Beamforming for source localization

I have a situation:

I have carried out Delay & Sum Beamforming for my 3D microphone array geometry containing 8 mics (nearfield). I have succesfully able to localize the azimuth and elevation of source anywhere in space by fixing the range of source('rs') equal to range of beamformer('rb'). So, when I plot the energies on azimuth vs elevation, I get max energy on correct location where I have placed the source.

But the problem is when the ranges are unequal (that is 'rs' not equal to 'rb'), I get unsatisfactory results. For example: rs=1m ,rb=5m Iam still able to localize the source but when rs=5m and rb=1m, I get absurd plot.

What could be the reason? How can I check the dependency of the beamformer on Ranges?

please help with your ideas.

[Honglei Chen]

What are rs and rb? I can kind of guess what you mean by range of source, but I don't understand what you mean by range of beamformer. Could you clarify?

[zozo]

The algorithm is for localization of point source in 3D space given by (range,azimith,elevation).

I place a source S(say at 1,45°,20°) and simulate the signals(sine) at each of 8 mics by delaying them. Now I have 8 channels but do not know where exactly the source S was placed. My task is to find its location by using these 8 channels. So, I set the range of beamformer 'rb' to say 1m and sweep azimuth (-179:180) and elevation(-89:90) of beamformer and plot in a 3D mesh. At(45,20), I get max. energy (main lobe) and hence localise the source. But from plots, Iam unalbe to find a clear relation between 'rb' and 'rs' when they r unequal as stated by my question above.

Hope you get this now.

[Honglei Chen]

So you are varying rb in your algorithm to search for rs? Then obviously when rb and rs are the same, you get the best result. Because you are using spherical wavefront, the phase progress between elements is related to the range and that's why you see the mismatch. You should be able to calculate this mismatch using a mathematical equation.