I noticed a really puzzling behavior on iPhone:
If I hold the phone in the vertical, and tilt it, the compass change.
I already figured the amount it changes is the same amount it would change for the same amount of tilting if it was in horizontal (ie: suppose that a vector coming from the screen is called Y, turning around Y does not matter the attitude of the iPhone results in a compass change).
I want to compensate that, my app was not made to you hold the phone in the horizontal (although I do plan also to allow some tilting in the X axis let's call it, from like 10 degrees to 135)
But I really could not figure how iPhone calculate the heading, thus where the heading vector actually points...
After some scientific style experiments, I found:
The iPhone has magnetometer, it has 3 axis, X, that goes from left to right from the screen. Y, that goes from bottom to up. And Z, that comes from behind the phone and comes to the front.
Earth magnetic field is as expected by the laws of physics not a sphere, in the location I am (brazil), it is slanted about 30 degrees. (meaning that I have to hold the phone in a 30 degrees angle to zero 2 axis).
One possible technique to calculate north, is use cross product of a vector tangential to the magnetic field (ie: the vector the magnetometer reports to you), and gravity. The result will be a vector that points east. If you wish you can make another cross product between east and gravity, resulting in a vector that points north.
Know that iPhone sensors are quite good, and every minor fluctuation and vibration is caught, thus it is good idea to use a lowpass filter, to remove the noise from the signal.
The iPhone itself, has a complex routine to determine the "true heading", I don't figured it completely, but it uses the accelerometer in some way to compensate for tilt. You can use the accelerometer and compensate back if that is your wish, for example if the phone is tilted 70 degrees, you can change the true heading by 70 degrees too, and the result will be the phone ignoring tilting.
Also the routine of true heading, verify if the iPhone is upside down or not. If we consider it in horizontal, in front of you as 0, then more or less at 135 degrees it decides that it is upside down, flipping the results.
Note the same coordinate system also apply to the accelerometer, allowing the use of vectors operations between accelerometer and magnetometer data without much fiddling.