  Any audio recording encapsulates the unique fingerprint of the associated
acoustic environment, namely the background noise and reverberation.
Considering the scenario of a room equipped with a fixed smart speaker device
with one or more microphones and a wearable smart device (watch, glasses or
smartphone), we employed the improved proportionate normalized least mean
square adaptive filter to estimate the relative room impulse response mapping
the audio recordings of the two devices. We performed inter-device distance
estimation by exploiting a new set of features obtained extending the
definition of some acoustic attributes of the room impulse response to its
relative version. In combination with the sparseness measure of the estimated
relative room impulse response, the relative features allow precise
inter-device distance estimation which can be exploited for tasks such as best
microphone selection or acoustic scene analysis. Experimental results from
simulated rooms of different dimensions and reverberation times demonstrate the
effectiveness of this computationally lightweight approach for smart home
acoustic ranging applications
