Welcome to the forum
!
How big are the coordinates, i.e is the grid 10x10, so a grid 'square' is 40cm x 40cm?
You could try and do something with volume measuring with a band pass filter on each microphone set to one of the two frequencies of the speakers; two VERY sensitive voltage sensors, and measure the slight variations in voltage, and therefore volume, as the robot moves further away from the speakers.
I've never tried this before, so this is just off the top of my head
-HyperNerd