提升聲源位置估測準確度之麥克風陣列幾何配置

Abstract

本論文提出一套在麥克風數量固定與麥克風間距離有最大限制的情況，在不同訊噪比(SNR)下找出一個對角度估測與位置估測的最佳麥克風陣列排列方法。文中所使用的角度和位置的估測方法乃基於麥克風之間聲源傳遞的時間差(Time Difference of Arrival, TDOA)。因為此時間差的估測在實際狀況下有誤差，因此導致聲源角度和位置的估測不準，而此不準度與陣列的幾何配置有密切關係。本論文提出以估測矩陣的奇異值(singular value)對估測變異量的影響，進而探討麥克風陣列的最佳排列方法。在遠聲場的條件下，本論文得到精確的全域解析解可以使角度估測的Cramér-Rao Lower Bound (CRLB)最小，而在近聲場的情形下，其結果需要對非線性聯立方程式求解，且與聲源位置有關。因此本論文探討在額外的限制條件下，其數值解的結果與特性。

This work proposes an optimal structure of microphone array for sound source localization under the conditions of fixed microphone numbers, limited distance between each microphone pair and different signal-to-noise ratios (SNR). The location estimation algorithm is based on the time difference of arrival (TDOA) of each microphone pair. The estimation accuracy is influenced by the TDOA errors and is dependent on the microphone array geometry. This work proposes a geometry optimization formulation using the relationship between the singular values of the estimation matrix and the estimation error. Under the far field condition, an analytical solution can be derived to minimize the Cramér-Rao Lower Bound (CRLB). In near field, the result leads to a set of nonlinear equations and is source location dependent. With additional constraints, several numerical solutions are discussed.