NavList:

There are a number of methods, but they all use the magnitude output of the watch's three internal magnetometers.  There are more formal discussions (here's a short one from a manufacturer: http://www.vectornav.com/support/library/magnetometer), but in summary you need a compass that can tell you how strong the magnetic field is in a given direction.

If you had a compass needle that magically grew or shrank in length with the strenth of the measured field, swinging the vessel around while plotting the location of the needle would ideally draw a circle with a radius equal to the local strength of the Earth's magnetic field.  What Bowditch calls "permenent magnetic deviation"-- commonly called the "hard iron" effect-- moves the circle off-center.  Induced magnetism (also called "soft iron") squashes the circle into an ellipse.  One approach is to take data from your spinning watch and fit an ellipse to find how squashed and off-center those readings are.  I suspect this is "spiritually" similar to the Fourier method mentioned earlier but exploits the additional data provided by these newfangled sensors.

It is often a little more complicated in practice.  The processing for these little MEMS systems is comparable to a full solid-state INS, albiet much less accurate.  Some modern systems use a non-linear Kalman-style filter that can solve for calibration parameters in real-time.  The math gets really hairy awfully fast-- for example, care must be taken to avoid mathematical "gimbal lock" even though there are no physical gimbals.

In practical terms, non-magnetic heading measurement has come way down in price, with tolerable solid-state gyrocompasses available for ~$500 and multi-antenna GPS units for around $3,000.  Do folks commonly use these sorts of things on "pleasure" craft?  Not that that in any way obviates the magnetic calibration problem, especially in a crowd that prefers a sextant to a third (or fourth) GPS unit.

Incidentally, I'm a bit new to posting on NavList, and am a bit more up to speed on computational wizardry than traditional navigation methods.  Last year, I was on a research ship during calibration of the binnacle compass by solar azimuths.  These references seem to answer most of the questions I had at the time (thanks!).  Compass calibration is rightfully left to the licensed mariners-- my job is more "research" than "ship"-- and we were all too busy to chat about it afterwards.  So to answer a question from some time ago, yes, some CelNav is still occasionally used commercially.

-- Ian Vaughn