# Determining the location of a signal using only 2 receivers

1. Sep 17, 2015

### DDH

I'm currently writing a book. In the book the main characters need to find the source of a signal but they can only use two primitive, non-directional receivers.
I think it is possible to calculate the location providing they have access to a very accurate timebase which will tell them the time difference it takes the signal to reach the receivers. Each measurement would give them a plane in which the source should lie. After each measurement they move to a different location (at a considerable distance of the previous location). After two measurements they would have an line on which the source should be, the intersection between the two planes. Three measurements would give them the location of the source, the intersection between the line and the third plane. (assuming none of the planes are the same or parallel)
Am i correct? And if so, how should the calculations be done.
If not, is there an other way to do it with just time difference as data, f.e. using more receivers.

2. Sep 17, 2015

### RUber

Since signals travel radially, you should be looking a circles. If you have perfect time difference data and clear line of sight, your 'planes' are spherical shells, and instead of lines, you should have the intersections of spherical shells.
If you now something a priori about the signal, like it is stationary and on the ground, you will have the possible source locations reduced to 2 points with two measurements.
A third measurement, as long as it is not collinear with the first two should be the tiebreaker.

3. Sep 17, 2015

### DEvens

Suppose your two receivers are 1 km apart. And suppose the source is on a line fairly close to the line between the two receivers. The signal arrives at the two detectors just 3 microseconds apart. If your timing is good to only +/-1 microsecond, then you have a directional resolution of round about 30 degrees.

Also, as RUber referred to, you have a left-right issue. If the delay is (2 +/- 1) microseconds, you can't distinguish anything from 45 degrees to the left to 45 degrees to the right.

If your detectors were 10 km apart with the same electronics, then you could distinguish a smaller angle. Does your story allow for the antenna to be that far apart and have wires leading to a central receiver?

It seems kind of far-fetched though. You can make a simple di-pole antenna that will be directional to better than that kind of accuracy out of a hoop. Supposing the signal is only pulses that don't give you time to rotate a hoop to find the max and min. Then you want three or four hoops arranged at different angles.

4. Sep 17, 2015

### DDH

Thank you for the reply, RUber and DEvens.
First of all, nothing is known about the signal a priori, except that it propagates with the speed of light and it's not blocked by matter what so ever.
Secondly, i realise i've been looking at it in a two dimensional way applied on a three dimensional reality.
Third, i've used some wrong words to describe the problem. I tried to write down an analogy so i didn't have to disclose too much about the story. My apologies.

Last edited: Sep 17, 2015