1. Geomagnetic orbit determination: EKF or UKF?
- Author
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Zebo Zhou, Jin Wu, Ming Liu, Chengxi Zhang, and Yulong Huang
- Subjects
020301 aerospace & aeronautics ,0209 industrial biotechnology ,Spacecraft ,Computer science ,business.industry ,Aerospace Engineering ,02 engineering and technology ,Kalman filter ,Nonlinear system ,Extended Kalman filter ,020901 industrial engineering & automation ,Earth's magnetic field ,0203 mechanical engineering ,Orthogonality ,Control theory ,Orbit (control theory) ,Orbit determination ,business - Abstract
Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.
- Published
- 2021