Distributed estimation of cross-correlation functions in ad-hoc microphone arrays

In this paper, we address the problem of estimating the cross-correlation function between two microphone signals recorded in different nodes of an ad-hoc microphone array or wireless acoustic sensor network, where the transmission of the entire microphone signal from one node to another is undesirable due to power and/or bandwidth constraints. We show that instead of directly computing the cross-correlation function, it can be estimated as the solution to a deconvolution problem. This deconvolution problem can be separated into two subproblems, each of which depends on one microphone signal and an auxiliary signal derived from the other microphone signal. Three different strategies for solving this deconvolution problem are proposed, in which the two subproblems are solved jointly (symmetric deconvolution), separately (asymmetric deconvolution) or in a consensus framework (consensus deconvolution). Simulation results illustrate the performance difference in terms of estimation accuracy, noise robustness, and transmission requirements.