I was working on this before savageag posted so I'll post it even though it is similar.

Lets say the speed of the tranducer wave be 1 metre per second for simplicity.

Lets say the square measures 10 metres diagnally, again for simplicity.

Let A be the top left receiver, B be top right, C be bottom right and D be bottom left (ie. Clockwise).

A receives a signal and starts a timer.

C, in the opposite corner, receives a signal and works out the time difference between A and C.

Now if the bot was exactly in the middle of A and C the time difference would be 0.

The closer the bot is to A the greater the time the signal will take to reach C.

Now if the bot is at A (ten metres away from C) the time difference will be ten seconds(with signal travelling at one metre per second).

If the bot is halfway between A and the middle(7.5 metres from C, 2.5 metres from A) the time difference will be 5 seconds(7.5 seconds to travel to C minus 2.5 seconds to A).

So we have worked out how to find where it is on this line.

Code:

Time from A to C:
1s: 5.5m from C, 4.5m from A. (5.5 secs - 4.5secs)
2s: 6m from C, 4m from A. (6secs - 4secs)
3s: 6.5m from C, 3.5m from A. (6.5secs - 3.5secs)
4s: 7m from C, 3m from A. (7secs - 3secs)
6s: 8m from C, 2m from A. (8secs - 2secs)
9s: 9.5m from C, .5m from A. (9.5 secs - .5secs)
If the signal reaches C before A we can reverse these values.
Time from C to A:
2s: 6m from A, 4m from C. (6secs - 4secs)

We can do the same thing for the BD line.

When it is not on one of the intersecting lines the problem seems to get much harder. I think what we have to do is draw the possible curves.

If you haven't read this article I suggest you do it now:

http://travel.howstuffworks.com/gps.htm

For example: given a time of 2 seconds from signal received at A to C we look above and find 6m to C and 4m to A. So we get out our compass and draw a 4m arc from point A and a 6m arc from point C (you might have to do this in scale!).

We then do the same thing for the value we work out for B and D. Hopefully, we should find that the point is on the intersection of two of these arcs. The other arcs should not intersect.

To put all this in some sort of algorithm is beyond me but it should be possible.

Edit: After reading savageag's post it seems I was making the problem way too hard. I forgot we could also get the distance between A and D, etc. If you have the distance between A and C as well as A and D the problem becomes quite simple. The arc solution may work but is a lot more complex. If you try the arc solution, please tell me if it works!

End Edit.

Please post back when you find the solution to this problem.