This is probably not complete thought as have to figure out how to adjust the equations for non-linear travel to sensor (i.e. diagonal - being in a corner) but at least a start if a sensor reads time to hit each wall.

Assumptions:

Location on an axis W-E or N-S is expressed as a straight line from that wall.

West wall is 0 and East wall is full width of room (W).

North wall is 0 and South wall is full length of room (L).

Amount of time (N) that it takes to get a wall/sensor is equivalent to (time received - time sent) expressed in some time interval (t). Nw = west wall, Ne = east wall, Nn = north wall, Ns = south wall.

There is a set rate of travel for a signal in this room expressed by distance over time interval (d/t).

So each of the coordinates x (W-E axis) and y (N-S axis) have two equations each.

x = Nw * d/t

x = W - (Ne * d/t)

y = Nn * d/t

y = L - (Ns * d/t)

Solving for x and y will give you your (x, y) coordinate.

Just some thoughts -- hopefully not totally useless :).

Assumptions:

Location on an axis W-E or N-S is expressed as a straight line from that wall.

West wall is 0 and East wall is full width of room (W).

North wall is 0 and South wall is full length of room (L).

Amount of time (N) that it takes to get a wall/sensor is equivalent to (time received - time sent) expressed in some time interval (t). Nw = west wall, Ne = east wall, Nn = north wall, Ns = south wall.

There is a set rate of travel for a signal in this room expressed by distance over time interval (d/t).

So each of the coordinates x (W-E axis) and y (N-S axis) have two equations each.

x = Nw * d/t

x = W - (Ne * d/t)

y = Nn * d/t

y = L - (Ns * d/t)

Solving for x and y will give you your (x, y) coordinate.

Just some thoughts -- hopefully not totally useless :).