I made a map like DVR and discovered that there are 3 different positions we could be in. Two of them were gave pretty similar surroundings to us and are marked in dark-green on the map, and the third is not very good because that'd mean we are in the middle of a no-special area and is marked with orange.
If we discover a special to the south and then east of the archer, all the green squares are true, if not - the closest special is the orange dot.
EDIT: I see DVR beat me to it...