Time Difference of Arrival Estimation Based on a Kronecker Product Decomposition

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.