Three basic IMU sensor fusion – filters approaches are discussed and developed by many developers and researchers,

1. complementary filter

2. Kalman filter (with constant matrices)

3. Madgwick filter

These are ref. are used from –

Appendix: References

[SC] Fun with the Complementary Filter [link] and The Balance Filter (Jun. ’07) [.pdf] – by Shane Colton
[PB] Direction Cosine Matrix IMU: Theory (May ’09) [.pdf] – by William Premerlani, Paul Bizard,
see also the google repository gentlenav [link] (it hosts also some of Mahony’s papers)
[St1] A Guide To using IMU (Accelerometer and Gyroscope Devices) in Embedded Applications (Dez. ’09) [link] – by Starlino
[St2] DCM Tutorial – An Introduction to Orientation Kinematics (May ’11) [link] – by Starlino (or as [.pdf])
[La] A practical approach to Kalman filter and how to implement it (Sep. ’12) [link] – by Lauszus, TKJ Electronics

Mahony’s papers:
[RM05] Complementary filter design on the special orthogonal group SO(3) (Dec. ’05) [.pdf] – by Robert Mahony, Tarek Hamel, Jean-Michel Pflimlin
[RM07] Complementary filter design on the Special Euclidean group SO(3) (’07) [.pdf] – by Grant Baldwin, Robert Mahony, Jochen Trumpf, Tarek Hamel, Thibault Cheviron
[RM08] Nonlinear Complementary Filters on the Special Orthogonal Group (Jun. ’08) [link] – by Robert Mahony, Tarek Hamel, Jean-Michel Pflimlin (it is also hosted on gentlenav)

Madgwick’s report and codes:
[SM1] An efficient orientation filter for inertial and inertial/magnetic sensor arrays (Apr.’10) [.pdf] – by Sebastian Madgwick (internal report on his thesis and MARG)
[SM2] Codes and Resources: Open source IMU and AHRS algorithms [link] (original repositoryimumargalgorithm30042010sohm)

Kalman filter:
[KA1] Kalman Filtering (June ’01) – by Dan Simon
[KA2] An Introduction to the Kalman Filter – by Greg Welch, Gary Bishop (or here)
[KA3] Understanding the Basis of the Kalman Filter Via a Simple and Intuitive Derivation (Sep. ’12) – by Ramsey Faragher
[KA4] What is the Kalman Filter and How can it be used for Data Fusion? (Dec. ’05) – by Sandra Mau (Note: This ref should be considered with caution, I added it because the first two presented filters are of pedagogical value, but otherwise the work shouldn’t be taken seriously)

Rotation representations:
[RO1] Representing Attitude: Euler Angles, Unit Quaternions, and Rotation Vectors – by James Diebel (excellent!)
[RO2] Rotation Representations and Performance Issues – by David Eberly
[RO3] Rotation formalisms in three dimensions [link] – Wikipedia
[RO4] on Euler, Tait-Bryan and Cardan angles see Euler Angles [link] – Wikipedia
[RO5] Application of Quaternions to Computation with Rotations – by Eugene Salamin

[LTB] Other MARG/AHRS/IMU/INS Open Code Projects – by Lewis De Payne (Lew’s Tech Blog)
[SHO] Quaternions – by Ken Shoemake
[WTH] A Comparison of Complementary and Kalman Filtering – by Walter T. Higgins