Does the alarm system have a back up recharging battery? Mine does and when I had a phantom beep experience, it turned out that the battery was at the end of its life span and not recharging properly. As it was in an obscure corner, I had the damndest time locating the source of the noise. It happened again when the battery connection broke. Now when I hear an unlocalized beep that is the first place I look. Then I check for a portable oven timer that has (1) some how turned on and(2) hidden itself, or a radio alarm that I had mistakenly set.
Hope you find it. Happy exorcism.