Rough estimate of how close a human speaker is to a microphone?
Here is one possible suggestion: use a second order microphone (e.g. cardioid microphone). The human voice is a point source and has strong reactive velocity near-field component which velocity mics are sensitive too. In plain English this means you get substantially more relative bass when the speaker is close by. You could leverage to compare the energy in the 500-1kHz Band to the energy in the 100-200Hz band. With some reasonable calibration you ought be to able to tell whether the speaker is close or far.