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The Calibration Problem in Inertial Navigation

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Abstract

This paper describes a generalization of a method used for precision calibration of a strapdown INS. This method was proposed at the Laboratory of Control and Navigation and at the Department of Applied Mechanics and Control, Lomonosov Moscow State University. The method is in practice used in specific applications. The purpose of a strapdown INS calibration is to determine the parameters of instrument errors of inertial sensors: accelerometers and gyros (angular rate sensors) to provide compensation in INS navigation mode. It is assumed that the assembled strapdown INS is located on the platform of a test bench. Test bench performs a set of rotations, the choice of which is part of the calibration task. The main source of data used for calibration are the readings of accelerometers and gyros themselves. Two modifications of the proposed method are described. In the first modification, only data from the accelerometers and gyros are used; in the second modification, the angular data provided by the test bench are also used. The estimation algorithms used are Kalman-type filtering algorithms.

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References

  1. G. I. Emeliantsev, B. A. Blazhnov, E. V. Dranitsyna, and A. P. Stepanov, “Calibration of a precision SINS IMU and construction of IMU-bound orthogonal frame,” Gyroscopy Navigation, No. 3, 205–213 (2016).

    Article  Google Scholar 

  2. A. A. Golovan and N. A. Parusnikov, Mathematical Foundations of Navigation Systems. Pt. I. Mathematical Models of Inertial Navigation [in Russian], MAKS Press, Moscow (2011).

    Google Scholar 

  3. A. A. Golovan and N. A. Parusnikov, Mathematical Foundations of Navigation Systems. Pt. II. Applications of Optimal Estimation Methods to the Problems of Navigation [in Russian], MAKS Press, Moscow (2012).

    Google Scholar 

  4. E. A. Izmaylov, S. N. Lepe, A. V. Molchanov, and E. F. Polikovskiy, “Scalar method of calibration and balancing of strapdown inertial navigation systems,” in: 15th St. Petersburg Int. Conf. on Integrated Navigation Systems. Proceedings, CSRI Elektropribor, St. Petersburg (2008).

    Google Scholar 

  5. A. V. Kozlov, I. Yu. Sazonov, N. B. Vavilova, and N. A. Parusnikov, “Calibration of an inertial measurement unit on a low-grade turntable with consideration of spatial offsets of accelerometer proof masses,” in: 20th St. Petersburg Int. Conf. on Integrated Navigation Systems. Proceedings, CSRI Elektropribor, St. Petersburg (2013), pp. 126–129.

    Google Scholar 

  6. A. V. Kozlov, I. E. Tarygin, A. A. Golovan, I. Kh. Shaymardanov, and A. A. Dzuev, “Calibration of an inertial measurement unit at changing temperature with simultaneous estimation of temperature variation coefficients: a case study on BINS-RT,” in: 24th St. Petersburg Int. Conf. on Integrated Navigation Systems. Proceedings, CSRI Elektropribor, St. Petersburg (2017), pp. 314–317.

    Google Scholar 

  7. N. A. Parusnikov, “Bench calibration problem for a strapdown inertial navigation system,” Mech. Solids, 44, No. 4, 497–501 (2009).

    Article  Google Scholar 

  8. P. G. Savage, Improved Strapdown Inertial System Calibration Procedures. Pt. 1. Procedures and Accuracy Analysis, Strapdown Associates, Maple Plain (2017).

    Google Scholar 

  9. P. G. Savage, Improved Strapdown Inertial System Calibration Procedures. Pt. 2. Analytical Derivations, Strapdown Associates, Maple Plain (2017).

    Google Scholar 

  10. N. B. Vavilova, A. A. Golovan, and N. A. Parusnikov, “Problem of information equivalent functional schemes in aided inertial navigation systems,” Mech. Solids, 43, No. 3, 391–399 (2008).

    Article  Google Scholar 

  11. N. B. Vavilova, N. A. Parusnikov, and I. Yu. Sazonov, “Calibration of strapdown inertial navigation systems using coarse low-grade turntables,” Sovrem. Probl. Mat. Mech., 1, 212–223 (2009).

    Google Scholar 

  12. N. B. Vavilova and I. Yu. Sazonov, “Calibration of a ready-mounted strapdown inertial navigation system on a low-accuracy turntable with one degree of freedom,” Moscow Univ. Mech. Bull., No. 4, 96–98 (2012).

    Article  Google Scholar 

  13. N. B. Vavilova, I. A. Vasineva, and N. A. Parusnikov, “On calibration of an aircraft strapdown inertial navigation system using high-precision turntable,” Tr. MAI, No. 84 (2015).

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    N. B. Vavilova, I. A. Vasineva, A. A. Golovan, A. V. Kozlov, I. A. Papusha & N. A. Parusnikov

Authors
  1. N. B. Vavilova
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  2. I. A. Vasineva
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  3. A. A. Golovan
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  4. A. V. Kozlov
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  5. I. A. Papusha
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  6. N. A. Parusnikov
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Corresponding author

Correspondence to N. B. Vavilova.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 22, No. 2, pp. 89–115, 2018.

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Vavilova, N.B., Vasineva, I.A., Golovan, A.A. et al. The Calibration Problem in Inertial Navigation. J Math Sci 253, 818–836 (2021). https://doi.org/10.1007/s10958-021-05272-y

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  • DOI: https://doi.org/10.1007/s10958-021-05272-y

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