Distributed Microphone Array Localization Problem via SDP-SOCP Method

In multimedia applications, it is common to employ acoustic sensors collectively to enhance signals and to locate sound sources. A direct problem can be formulated to locate sound sources from a set of known sensors. In order to form the acoustic sensor network, it is important to locate the sensor array locations first. However, unlike other networks in which direct time-of-arrival (TOA) measurements might be possible, acoustic distributed network can only obtain time-difference-of-arrival (TDOA) measures indirectly from various sound source anchors. While it is common to employ convex optimization techniques to localize sensor locations in a network with TOA information, it has not been studied properly when it comes to TDOAs. This article considers the microphone array localization problem in a distributed acoustic network with TDOA measurements. We formulate the inverse problem which applied the known source locations to identify the wireless array configuration and estimate the location for each array. The proposed method formulates a mixed semidefinite programming (SDP) and second-order cone programming (SOCP) relaxation model, and then the acoustic geometry is obtained by solving a linear optimal programming. Furthermore, the characteristics of the optimal solution are studied and exact relaxation conditions are given. Experimental results demonstrate that the proposed mixed model can successfully estimate the sensor locations in noisy and reverberant environments for 2-dimensional and 3-dimensional space, which outperforms other relaxation methods.