Hi, I am trying to work out the math and possibly come up with a simpler update algorithm. My question is about the document named AN5023 v2p0.pdf which describes the EKF used for the Sensor Fusion. Equation (55), relates the a priori error in the angular speed to the apriori error in the gyrometer bias. The second equality does not seem correct, using equation (49), the w_{b,k} term in the final equation should be omitted. In any case, this may not matter much, as it only affects the covariance matrix (with a fixed scaling). But it would be good if it gets corrected.

I'm not sure I agree with you. Equation (49) follows algebraically from its predecessors and makes intuitive sense since it's the noise (change) in the gyro offset random walk from sample to sample that degrades the a priori estimate for iteration k from the a posteriori estimate from iteration k-1. Similarly the terms in equation (55) make physical sense. I would agree that in practice it's difficult to separate out some of the noise terms from each other. Zero mean white noise in the gyro offset is indistinguishable from zero mean gyro sensor noise for example in that the net result is also white.