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.

中文翻译：

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地磁轨道确定：EKF 还是 UKF？

目的

使用地磁测量进行自主轨道确定是仅使用磁力计进行安全航天器导航的重要备用技术。地磁模型用于轨道要素的状态估计，但该模型是高度非线性的。因此，人们在开发基于扩展卡尔曼滤波器（EKF）和无迹卡尔曼滤波器（UKF）的非线性滤波器方面付出了很多努力。本文旨在分析是使用UKF还是EKF来解决地磁定轨问题，并试图给出一个一般性的结论。

设计/方法/方法

本文重新审视了这个问题，从理论和工程结果来看，作者表明，在地磁模型中存在非线性的情况下，EKF 和 UKF 表现出相同的估计性能。

发现

虽然 EKF 消耗的计算时间较少，但 UKF 在计算上效率低下，但对大多数非线性模型具有更好的准确性。还需要注意的是，其他一些导航技术也与地磁轨道确定非常相似。

实际影响

这种等价性的内在原因是球谐函数的正交性，这在以前的研究中没有发现。因此，所提出的发现的适用性不仅限于本文中的主要问题，而且可以扩展到所有具有球谐模型的方案。

原创性/价值

本文的结果提供了一个事实，即无需选择 UKF 作为确定轨道的首选候选者。由于 UKF 达到了与 EKF 几乎相同的精度，其计算效率的损失将成为实时实现的重大障碍。