Joonsy,
The "thumb shift" method works for known size objects that are in the medium distance range - say a few feet to a hundred yards or so. You hold out your thumb and by closing first one eye then the other, estimate the apparent side-shift distance - multiply this by a factor of 8 (though each person will be slightly different) to get the range to the target - it relies upon the correlation of distance between your eyes and from your dominant eye to your thumb which is somewhere near 1:8 ratio.
Using a compass would necessitate some ultra accurate bearing reading and a good dollop of trigonometry. You'd have to take two bearings to the "distant object" moving along a line perpendicular to one of the bearing lines - building a right angled triangle. The two angles would need to be subtracted, then calculated with the distance you moved sideways to get an approximation as even tiny fractions of a degree error would mean huge errors in the predicted distance. I suppose if you were to get somewhere towards the 60 to 90 degree intersection you may get something reasonably accurate - but you'd end up knackered from making all the bearing taking rather than actually closing on your target!
You can make a "range card", calibrated to yourself to indicate the size of common items at known distances (person, vehicle, building etc) but it is something else to loose.
ATB
Ogri the trog