http://diydrones.com/forum/topics/robust-estimator-of-the?id=705844%3ATopic%3A61100&page=4#comments

The cross product of two vectors is a vector that is perpendicular to both of them, with a magnitude equal to the product of their magnitudes, times the sine of the angle between them. Since the cross product is perpendicular to both vectors, it is parallel to the axis that you would have to rotate one of the vectors around to bring it into parallel alignment with the other. This is perfect for what we want to do: we want to know how much more or less gyro rotation we would need to line the reference vectors up.

The cross product of gplane with rbuff[6 7 8] is measuring the misalignment between gravity as measured by the accelerometers (adjusted for centrifugal acceleration), and the vertical axis of the ground reference frame. It produces a rotation vector that you would need to bring those two vectors in alignments.

Regarding the feedback gains, Paul and I worked together. Paul performed lots of simulations to see how accuracy and transient response depended on the gains. I did a lot of walking around my neighborhood carrying the demo in my hands. There is a broad optimum for the roll-pitch gains. If you raise the gains, the recovery from gyro saturation is faster, but the accuracy is not as good. If you lower the gains, accuracy improves, but recovering from gyro saturation is slower.

In practice, there is a wide range of gains that will work for roll-pitch drift compensation.

Yaw drift is another matter. I found that the EM406 has about a 15 second delay in reporting course over ground. As a result, you have to keep the yaw drift feedback gains on the low side to prevent oscillations. You also have to account for the delay, which we partially account for by delaying the stream of Rmatrix vectors to the yaw drift calculation by 11 seconds.

The gyro feedback that I use in the rudder control loop keeps the yaw gyro from saturating.

Regarding MatrixNav, its almost done. I have made several test flights, working mostly on the elevator and rudder control feedback gains. I think I have the right gains now, but the weather forecast for the next few weeks is for rain and high winds. As soon as the weather breaks, I will go for one more test flight, and then I will release the firmware.

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