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Geomagnetic orbit determination: EKF or UKF?

Jin Wu (Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong, China)
Ming Liu (Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong, China)
Chengxi Zhang (School of Electronic and Information Engineering, Harbin Institute of Technology, Shenzhen, China)
Yulong Huang (Harbin Engineering University, Harbin, China)
Zebo Zhou (School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu, China)

Aircraft Engineering and Aerospace Technology

ISSN: 0002-2667

Article publication date: 26 July 2021

Issue publication date: 12 August 2021




Autonomous orbit determination using geomagnetic measurements is an important backup technique for safe spacecraft navigation with a mere magnetometer. The geomagnetic model is used for the state estimation of orbit elements, but this model is highly nonlinear. Therefore, many efforts have been paid to developing nonlinear filters based on extended Kalman filter (EKF) and unscented Kalman filter (UKF). This paper aims to analyze whether to use UKF or EKF in solving the geomagnetic orbit determination problem and try to give a general conclusion.


This paper revisits the problem and from both the theoretical and engineering results, the authors show that the EKF and UKF show identical estimation performances in the presence of nonlinearity in the geomagnetic model.


While EKF consumes less computational time, the UKF is computationally inefficient but owns better accuracy for most nonlinear models. It is also noted that some other navigation techniques are also very similar with the geomagnetic orbit determination.

Practical implications

The intrinsic reason of such equivalence is because of the orthogonality of the spherical harmonics which has not been discovered in previous studies. Thus, the applicability of the presented findings are not limited only to the major problem in this paper but can be extended to all those schemes with spherical harmonic models.


The results of this paper provide a fact that there is no need to choose UKF as a preferred candidate in orbit determination. As UKF achieves almost the same accuracy as that of EKF, its loss in computational efficiency will be a significant obstacle in real-time implementation.



This research was supported in part by the National Natural Science Foundation of China under the grant of No. 41604025, No. 42074038 and No. 62003112, in part by the Sichuan Science and Technology Program under the grant of No. 2021YJ0104, and in part by the Sichuan Province Scienceand Technology Project 2018SZ0364.


Wu, J., Liu, M., Zhang, C., Huang, Y. and Zhou, Z. (2021), "Geomagnetic orbit determination: EKF or UKF?", Aircraft Engineering and Aerospace Technology, Vol. 93 No. 6, pp. 985-994.



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