., Sum of Gaussian single beacon range-only localization for AUV homing, Annual Reviews in Control, 2016, vol. 42, pp. 177–187.

    Article  Google Scholar 

  16. Magill, D.T., Optimal adaptive estimation of sampled stochastic processes, IEEE Transactions on Automatic Control, 1965, vol. 10, no. 4, pp. 434–439.

    Article  MathSciNet  Google Scholar 

  17. Bar-Shalom, Y., Li, X.R., and Kirubarajan, T., Estimation with Applications to Tracking and Navigation, New York: J. Wiley and Sons, 2001.

    Book  Google Scholar 

  18. Stepanov, O.A., Nonlinear Filtering and Its Application in Navigation, St. Petersburg, Russia: Concern CSRI Elektropribor, JSC, 2003.

  19. Dmitriev, S.P., Stepanov, O.A., Multiple model filtering for navigation problems of information processing, Radiotekhnika, 2004, no. 7, pp. 11–17.

  20. Li, X.R., Jilkov, V.P., Survey of maneuvering target tracking. Part V. Multiple-model methods, IEEE Transactions on Aerospace and Electronic Systems, 2005, vol. 41, no. 4, pp. 1255–1321.

    Article  Google Scholar 

  21. Koshaev, D.A., Kalman filter-based multialternative method for fault detection and estimation, Autom. Remote Control, 2010, vol. 71, no. 5, pp. 790–802.

    Article  MathSciNet  Google Scholar 

  22. Stepanov, O.A. and Motorin, A.V., Adaptive estimation methods in navigation problems of information processing, Proc. 13th Russian National Meeting on Control Issues VSPU-2019, 2019, Moscow, pp. 1359–1366.

  23. Siek, Yu.L. and Borisov, A.N., Multiple model estimation of AUV state vector, Proc. 8th Russian National Scientific and Engineering Conference “Technical Challenges of the World Ocean Development”, Vladivostok, 2019, pp. 334−339.

  24. Julier, S.J., Uhlmann, J.K., Unscented filtering and nonlinear estimation, Proceedings of the IEEE, 2004, vol. 92, no. 3, pp. 401–422.

    Article  Google Scholar 

  25. Kulikova, M.V. and Kulikov, G.Yu., Numerical methods for nonlinear filtering of signals and measurements, Computational Technologies, 2016, vol. 21, no. 4, pp. 64–98.

    MATH  Google Scholar 

  26. Rivkin, S.S., Ivanovskii, R.I., and Kostrov, A.V., Statisticheskaya optimizatsiya navigatsionnykh sistem (Statistical Optimization of Navigation Systems), Leningrad: Sudostroenie, 1976.

  27. Doucet, A. and Johansen, A., A tutorial on particle filtering and smoothing: Fifteen years later, In: The Oxford Handbook of Nonlinear Filtering, D. Crisan, B. Rozovsky, Eds., Oxford University Press, 2011, pp. 656–704.

    Google Scholar 

Download references

ACKNOWLEDGMENTS

This work was financially supported by the Government of the Russian Federation (Grant 08-08).

Author information

Authors and Affiliations

  1. Concern CSRI Elektropribor, JSC, 197046, St. Petersburg, Russia

    D. A. Koshaev

  2. ITMO University, 197101, St. Petersburg, Russia

    D. A. Koshaev

Authors
  1. D. A. Koshaev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. A. Koshaev.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Koshaev, D.A. Multiple Model Algorithm for Single-Beacon Navigation of Autonomous Underwater Vehicle without Its A Priori Position. Part 1. Mathematical Formulation. Gyroscopy Navig. 11, 230–243 (2020). https://doi.org/10.1134/S2075108720030037

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2075108720030037

Keywords:

Search

Navigation