How do I convert a 3-axis quaternion to a 1-axis x-y axis plane?

Other Hardware Sensors
11

This code calculates the estimated direction of the gravity vector, based on the current value of the quaternion.

  // Estimated direction of gravity in the body frame (factor of two divided out)
    vx = q[1] * q[3] - q[0] * q[2];
    vy = q[0] * q[1] + q[2] * q[3];
    vz = q[0] * q[0] - 0.5f + q[3] * q[3];

To obtain the so-called "linear acceleration" you subtract this from the measured acceleration (eg. ax, ay, az) after scaling the two vectors appropriately.

After they are both scaled in terms of m/s^2 ( 1 g = 9.8 m/s^2) then you can subtract the individual terms directly, e.g. the x acceleration in the body frame is (ax-vx) m/s^2.