Solving ambiguity of direction finding using phase comparison?

[hoz]

Suppose you have three antennas a1,a2 and a3, and the distance of the antennas (a2,a3) to the first antenna (a1) are d12 and d13. When d12 <=lambda/2, you can resolve the angle of arrival of incoming signal with only two antennas (a1 and a2). When you can't position the antennas so close (d12>lambda/2) there will be multiple solutions of possible signal arrival angle. So you both measure the phase difference between a1-a2, and a1-a3. Then you find the true direction of signal incoming. This is ok. But how to do that?

For example s1=exp(j*2pi*f*t), s2=exp(j*2pi*f*t+phi1), s3=exp(j*2pi*f*t+phi2). Suppose that you could extract phi1 and phi2, and you know the antenna distances. Lets say d12=5/2*lambda and d13=9/2*lambda. How do you find the true arrival angle of the signal?

A piece of matlab code would be very helpful.

Thanks

 

[BradtheRad]

Just to give some answer...

Having a phase difference, allows you derive a time differential.

After you get a simultaneous reading from two antennas, you can plot a curved line, containing all possible sources. This is only one part of the answer of course.

By taking data from three antennas, you can plot three curves. Then you can find the one location where they intersect.

This thread might be of interest.

https://www.edaboard.com/threads/327358/