I am trying to implement an indirect/error state kalman filter following Quaternion kinematics for the error-state Kalman filter. However, instead of modelling the orientation and error in orientation I have chosen to utilize Madwick to estimate the orientation.
The problem is that when I create the transition matrix from the first paper it expects the orientation error which it multiplies with the skew matrix of the measured acceleration and the accelerometer bias (page 40, equation 204). Since I have removed that from my states I can't use it, but then the measured acceleration is never considered (which I assume makes the filter worse). Is there any change I can make to the transition matrix so that it accounts for the acceleration?