Fast Cross-Correlation for TDoA Estimation on Small Aperture Microphone Arrays

This paper introduces the Fast Cross-Correlation (FCC) method for Time Difference of Arrival (TDoA) Estimation for pairs of microphones on a small aperture microphone array. FCC relies on low-rank decomposition and exploits symmetry in even and odd bases to speed up computation while preserving TDoA accuracy. FCC reduces the number of flops by a factor of 4.5 and the execution speed by factors of 8.2, 2.6 and 2.7 on a Raspberry Pi Zero, a Raspberry Pi 4 and a Nvidia Jetson TX2 devices, respectively, compared to the state-of-the-art Generalized Cross-Correlation (GCC) method that relies on the Fast Fourier Transform (FFT). This improvement can provide portable microphone arrays with extended battery life and allow real-time processing on low-cost hardware.