Skip to main content
SpringerLink
Log in

Polynomial Filtering Algorithm Applied to Navigation Data Processing under Quadratic Nonlinearities in System and Measurement Equations. Part 2. Solution Examples

  • Published:
Gyroscopy and Navigation Aims and scope Submit manuscript

Abstract

In the first part of the paper, a polynomial filter has been proposed for filtering under quadratic nonlinearities both in the system and measurement equations. The second part details its features and advantages over the extended Kalman filter and illustrates them using a methodological example and examples of navigation data processing.

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. Stepanov, O.A., Litvinenko, Yu.A., Vasiliev, V.A., Toropov, A.B., and Basin, M. V., Polynomial filtering algorithm applied to navigation data processing under quadratic nonlinearities in system and measurement equations. Part 1. Description and comparison with Kalman type algorithms, Gyroscopy and Navigation, 2021, vol. 12, no. 3, pp. 205–223.

    Article  Google Scholar 

  2. Toropov, A.B., Stepanov, O.A., Basin, M.V., Vasiliev, V.A., and Loparev, A.V., Polynomial filtering algorithm for single-beacon navigation problem, 17th IFAC Workshop on Control Applications of Optimization (CAO 2018), IFAC-PapersOnLine, 2018, vol. 51, no. 32, pp. 619–623.

  3. Vasiliev, V.A., Application of the polynomial filtering algorithm to identification of the narrowband process parameters, International Workshop on Navigation and Motion Control (NMC 2020), Samara, Russia, Belokonov, I.V., Ed., pp. 79–81.

  4. Pelevin, A.E., Identification of vehicle model parameters under external disturbances, Gyroscopy and Navigation, 2015, vol. 6, no. 2, pp. 143–148.

    Article  Google Scholar 

  5. 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, pp. 5573–5591.

    Article  MathSciNet  Google Scholar 

  6. Toropov, A.B., Loparev, A.V., and Pelevin, A.E., Comparing AUV positioning algorithms applied in single-beacon navigation, XXXII konferentsiya pamyati vydayushchegosya konstruktora giroskopicheskikh priborov N.N. Ostryakova (32nd Conference in Memory of N.N. Ostryakov), St. Petersburg: Elektrorpibor, 2020, pp. 332–336.

  7. Kashintsev, N.A. and Loparev, A.V., Using the polynomial filtering method for AUV positioning, XX konferentsiya molodykh uchenykh “Navigatsiya i upravlenie dvizheniem” (20th Anniversary Conference of Young Scientists “Navigation and Motion Control”), 2018, St. Petersburg: Elektropribor, pp. 177–179.

  8. Loparev, A.V., Zaitsev, O.V., and Antonov, D.V., Using adaptive algorithms for predicting the ship oscillation angles, Upravlenie v morskikh sistemakh (Control in Maritime Systems), 13 mul’tikonferentsiya po problemam upravleniya (13th Multiconference on Control Problems), St. Petersburg: Elektropribor, 2020, pp. 127–130.

  9. Simon, D., Optimal State Estimation: Kalman, H-infinity, and Nonlinear Approaches, Hoboken, NJ: Wiley, 2006.

    Book  Google Scholar 

  10. Stepanov, O.A., Primenenie teorii nelineinoi fil’tratsii v zadachakh obrabotki navigatsionnoi informatsii (Application of Nonlinear Filtering Theory to Navigation Data Processing), St. Petersburg: CSRI Elektropribor, 2003.

  11. Doucet, A., Freitas, N., and Gordon, N., Sequential Monte Carlo Methods in Practice, New York, NY: Springer New York, 2001.

    Book  Google Scholar 

  12. Gustafsson, F., Gunnarsson, F., Bergman, N., et al., Particle filters for positioning, navigation, and tracking, IEEE Transactions on Signal Processing, 2002, vol. 50, no. 2, pp. 425–437.

    Article  Google Scholar 

  13. Dunaevskaya, K.V., Kiselev. L.V., and Kostousov, V.B., Study of a method for calculating the current accuracy in map-aided navigation problem, Gyroscopy and Navigation, 2021, vol. 12, no. 1, pp. 50–60.

    Article  Google Scholar 

  14. Stepanov, O.A. and Toropov, A.B., Nonlinear filtering for map-aided navigation. Part 1. An overview of algorithms, Gyroscopy and Navigation, 2015, vol. 6, no. 4, pp. 324–337.

    Article  Google Scholar 

  15. Vasiliev, V.A. and Sokolov, A.V., Comparing the calculated accuracy of gravimetric data postprocessing algorithms and depth field measurements in the problem of constructing a navigation geophysical polygon, XXVIII konferentsiya pamyati vydayushchegosya konstruktora giroskopicheskikh priborov N.N. Ostryakova (28th Conference in Memory of N.N. Ostryakov), St. Petersburg: Elektrorpibor, 2012, pp. 46–47.

  16. Stepanov, O.A., Nosov, A.S., and Toropov, A.B., Navigation informativity of geophysical fields and selection of trajectories in position map aiding, Izvestiya Tul’skogo gosudarstvennogo universiteta. Tekhnicheskie nauki, 2018, no. 5, pp. 74–92.

Download references

Funding

This research was supported by Russian Science Foundation, grant no. 18-19-00627, https://rscf.ru/project/18-19-00627/.

Author information

Authors and Affiliations

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

    O. A. Stepanov, Yu. A. Litvinenko, V. A. Vasiliev & A. B. Toropov

  2. ITMO University, St. Petersburg, Russia

    O. A. Stepanov, Yu. A. Litvinenko, V. A. Vasiliev & M. V. Basin

  3. St. Petersburg Electrotechnical University LETI, St. Petersburg, Russia

    V. A. Vasiliev

  4. Autonomous University of Nuevo León, San Nicolás de los Garza, Mexico

    M. V. Basin

Authors
  1. O. A. Stepanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. A. Litvinenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. A. Vasiliev
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. B. Toropov
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. M. V. Basin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to O. A. Stepanov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Stepanov, O.A., Litvinenko, Y.A., Vasiliev, V.A. et al. Polynomial Filtering Algorithm Applied to Navigation Data Processing under Quadratic Nonlinearities in System and Measurement Equations. Part 2. Solution Examples. Gyroscopy Navig. 12, 314–328 (2021). https://doi.org/10.1134/S2075108721040088

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2075108721040088

Keywords:

Search

Navigation