I was asked to help determine head angular and linear acceleration during soccer heading. The data came from an accelerometer that measured linear acceleration and angular velocity about 3 axes. The accelerometer was securely strapped to the back of the head. The challenge was to estimate what was happening in the middle of the cranium (i.e. in the center of the brain), based on the measured values at the back of the cranium.
My problem was not exactly the same as yours, but it is related. I found that various methods have been proposed in the literature. I evaluated and compared them, and made an algorithm based on my analysis. Since you asked for any suggestions or leads, I recommend the sources I used:
Suh YS 2010 [Suh2010]. “Orientation estimation using a quaternion-based indirect Kalman filter”, IEEE Trans Instrum Measure 59(12): 3296-3305.
Trawny & Roumeliotis 2005 [Trawny2005]. “Indirect Kalman Filter for 3D Attitude Estimation: A Tutorial for Quaternion Algebra” Technical Report 2005-002, http://www.users.cs.umn.edu/~trawny/Publications/Quaternions_3D.pdf.
Phillips et al 2001 [Phillips2001]. “Review of attitude representation used for aircraft kinematics”, Journal of Aircraft 38 (4): 718-737.
Hendeby G, 2014 [Hendeby2014]. “Orientation Estimation Using Smartphone Sensors.” http://www.control.isy.liu.se/student/tsrt14/file/orientation.pdf.
Kim & Golnaraghi, 2004 [Kim2004]. “A Quaternion-Based Orientation Estimation Algorithm Using an Inertial Measurement Unit”, IEEE Position Location and Navigation Symposium 2004.
The different sources use different notation and sometimes have mistakes or typographical errors. Some of the sources have hundreds of equations and hundreds of references. This made the analysis non-trivial. I ended up deriving an equation based on equaitons 98, 99, 110, and 130 of Phillips et al 2001. This equation was very smiliar to equation 18 of Suh 2010, but Suh's equation 18 has some problems.
Good luck with your work.
