How to emulate human sound recognition
I do not think that there is a standard approach to this problem, because as far as I know it has not yet been solved satisfactorily. I believe that you can find a solution to a (very) simplified version of the problem by restricting it for example to the recognition of a fixed set of animal sounds. The way to go would probably be to use methods from speech recognition (Hidden Markov Models, HMM), because the problem is similar to voice control systems, where commands from a fixed set of predefined commands are identified. With some good engineering, these systems can work relatively well.

In the case of animal sounds you would need to define a fixed set of animal sounds that you want to be able to recognize, collect a large database of such sounds, and use the data to train HMM models, which can then be used to score unknown sounds. Of course, such a system does not even come close to human capability of distinguishing sounds, but for such a restricted application it may work well enough.

So in that sense I do not agree that voice control systems are "very inaccurate" if there is no context available, because that's the usual scenario for simple voice control systems, which can in fact be made to work in practice.