DOA-Based Three-Dimensional Node Geometry Calibration in Acoustic Sensor Networks and Its Cramér–Rao Bound and Sensitivity Analysis

Acoustic sensor networks (ASNs) are widely applied in scenarios like teleconference, teaching, and theatre. ASNs can be used in tracking speakers, enhancing the speaker's speech and human-machine interactions, etc., but the geometric structure of the ASN has to be calibrated. ASN geometry calibration is a challenging task due to the irregular geometric structures of ASNs. A three-dimensional (3D) node geometry calibration approach based on direction of arrival (DOA) measurements and artificial bee colony (ABC) algorithm is proposed in this paper. The theoretical DOAs of sound sources relative to nodes are first derived based on 3D rotation matrices and translation vectors, and the corresponding measured DOAs are estimated by the time-difference-of-arrival. Then, the node geometry calibration problem is formulated as the minimization of a cost function measuring the mismatch between theoretical and measured DOAs, and such non-convex minimization is effectively solved by the ABC algorithm. Next, Cramér-Rao bound is presented to provide a theoretical lower bound for DOA-based node geometry calibration. Finally, the sensitivity of the proposed method to the sound source position error is discussed. The proposed method can calibrate node geometry positions successfully in both 2D plane and 3D space and requires no information transmission among nodes when the positions of few sound sources and the relative geometry of microphones in each node are known. Experimental results reveal the validity of the proposed node geometry calibration method.