Strapdown inertial measurement unit precision parameters calculation errors during calibration with canonical method and linear regression method analysis

Аuthors

Ilyushin P. A.

JSC «TsENKI» – «NII PM», Moscow, Russia

e-mail: P.Ilyushin@russian.space

Abstract

Metrological chain described in the article occurs during calibration of the strapdown inertial measurement unit with accelerometric and gyroscopic measuring channels. Sensitive elements of the considering unit are high-precision vibrational-string accelerometers and fiber-optic gyroscopes. However, these sensitive elements as a part of strapdown inertial system mounted in control object, despite of gimbal inertial system, do not have a possibility to self-calibrate. Thus, manufacturer must reliably calibrate precision parameters at the end of the inertial measurement unit production. Currently, it is not possible to use non-linear models describing the instrument measurements due to limits in productivity in high-reliability spacecraft on-board computing systems. Therefore, linear or power (three order and lower) functions describes the model of measurements and instrument error. The paper estimates relative mistakes of canonical calibration with exact formulas for individual measurement parameters, when used a part of measurements in positions of turntable, and for calibration via linear regression when used the whole measurements set. This estimation makes a conclusion about the calibration via linear regression suitability in terms of closeness its mistakes to canonical method calibration mistakes, and allows providing experimental calibration via linear regression results for units of three different types. The obtained results confirm the advantages of suggested calibration method and open up additional perspectives with service files consisting information about the device features. Moreover, the research equipment allows working with service files that have a common XML format, which makes it much easier to prepare for experiments and to analyze the results. At this stage, the device during its exploitation includes in the measurement system of a spacecraft by loosely coupled scheme, where higher-level algorithm calculates acceleration values for gyroscope channels. However, the advantages of described approach are even more evident in the deeply integrated measurement systems. Further development of the proposed approach excludes the terms of accelerometers, gyroscopes, temperatures sensors, because transform matrix coefficients neutralize the sensitivity to the input value of a specific type.

Keywords:

strapdown inertial measurement unit, calibration, linear regression, metrological chain, variation method

References

1. Matejček M. and Šostronek M., The influence of inertial sensors parameters on guidance systems. New trends in signal processing (NTSP), Demanovska dolina, Slovakia, 2020, pp. 1–6.
2. Kuznetsov Yu.L., Vladimirov A.V. Trudy MAI: elektron. zhurn., 2024, no. 139, 27 p. Avialable at: https://trudymai.ru/published.php?ID=183470.
3. Naumchenko V.P., Ilyushin P.A., Pikunov D.G., Solovyov A.V. Aerospace MAI Journal, 2023, vol. 30, no. 2, pp. 158–168. DOI 10.34759/vst-2023-2-158-168. 
4. Bogdanov M.B., Prokhortsov A.V., Smirnov V.A. Izvestiya Tula State University (Izvestiya TulGU), 2021, no. 5, pp. 180–184. Avialable at: https://cyberleninka.ru/article/n/analiticheskiy-obzor-suschestvuyuschih-modeley-i-metodov-kalibrovk... (access date: 25.06.2025).
5. Nikolenko S.I., Kadurin A.A., Arkhangel’skaya E.O. Glubokoe obuchenie. Pogruzhenie v mir neironnykh setei [Deep learning. Immersion in the world of neural networks], St. Petersburg, Piter, 2024, 480 p.
6. Zubkov A.V. Trudy MAI: elektron. zhurn., 2024, no. 139, 24 p. Avialable at: https://trudymai.ru/published.php?ID=183466.
7. Dong C., Ren S., Chen X., Wang Z. A separated calibration method for inertial measurement units mounted on three-axis turntables. Sensors, 2018, vol. 18, art. 2846. DOI 10.3390/s18092846.
8. Naumchenko V.P., Ilushin P.A., Pikunov D.G., Solovyov A.V. Voprosy jelektromehaniki. Trudy VNIIJeM, 2023, vol. 195, no 4, pp. 8–16. 
9. Tashkov S.A., Bulochnikov D.Yu., Shatovkin R.R. NovaInfo, 2018, no. 91, pp. 49–62. Avialable at: https://novainfo.ru/article/15811 (access date: 24.06.2025).
10. Bobronnikov V.T., Kadochnikova A.R. Trudy MAI: elektron. zhurn., 2013, no. 71, 17 p. Avialable at: https://cyberleninka.ru/article/n/algoritm-kompleksirovaniya-besplatformennoy-inertsialnoy-navigatsi... (access date: 24.06.2025).
11. Besekerskij V.A., Popov E.P. Teoriya sistem avtomaticheskogo regulirovaniya [Theory of automatic control systems], Moscow, Nauka, 1972, 768 p.
12. Zhou Ch., Xia M., Xu Zh. A six dimensional dynamic force/moment measurement platform based on matrix sensors designed for large equipment. Sensors and Actuators A: Physical, 2023, vol. 349, art. 114085. DOI 10.1016/j.sna.2022.114085.
13. Fontanella R., Accardo D., Moriello R.S.L., Angrisani L., Simone D. MEMS gyros temperature calibration through artificial neural networks. Sensors and Actuators A: Physical, 2018, vol. 279, pp. 553–565. DOI 10.1016/j.sna.2018.04.008.
14. Jurado J., Schubert Kabban C.M., Raquet J. A regression-based methodology to improve estimation of inertial sensor errors using Allan variance data. NAVIGATION: Journal of the Institute of Navigation, 2019, vol. 66, no. 1, pp. 251–263. DOI 10.1002/navi.278.
15. Rahimi H., Nikkhah A.A. Improving the calibration process of inertial measurement unit for marine applications. NAVIGATION: Journal of the Institute of Navigation, 2020, vol. 67, no. 4, pp. 763–774. DOI 10.1002/navi.400.
16. Yu H., Lee I., Oh J., Sung C.-K., Lee T., Kim C. Performance improvement of an inertial navigation system based on FOG and SA using a two-step indirect calibration method. IEEE International Symposium on Inertial Sensors and Systems (INERTIAL), 2025, pp. 1–4. DOI 10.1109/INERTIAL63280.2025.11036733.
17. Xu D., Jiang P., Zhang Y., Fan Sh., Wan G. Fast self – calibration of fiber – optic strapdown inertial navigation system. 2018 IEEE/ION Position, Location and Navigation Symposium (PLANS), Monterey, CA, 23–26 April 2018, pp. 541–545. DOI 10.1109/PLANS.2018.8373424.
18. Rumyancev N.V., Solovyov S.V., Pavlov D.V. Trudy MAI: elektron. zhurn., 2024, no. 136, 32 p. Avialable at: https://trudymai.ru/published.php?ID=180688 
19. Ryabev V.I. Trudy MAI: elektron. zhurn., 2025, no. 140, 27 p. . Avialable at: https://trudymai.ru/published.php?ID=184073.

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