Extended Kalman Filter for Attitude Estimation

Learned something about the attitude estimation EKF used in several books and papers. Try to note something here to clarify their relationships.

The only thing I’m sure about is:
The quaternion attitude + gyro bias estimator is widely used in practice.

no symbol

[0] E.J. Lefferts, F.L. Markley, and M.D. Shuster, “Kalman Filtering for Spacecraft Attitude Estimation”, Journal of Guidance, Control, and Dynamics, vol. 5, Sep. 1982, pp. 417–429.

这里讲的三种形式,第一种和第三种应该是等价的。
与 [3] 中 6.2.4 应该是等价的(还没有完全搞明白)

no symbol

[1] Hanspeter Schaub, and John L. Junkins, Analytical Mechanics of Space Systems (Second Edition), Reston, VA: American Institute of Aeronautics and Astronautics, 2009.

详细讨论了 quaternion based kinematics,但是没有讲 attitude estimation 相关的东西。
阅读笔记在另一篇单独的 post 里。

no symbol

[2] John L. Crassidis, and John L. Junkins, Optimal Estimation of Dynamic Systems, CRC Press, 2011.

7.1.2 Discrete-Time Attitude Estimation 给出了全部推导(有一点是只给了推导方法),得到的 EKF 与 [0] 中的第 3 种应该是等价的;用了 multiplicative quaternion error 的推导方法。
和下面 [3] 中的推导基本相同,符号不同。

no symbol

[3] F. Landis Markley, and John L. Crassidis, Fundamentals of Spacecraft Attitude Determination and Control, New York, NY: Springer New York, 2014.

6.2.4 Mission Mode Kalman Filter 中的 filter 与 [4] 中 7.10 Recursive Attitude Plus Gyro Bias Estimation 的 filter 基本相同,除了差一个正负号

在前面几个小节还讲了 calibrate 所有 gyro error parameters 的 EKF。

缺失的推导,基本可以在 [2] 中找到。

no symbol

[4] Harold L. Hallock, Gary Welter, David G. Simpson, and Christopher Rouff, ACS without an attitude, London: Springer, 2017.

Folks in the NASA/GSFC flight software branch pretty much use “Kalman filter” to mean a recursive filter for attitude-plus-gyro bias estimation - well, at least until recently.

有一个疑问(哪一页?):为什么地面定轨之后,可以直接上传误差 quaternion,然后星上可以自动更正用过去的误差,来修正当前的姿态? 是因为 EKF 使用了误差 quaternion 推导?还是因为什么 bilinear 之类的性质? (!!完全没有搞明白)

no symbol

[5] Yaguang Yang, Spacecraft Modeling, Attitude Determination, and Control Quaternion-based Approach, Boca Raton, FL : CRC Press, 2019. | “A science publishers book.”: CRC Press, 2019.

用的是同时包含 dynamics and kinematics 的 EKF,与其它几个不同。

[11] Valdemir Carrara, Hélio Koiti Kuga, Philipe M Bringhenti, and Manoel J M de, “Attitude Determination, Control and Operating Modes for CONASAT Cubesats”, 24th International Symposium on Space Flight Dynamics (ISSFD), Laurel, MD: 2014, p. 19.

我现在实现的是这篇文献中的算法,与 [0] 等价,[0] 与 [2], [3] 等价,所以应该暂时没有大的错误。
对 transition matrix 和 process noise 的近似,我没有完全按照 [2] 中的公式进行近似,可以修改一下。