Refinement of TDOA Measurements for Flush Mounting Planar Microphone Arrays Using Low Rank and Linear Geometric Constraints

Estimating time difference of arrival (TDOA) is an essential prerequisite for microphone arrays in many applications such as passive sound source localization and self-calibration. In addition to measurement noise and outliers, time of arrival (TOA) deviations derived from shell-related diffraction propagation also contribute to TDOA measurements when a flush mounting array is used which consists of all sensors flush mounted into the shell. Based on the observation that the TDOAs of two pairs of sensors forming equilong parallel lines (EPLs) are equal regardless of the far-field source direction under the line-of-sight condition, we propose a novel method for flush mounting planar arrays to refine TDOA measurements applying both the linear geometric constraint corresponding to EPLs and the rank-2 algebraic constraint to the measured TDOA matrix build from all TDOA measurements. This method is capable of effectively suppressing measurement noise, TDOA outliers, and diffraction induced TOA deviations simultaneously. A closed-form, analytic solution is presented which is computationally efficient and suitable for real-time applications. Simulated and field experiments demonstrate that the proposed method outperforms the state-of-the-art algorithms if the array shape contains at least one pair of EPLs. Furthermore, explicit performance improvement can be achieved when the number of linearly independent EPLs increases. The proposed method is beneficial to further performance improvement of TDOA-based applications such as sound source localization when flush mounting planar arrays are used.