用于卫星姿态确定的加性扩展卡尔曼滤波器与乘性扩展卡尔曼滤波器的比较分析
A Comparative Analysis Between the Additive and the Multiplicative Extended Kalman Filter for Satellite Attitude Determination
AI总结：
本文通过仿真对比AEKF与MEKF在卫星姿态估计中的状态表示、校正方式、精度、不确定性及计算开销，验证MEKF整体更优。
摘要：
基于大量理论证据，普遍共识是乘性扩展卡尔曼滤波器（MEKF）优于加性扩展卡尔曼滤波器（AEKF）。本文在仿真中对这两种滤波器进行实际比较，旨在验证先前的理论基础是否成立。AEKF和MEKF是扩展卡尔曼滤波器的两种变体，其区别在于对系统动力学进行线性化的方法。AEKF使用加性校正项更新状态估计，而MEKF使用乘性校正项。两者在所使用的状态上也有所不同：AEKF使用四元数作为其状态，而MEKF使用Gibbs向量作为其状态。结果表明，MEKF在估计精度方面始终优于AEKF，且具有更低的不确定性。AEKF的计算效率更高，但差异极小，几乎可以忽略不计，并且不会对实时应用产生影响。总体而言，结果表明，由于MEKF具有更优的估计精度和更低的不确定性，它是卫星姿态估计的更好选择，这与先前工作的陈述一致。
英文摘要：
The general consensus is that the Multiplicative Extended Kalman Filter (MEKF) is superior to the Additive Extended Kalman Filter (AEKF) based on a wealth of theoretical evidence. This paper deals with a practical comparison between the two filters in simulation with the goal of verifying if the previous theoretical foundations are true. The AEKF and MEKF are two variants of the Extended Kalman Filter that differ in their approach to linearizing the system dynamics. The AEKF uses an additive correction term to update the state estimate, while the MEKF uses a multiplicative correction term. The two also differ in the state of which they use. The AEKF uses the quaternion as its state while the MEKF uses the Gibbs vector as its state. The results show that the MEKF consistently outperforms the AEKF in terms of estimation accuracy with lower uncertainty. The AEKF is more computationally efficient, but the difference is so low that it is almost negligible and it has no effect on a real-time application. Overall, the results suggest that the MEKF is a better choise for satellite attitude estimation due to its superior estimation accuracy and lower uncertainty, which agrees with the statements from previous work
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