The challenge to single out the sound from each source is called signal separation and is an important problem in nonlinear dynamics (or so I'm told.) You may also call this noise removal if one or more of the signal sources are noise to you.
Blind Signal Separation (BSS) is one method to do this. The most heavily cited paper on it is A New Learning Algorithm for Blind Signal Separation and a good introduction (atleast the first few pages are) is Blind Signal Separation: Statistical Principles.
I'm new to the field and trying to get a feeling for where the "forefront in technology" is, especially regarding signals and simulation of non-linear systems. BSS seemed interesting, having little need for knowledge about the source of the signal. However, papers about this method have been reduced to a trickle over the last few years. Why is this? The 2001 paper A Proof of the Non-Existence of Universal Nonlinearities for Blind Signal Separation could have something to do with it..
Is BSS a dead topic? If so, what are currently good methods in signal separation and prediction of nonlinear systems?
With apologies for crossposting