Hi Yawei,

As far as I know I guess the measurement should still be correct (up to some point) in the case of the electronic compass not being perfectly aligned with the horizontal plane.
The reason being that if not perfectly in the horizontal plane the e-compass will still detect the perpendicular component of the applied magnetic field.
As long as such component is strong enough in order to be properly detected by the e-compass, then it will be ok.
The question is how weak the perpendicular B can be in order to be properly detected?
The answer is directly related to the sensitivity of the hall plate used in the e-compass, and the sensor noise and offset levels: in other words the sensor's S/N and S/O ratios.
As for the noise levels, typically noise densities are in the order of few mGpp (6 sigma) while as for offset levels these can be as low as below 0.5G.
Such offset / noise levels are usually achieved by combining hall plate spinning techniques with chopping modulation schemes. Additionally spinning is usually performed over several current directions to get as much averaging as possible over all the offset contributions coming from the hall plate.

Summarizing, if the e-compass hall plate sensitivity is high enough, and its offset/noise levels are kept low enough then there is a good margin for getting the e-compass significantly misaligned with the horizontal plane and still get and accurate reading out of it.

I hope this is close to what you were looking for.
Best

Tosei