Time difference of arrival (TDOA) estimation, which often serves as the fundamental step for a source localization or a beamforming system, has a significant practical importance in a wide spectrum of applications. To deal with reverberation, the TDOA estimation problem is often transformed into one of identifying the relative acoustic impulse responses. This letter presents a method to efficiently identify the relative acoustic impulse response between two microphones for TDOA estimation based on the so-called Kronecker product decomposition. By decomposing the relative impulse response into a series of Kronecker products of shorter filters, the original channel identification problem with a long impulse response is converted into one of identifying a number of short filters. Since the TDOA information is embedded only in the direct path of the relative impulse response, the dimension of the Kronecker product decomposition can be very small and, as a result, the developed algorithm is expected to work well in real environments with a small number of data snapshots.

中文翻译：

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基于Kronecker积分解的到达时间差估计

到达时间差 (TDOA) 估计通常作为源定位或波束成形系统的基本步骤，在广泛的应用中具有重要的实际意义。为了处理混响，TDOA 估计问题通常转化为识别相对声脉冲响应的问题之一。这封信提出了一种基于所谓的 Kronecker 乘积分解有效识别两个麦克风之间的相对声学脉冲响应以进行 TDOA 估计的方法。通过将相对脉冲响应分解为一系列较短滤波器的克罗内克乘积，将原始脉冲响应较长的信道识别问题转化为多个短滤波器的识别问题。