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Having a perfect gyro (with no noise/drift or bias), the gyro produces angular velocities in the form (wx, wy, wz) in rad/sec.

I would like to convert the rate gyro readings (which are expressed in gyro's case frame) to be in the inertial frame(earth)

At the beginning, i have a quaternion q the represents the rotation from earth's frame to gyro's starting orientation.

I am looking for a way to convert the (wx, wy, wz) rates the gyro produces to be in the inertial frame using the quaternion q.

Thank you,

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I think you can just convert the quaternions into a rotation matrix, matrix equation

and multiply the gyro vector by that. I have used this to adjust linear acceleration in the past, and I think it should work for rotation, but please let me know how it goes.

The quaternion should be normalized first, meaning the sum of the squares should equal one. This is standard for quaternion orientation outputs. I discuss some quaternion basics here, if you're unfamiliar.

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  • $\begingroup$ Thank you, just to be sure, when you say the gyro vector, do you mean a vector in the form [Wx, Wy, Wz] where Wx, Wy, Wz are the output of the gyro in degrees per second? $\endgroup$
    – User.t
    Commented Dec 16, 2017 at 18:49
  • $\begingroup$ Yes, the rotation matrix is unitless, so the units of the gyro do not matter $\endgroup$
    – pscheidler
    Commented Dec 16, 2017 at 20:02

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