Sorry, you should find the answer on page 6. The principal is easy. Whenever you apply a reset pulse to the strap the magnetometer will function with negative sensitivity the rest of the time.
In your equation (8) you have an "exact formula" for the offset in the plane perpendicular to the rotation
axis. You use instead the variable vector: the numerator of that equation. In equation (11) you update
the offset estimation by…"