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Nonlinear Information Processing Algorithm for Navigation Complex with Increased Degree of Parametric Identifiability

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Recent Research in Control Engineering and Decision Making (ICIT 2019)

Abstract

The aircraft navigation system with the error compensation algorithm of the basic inertial navigation system is considered. A nonlinear correction algorithm has been developed using an SDC representation of the navigation system’s error model matrix. To improve the accuracy of the model, a method is proposed for increasing the degree of identifiability of the parameters in the model matrix. The problem of identification of nonlinear systems is investigated. A numerical criterion for the degree of identifiability of the parameters of a non-linear model of one class, based on the SDC representation of the non-linear model, has been developed.

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References

  1. Groves, P.D.: Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems. Artech House, Boston (2013)

    MATH  Google Scholar 

  2. Neusypin, K.A.: Sovremennye sistemy i metody navedeniya, navigatsii i upravleniya letatelnymi apparatami [Modern systems and methods of guidance, navigation and aircraft control]. MGOU (2009). (in Russian)

    Google Scholar 

  3. Selezneva, M.S., Neusypin, K.A.: Development of a measurement complex with intelligent component. Meas. Tech. 59(9), 916–922 (2016)

    Article  Google Scholar 

  4. Shen, K., Selezneva, M.S., Neusypin, K.A., Proletarsky, A.V.: Novel variable structure measurement system with intelligent components for flight vehicles. Metrol. Meas. Syst. 24(2), 347–356 (2017)

    Article  Google Scholar 

  5. Proletarsky, A.V., Neusypin, K.A., Shen, K., Selezneva, M.S., Grout, V.: Development and analysis of the numerical criterion for the degree of observability of state variables in nonlinear systems. In: Proceedings of the 7th International Conference, vol. 7, pp. 150–154 (2017)

    Google Scholar 

  6. Noureldin, A., Karamat, T.B., Georgy, J.: Fundamentals of Inertial Navigation, Satellite-Based Positioning and Their Integration. Springer, Heidelberg (2013)

    Book  Google Scholar 

  7. Van Trees, H.L., Bell, K.L.: Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking. Wiley-IEEE Press, New York (2007)

    Google Scholar 

  8. James, R.C., Christopher, N.D., Curtis, P.M.: Nonlinear regulation and nonlinear H∞ control via the state-dependent Riccati equation technique: part 1, theory. In: Proceedings of the First International Conference on Nonlinear Problems in Aviation and Aerospace, Daytona Beach, FL, USA, pp. 117–141 (1996)

    Google Scholar 

  9. Ham, F.M., Brown, R.G.: Observability, eigenvalues, and Kalman filtering. IEEE Trans. Aerosp. Electron. Syst. AES-19(2), 269–273 (1983)

    Article  Google Scholar 

  10. Kalman, R.E., Ho, Y.C., Narendra, K.S.: Controllability of linear dynamical systems. In: Contributions to the Theory of Differential Equations, vol. I, no. 2, pp. 189–213 (1963)

    Google Scholar 

  11. Van Trees, H.L., Bell, K.L.: Bayesian bounds for parameter estimation and nonlinear filtering/tracking, p. 951. Wiley-IEEE Press (2007)

    Google Scholar 

  12. Stepanov, O.A.: Application of the theory of nonlinear filtering in tasks of processing navigation information. Central Scientific Research Institute “Electrical device” (2003)

    Google Scholar 

  13. Ivakhnenko, A.G.: Polynomial theory of complex systems. IEEE Trans. Syst. Man Cybern. SMC-1(4), 364–378 (1971)

    Article  MathSciNet  Google Scholar 

  14. Shen, K., et al.: Technology of error compensation in navigation systems based on nonlinear Kalman filter. J. Natl. Univ. Defense Technol. 2, 84–90 (2017)

    Google Scholar 

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Acknowledgments

This work was supported by the Russian Fund for Fundamental Research (Project 16-8-00522), the State Mission of the Ministry of Education and Science of the Russian Federation (Project No. 2.7486.2017) and the Program of Introducing Talents of Discipline to Universities in China (Program 111, No. B 16025).

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Correspondence to Maria Selezneva .

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Neusypin, K., Selezneva, M., Proletarsky, A. (2019). Nonlinear Information Processing Algorithm for Navigation Complex with Increased Degree of Parametric Identifiability. In: Dolinina, O., Brovko, A., Pechenkin, V., Lvov, A., Zhmud, V., Kreinovich, V. (eds) Recent Research in Control Engineering and Decision Making. ICIT 2019. Studies in Systems, Decision and Control, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-030-12072-6_4

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