Skip to main content
SpringerLink
Log in

Application of the Guaranteeing Approach to the Accelerometer Unit Calibration Problem

  • Control in Technical Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

The guaranteeing approach is applied to the joint calibration problem of an accelerometer unit and a high-precision bench. An optimal calibration design with the minimum total number of angular positions of the bench is obtained. Optimal guaranteeing estimates of the requisite parameters are constructed. In practice, the necessary positions of the bench are often difficult to implement precisely; due to this fact, a procedure to take into account the inaccurate setup errors of the bench is discussed.

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

Similar content being viewed by others

References

  1. Lidov, M.L., On Prior Estimation of Accuracy of Parameters Calculated by the Least Squares Method, Kosm. Issled., 1964, vol. 2, no. 5, pp. 713–715.

    Google Scholar 

  2. Krasovskii, N.N., On the Theory of Controllability and Observability of Linear Dynamic Systems, J. Appl. Math. Mech., 1964, vol. 28, no. 1, pp. 1–14.

    Article  MathSciNet  Google Scholar 

  3. Krasovskii, N.N., Teoriya upravleniya dvizheniem (Theory of Motion Control), Moscow: Nauka, 1968.

    Google Scholar 

  4. Lidov, M.L., Minimax Estimation Methods, Preprint No. 71 of Keldysh Inst. of Applied Mathematics, Russ. Acad. Sci., Moscow, 2010.

    Google Scholar 

  5. Bakhshiyan, B.Ts., Nazirov, R.R., and El'yasberg, P.E., Opredelenie i korrektsiya dvizheniya (Determination and Correction of Motion), Moscow: Nauka, 1980.

    MATH  Google Scholar 

  6. Belousov, L.Yu., Otsenivanie parametrov dvizheniya kosmicheskikh apparatov (Estimation of Motion Parameters for Space Vehicles), Moscow: Fizmatlit, 2002.

    Google Scholar 

  7. Matasov, A.I., Metod garantiruyushchego otsenivaniya (Method of Guaranteeing Estimation), Moscow: Mosk. Gos. Univ., 2009.

    Google Scholar 

  8. Matasov, A.I., Estimators for Uncertain Dynamic Systems, Dordrecht: Springer Science+Business Media, 2013.

    MATH  Google Scholar 

  9. Bobrik, G.I. and Matasov, A.I., Optimal Guaranteeing Estimation of Parameters of an Accelerometer Unit, Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, 1993, no. 5, pp. 8–14.

    Google Scholar 

  10. Akimov, P.A., Derevyankin, A.V., and Matasov, A.I., Garantiruyushchee otsenivanie i l1-approksimatsiya v zadachakh otsenivaniya parametrov BINS pri stendovykh ispytaniyakh (Guaranteeing Estimation and l1-Approximation in Parameter Estimation Problems of Strapdown Inertial Navigation Systems in Bench Tests), Moscow: Mosk. Gos. Univ., 2012.

    Google Scholar 

  11. Ishlinskii, A.Yu., Orientatsiya, giroskopy i inertsial'naya navigatsiya (Orientation, Gyros and Inertial Navigation), Moscow: Nauka, 1976.

    Google Scholar 

  12. Golovan, A.A. and Parusnikov, N.A., Matematicheskie osnovy navigatsionnykh sistem, Ch. I: Matematicheskie modeli inertsial'noi navigatsii (Mathematical Foundations of Navigation Systems, part I: Mathematical Models of Inertial Navigation), Moscow: MAKS Press, 2011.

    Google Scholar 

  13. Bolotin, Yu.V., Golikov, V.P., Larionov, S.V., and Trebukhov, A.V., A Calibration Algorithm for a Gimbaled Inertial Navigation System, Giroskop. Navigats., 2008, no. 3, pp. 13–27.

    Google Scholar 

  14. Vavilova, N.B., Parusnikov, N.A., and Sazonov, I.Yu., Calibration of Strapdown Navigation Systems on Low-Accuracy Bench with One Degree of Freedom, in Sovremennye problemy matematiki i mekhaniki. Prikladnye issledovaniya (Modern Problems of Mathematics and Mechanics. Applied Research), Moscow: Mekh.-mat. Fak. Mosk. Gos. Univ., 2009, vol. 1, pp. 212–223.

    Google Scholar 

  15. Veremeenko, K.K. and Galai, I.A., Development of a Calibration Algorithm for an Inertial Navigation System on a Biaxial Test Bench, Tr. Mosk. Aviats. Univ., 2013, vol. 63.

  16. Golovan, A.A. and Matasov, A.I., Guaranteed Approach for Determining the Optimal Design of Accelerometer Unit Calibration, Fundam. Prikl. Mat., 2018, vol. 22, no. 2, pp. 133–145.

    MathSciNet  Google Scholar 

  17. Gusinskii, V.Z., Lesyuchevskii, V.M., Litmanovich, Yu.A., and Stolbov, A.A., A Calibration Algorithm for a Triaxial Accelerometer Unit Intended for Strapdown Inertial Navigation Systems, Giroskop. Navigats., 2000, no. 4, p. 86.

    Google Scholar 

  18. Derevyankin, A.V. and Matasov, A.I., Formalizing a Sequential Calibration Scheme for a Strapdown Inertial Navigation System, Autom. Remote Control, 2018, vol. 79, no. 1, pp. 52–66.

    Article  MathSciNet  Google Scholar 

  19. Dranitsyna, E.V., Calibration of a Measuring Unit by the Navigation Solution of a Strapdown Inertial Navigation System: Design of Bench Movements, Trudy XXIV SPb. mezhdunarodnoi konferentsii po integrirovannym navigatsionnym sistemam (Proc. 24th St. Petersburg Int. Conf. on Integrated Navigation Systems), St. Petersburg: Tsentr. Nauchno-Issled. Inst. Elektropribor, 2017, pp. 235–240.

    Google Scholar 

  20. Egorov, Yu.G. and Popov, E.A., A Study of Minimum Redundant Calibration Programs for an Accelerometer Triad, Aviakosm. Priborostr., 2016, no. 6, pp. 3–8.

    Google Scholar 

  21. Emel'yantsev, G.I. and Stepanov, A.P., Integrirovannye inertsial'no-sputnikovye sistemy orientatsii i navigatsii (Integrated Inertial-Satellite Orientation and Navigation Systems), St. Petersburg: Tsentr. Nauchno-Issled. Inst. Elektropribor, 2016.

    Google Scholar 

  22. Ermakov, V.S., Dunaev, D.A., Shirokov, A.A., et al., Calibration of Strapdown Inertial Navigation and Orientation Systems, Vestn. Perm. Gos. Tekh. Univ., Aerokosm. Tekh., 2004, no. 18, pp. 25–30.

    Google Scholar 

  23. Izmailov, E.A., Lepe, S.N., Molchanov, A.V., and Polikovskii, E.F., Scalar Method for Calibration and Balancing Strapdown Inertial Navigation Systems, Trudy XV SPb. mezhdunarodnoi konferentsii po integrirovannym navigatsionnym sistemam (Proc. 15th St. Petersburg Int. Conf. on Integrated Navigation Systems), St. Petersburg: Tsentr. Nauchno-Issled. Inst. Elektropribor, 2008, pp. 145–154.

    Google Scholar 

  24. Sazonov, I.Yu. and Shaimardanov, I.Kh., Calibration of Strapdown Inertial Navigation System on Micromechanical Accelerometers and Gyros, in Vopr. Oboronn. Tekh., 2010, no. 3, pp. 73–82.

    Google Scholar 

  25. Cai, Q., Yang, G., Song, N., and Lin, Y., Systematic Calibration for Ultra-High Accuracy Inertial Measurement Unit, Sensors, 2016, vol. 16 (940).

    Google Scholar 

  26. Yu, M.-S., Yu, S.-B., and Lee, K.-S., Development of High-Precision Calibration Method for InertialMeasurement Unit, Int. J. Precision Engineer. Manufactur., 2014, vol. 15, no. 3, pp. 567–575.

    Article  Google Scholar 

  27. Panahandeh, G., Skog, I., and Jansson, M., Calibration of the Accelerometer Triad of an Inertial Measurement Unit, Maximum Likelihood Estimation and Cramer-Rao Bound, Proc. Int. Conf. on Indoor Positioning and Indoor Navigation, Zurich, Switzerland, 2010.

    Google Scholar 

  28. Paternain, S., Tailanian, M., and Canetti, R., Calibration of an Inertial Measurement Unit, Proc. 16th Int. Conf. on Advanced Robotics, 2013.

    Google Scholar 

  29. Secer, G. and Barshan, B., Improvements in Deterministic Error Modeling and Calibration of Inertial Sensors and Magnitometers, Sensors Actuat. A, 2016, vol. 247, pp. 522–538.

    Article  Google Scholar 

  30. Syed, Z.F., Aggarwal, P., Goodall, C., Niu, X., and El-Sheimy, N., A New Multi-Position Calibration Method for MEMS Inertial Navigation Systems, Meas. Sci. Technol., 2007, no. 18, pp. 1897–1907.

    Article  Google Scholar 

  31. Xu, Y., Wang, Y., Su, Y., and Zhu, X., Research on the Calibration Method for Micro Inertial Measurement Unit for Engineering Applications, IEEE Sens. J., 2016, ID 9108197.

    Google Scholar 

  32. www.acutronic.com/ru/produkcija/2-osevye-stendy.html

  33. Alekseev, V.M., Tikhomirov, V.M., and Fomin, S.V., Optimal'noe upravlenie (Optimal Control), Moscow: Fizmatlit, 2007.

    MATH  Google Scholar 

  34. Magaril-Il'yaev, G.G. and Tikhomirov, V.M., Vypuklyi analiz i ego prilozheniya (Convex Analysis and Its Applications), Moscow: Librokom, 2011.

    Google Scholar 

  35. Ekeland, I. and Temam, R., Convex Analysis and Variational Problems, Amsterdam: North-Holland, 1976. Translated under the title Vypuklyi analiz i variatsionnye problemy, Moscow: Mir, 1979.

    MATH  Google Scholar 

Download references

Funding

This work was supported by the Russian Foundation for Basic Research, project no. 18-01-00054-a.

Author information

Authors and Affiliations

  1. Laboratory of Control and Navigation, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia

    A. A. Golovan & A. I. Matasov

Authors
  1. A. A. Golovan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. I. Matasov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to A. A. Golovan or A. I. Matasov.

Additional information

This paper was recommended for publication by M.F. Karavai, a member of the Editorial Board

Russian Text © The Author(s), 2020, published in Avtomatika i Telemekhanika, 2020, No. 4, pp. 140-161.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Golovan, A.A., Matasov, A.I. Application of the Guaranteeing Approach to the Accelerometer Unit Calibration Problem. Autom Remote Control 81, 686–703 (2020). https://doi.org/10.1134/S0005117920040104

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117920040104

Keywords

Search

Navigation