A geometric solution to microphone array position calibration and its confidence interval analysis

Abstract

Wireless acoustic sensor networks (WASNs) comprised of spatially distributed acoustic nodes have been increasingly popular in many areas such as speech enhancement, blind source separation, and audio surveillance, where node position information is generally required to implement relevant processing algorithms. In this article, we focus on the node position calibration only using direction-of-arrival (DOA) information with each node consisting of a microphone array. State-of-the-art techniques translate the position calibration into optimization of DOA-based cost functions, and have shown notable success. However, a compromise between position calibration accuracy and computational load still exists. Furthermore, none of the existing studies can offer a quantitative evaluation of calibration performance before the optimization procedure is finished. To address these problems, a geometric solution to array node position calibration is proposed using DOA measurements. For a given array node, DOAs of three sources are first utilized to construct cylinder, plane, and cone equations. Next, the two-dimensional projection of intersections among these equations is calculated using Sylvesterresultantmatrix. Finally, a closed-form solution of node position in three-dimensional space is established. Moreover, explicit mathematical derivation of the confidence interval analysis on the calibration results under given node angle estimation error condition is presented, indicating that the proposed method can provide predictable performance with corresponding probabilities. The Cramér-Rao bound (CRB) is further investigated. Simulation results reveal that as compared with existing methods our approach achieves comparable calibration accuracy with much less computational burden. Real-world experiments also verify its effectiveness.