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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.

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.

For fixed-wing micro air vehicles, the attitude determination is usually produced by the horizon/Global Navigation Satellite System (GNSS) in which the GNSS provides yaw estimates, while roll and pitch are computed using horizon sensors. However, the attitude determination has been independently obtained from the two sensors, which will result in insufficient usage of data. Also, when implementing attitude determination algorithms on embedded platforms, the computational resources are highly restricted. This paper aims to propose a computationally efficient linear Kalman filter to solve the problem.

The observation model is in the form of a least-square optimization composed by GNSS and horizontal measurements. Analytical quaternion solution along with its covariance is derived to significantly speed up on-chip computation.

The reconstructed attitude from Horizon/GNSS is integrated with quaternion kinematic equation from gyroscopic data that builds up a fast linear Kalman filter. The proposed filter does not involve coupling effects presented in existing works and will be more robust encountering bad GNSS measurements.

Electronic systems are designed on a real-world fixed-wing plane. Experiments are conducted on this platform that show comparisons on the accuracy and computation execution time of the proposed method and existing representatives. The results indicate that the proposed algorithm is accurate and much faster computation speed in studied scenarios.