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.

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[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.

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

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[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。

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[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

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[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.

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[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.

[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.