V.V. Matveev1, A.V. Kalikanov2, D.S. Streltsov3, A.N. Khomyachkova4

1,2,3,4 Tula State University (Tula, Russia)

1 matweew.valery@yandex.ru, 2 kalikanov.aleksei@mail.ru, 3 waydaytk@yandex.ru, 4 khoma05_19@mail.ru

A gyroscope-free method for determining the orientation of an object using accelerometer and magnetometer data is proposed. The method extends the traditional algorithm for estimating the direction cosine matrix from vector measurements. To estimate the angular velocity of the object, the method employs Poisson's equation combined with numerical differentiation. The orientation problem is solved using the Bortz kinematic equation. The effectiveness of the method is confirmed by numerical simulation and experimental studies.

Problem statement. In low- and medium- accuracy orientation systems, MEMS sensors are widely used, enabling determination of both the object’s orientation and its angular velocity. The use of purely gyroscopic orientation systems entails error accumulation when integrating kinematic equations, which limits the duration of autonomous operation. Alternative gyroscope-free systems based on spatially separated accelerometers exhibit low sensitivity to small angular velocities and are susceptible to sensor misalignment errors. Hence, the problem of developing a method for estimating angular velocity and orientation of moving objects, realized using gyroscope-free measurements with the conventional arrangement of accelerometers and magnetometers, is relevant.

Objective. Development of a new gyroscope-free method for estimating angular velocity and orientation of a moving object based on joint processing of accelerometer and magnetometer measurements. The method should provide compensation for constant systematic sensor errors without their preliminary calibration.

Results. The paper presents a mathematical description of the method, which is an extension of the TRIAD algorithm. Numerical simulation and experimental studies on a test bench with an AHRS module – AH527C have been conducted, confirming the method’s effectiveness. The angular velocity estimates obtained from joint processing of accelerometer and magnetometer signals are consistent with gyroscope measurements. The orientation angles do not exhibit the drift characteristic of gyroscopic systems.

Practical significance. The method can be used for initial alignment of strapdown inertial navigation systems on a swinging base, enabling the extraction of the Earth’s daily rotation angular velocity from precision gyroscope signals against the background of base angular oscillations. The method is also applicable for integration with a triad of MEMS gyroscopes to estimate their systematic errors under moving conditions.

The research was carried out at the expense of a grant from the Russian Science Foundation "Conducting basic scientific research and exploratory scientific research by small individual scientific groups" (regional competition) No. 25-29-20077, https://rscf.ru/project/25-29-20077/ by topic: "Development of algorithms for orientation and navigation of mobile objects of various bases based on new kinematic parameters and methods of integrating measurement information." The authors also express their gratitude to the Government of the Tula region for providing a grant in the form of subsidies (Agreement No. 30-2025-000527 dated 04/03/2025).

Matveev V.V., Kalikanov A.V., Streltsov D.S., Khomyachkova A.N. Method for determining orientation using non-gyroscopic measurements // Radioengineering. 2026. V. 90. № 9. P. 159−166. DOI: https://doi.org/10.18127/j00338486-202609-17

1. Aggarwa P., Syed Z., Noureldin A., El-Sheimy N. MEMS-based integrated navigation. Boston; London: Artech House. 2010.
2. Belkhiat D.E.C., Fourati H. Multisensor attitude estimation: fundamental concepts and applications. Boca Raton. CRC Press. 2016. 607 p.
3. Peshekhonov V.G. Perspektivy razvitiya giroskopii. Giroskopiya i navigaciya. 2020. T. 28. № 2(109). S. 3−10. DOI: 10.17285/0869-7035.0028 (in Russian).
4. El-Sheimy N., Hou H., Niu X. Analysis and modeling of inertial sensors using allan variance. IEEE Transactions on Instrumentation and Measurement. 2008. V. 57. № 1. P. 140−149.
5. Devyanin E.A., Andreev V.D., Dem'yanovskij A.P. K teorii inercial'nyh sistem, ne soderzhashchih giroskopicheskih chuvstvi-tel'nyh elementov. Mekhanika tverdogo tela. 1966. № 1. S. 14–19 (in Russian).
6. Li Jie, Wang Bo, Liu William, Du Ying. A practical design of gyroscope-free inertial measurement unit. ICCASM 2010 - 2010 International Conference on Computer Application and System Modeling Proceedings. 2010. 9. 10.1109/ICCASM.2010.5622988.
7. Matveev V.V., Kalikanov A.V., Strel'cov D.S., Homyachkova A.N. Nachal'naya vystavka besplatformennoj inercial'noj navigacionnoj sistemy na kachayushchemsya osnovanii. Sb. materialov XXXIII Sankt-Peterburgskoj mezhdunar. konf. po integrirovannym navigacionnym sistemam. SPb. 2026. S. 159–163 (in Russian).
8. Matveev V.V, Raspopov V.Ya. Osnovy postroeniya besplatformennyh inercial'nyh navigacionnyh sistem: Uchebnoe posobie. SPb: GNC RF OAO «Koncern «CNII «Elektropribor». 2009. 280 s. (in Russian).
9. Savege P.G. Strapdown analytics. Strapdown Association. Pt. 1. Inc. Maple Plain. Minnesota. 2000. 817 p.
10. Bortz J.E. A new mathematical formulation for strapdown inertial navigation. IEEE Aerospace and Electronic Systems Magazine. 1971. V. AES-7. № 1. Р. 61–66.