Yevhen I. Bilous, Oleh I. Nesterenko


Background. One of the most common variants of correction of strapdown attitude and heading reference system (AHRS) is using of the Kalman filter (KF) algorithm. The algorithm makes it possible to estimate and compensate errors of the orientation calcu­lation, the gyros bias and reduces the influence of sensor noise. However, the main problem of known analogues is the excess of in­formation in the measurement model, which leads to an increased computational requirement of the algorithm. In turn it forces the use of more powerful and therefore expensive processors for construction of such systems. The paper considers the simplification of the measurement model of the KF.

Objective. The aim of the paper is to reduce the computational requirements of the AHRS algorithm using KF, by simplifying the measurement model.

Methods. To reduce the computational requirements of the AHRS algorithm, it is proposed to simplify the KF measurement vector. For this, the measurement model of the AHRS was developed and the transition from the error angles to the error quaternion was shown. The measurement vector was simplified from six components to three, by eliminating excess information from the me­asurement model. The observability of whole state vector of the AHRS errors was proved. The effectiveness of the measurement vec­-tor simplification is confirmed by estimating the computational requirements of the algorithm.

Results. The result of the research is low-order measurement model (from six components to three) of the KF for AHRS, which, as the original model, allows estimating all components of the state vector of the AHRS errors.

Conclusions. Variant of KF measurement model simplification for the AHRS algorithm is proposed. This allows essentially reducing amount of the algorithm calculations in comparison to known analogues.


Orientation system; Attitude and heading reference system; Quaternion; Kalman filter; Measurement model


D.S. Pelpor et al., Gyroscopic Systems. Gyroscopic Devices and Systems. Moscow, SU: High School, 1988.

M. Euston et al., “A complementary filter for attitude estimation of a fixed wing UAV”, in Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems, pp. 340–345, 2008. doi: 10.1109/IROS.2008.4650766

L. Ryzhkov, “Complementary filter design for attitude determination”, in Proc. IEEE 5th Int. Conf. Methods and Systems of Na­vigation and Motion Control (MSNMC), pp. 214–217, 2018. doi: 10.1109/MSNMC.2018.8576177

D. Gebre-Egziabher et al., “A gyro-free quaternion-based attitude determination system suitable for implementation using low cost sensors”, in Proc. IEEE Position Location and Navigation Symposium, pp. 185–192, 2000. doi: 10.1109/ PLANS.2000.838301

L. Wang et al., “Quaternion-based Kalman filter for AHRS using an adaptive-step gradient descent algorithm”, Int. J. Advan­ced Robotic Systems, 2015. doi: 10.5772/61313

K. Feng et al., “A new quaternion-based Kalman filter for real-time attitude estimation using the two-step geometrically-intuitive correction algorithm”, Sensors (Basel), vol. 17, no. 9, p. 2146, 2017. doi: 10.3390/s17092146

G. Zhong-yu et al., “Quaternion-based Kalman filter for micro-machined strapdown attitude heading reference system”, Chinese J. Aeronautics, vol. 15, pp. 171–175, 2002. doi: 10.1016/S1000-9361(11)60149-0

K. Brammer and G. Siffling, Kalman Bucy Filters. Moscow, SU: Science, 1982.

J. Mendel, “Computational requirements for a discrete Kalman filter”, IEEE Transactions on Automatic Control, vol. 16, pp. 748–758, 1971. doi: 10.1109/TAC.1971.1099837

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