Methods and required data for estimating a source’s φ and θ angles

[shakibmehr]

If I want to calculate the position of a source in spherical coordinates (φ and θ) or azimuth elavation, what method or formula should I use, and what data do I need.

[esarradj]

I am not sure if I understand what you are planning to do. If you need your results in spherical coordinates, you will simply have to convert the Cartesian coordinates of the grid.

[shakibmehr]

I want to have spherical coordinates (azimuth, elevation) instead of x and y.
If I convert Cartesian to spherical, won’t the error become large for far sources?
Because I don’t have z at all, and I always set z as constant.

[artpelling]

If you would like to use spherical coordinates, then it is just a matter of transformation, as said.

It is common to not know the exact position of the source — that is one of the reasons why microphone array methods are used. One designs the focus grid such that it contains points where the source could be. For your problem, you could guess z based on prior knowledge and/or use different values for z to find the best match. Note that all of this is independent of the coordinate system.

If you are trying to determine the source's direction rather than position, that is an entirely different problem known as "direction of arrival" (DOA) beamforming...