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

翻译：普遍共识基于大量理论证据认为乘性扩展卡尔曼滤波器（MEKF）优于加性扩展卡尔曼滤波器（AEKF）。本文通过仿真对两种滤波器进行实际比较，旨在验证先前理论基础的正确性。AEKF和MEKF是扩展卡尔曼滤波的两种变体，其区别在于对系统动力学进行线性化的方式不同：AEKF采用加性修正项更新状态估计，而MEKF则使用乘性修正项。两者所使用的状态变量也有所不同：AEKF以四元数作为状态变量，而MEKF则以吉布斯向量作为状态变量。结果表明，MEKF在估计精度和不确定性方面始终优于AEKF，其不确定性更低。AEKF的计算效率更高，但两者差异极小，几乎可忽略不计，且对实时应用无影响。总体而言，与前人研究的结论一致，MEKF因其更优的估计精度和更低的不确定性，更适合用于卫星姿态估计。