Measuring position in a room with mics synced with GPS modules in the corners, with 1 or 2 on the floor

so heres my idea play a tone of 120 Hz pulses in a frequency that cant be heard and measure the delay between spikes and do triangulation. the corners of a room looks really similar to those photo reflectors, wouldn't the corner reflect any sound that isn't in the direct corner? I'd just have to make sure all the mics are synced but I could do that with some GPS modules for time.
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