On Cross Correlation Based Discrete Time Delay Estimation

Abstract

Cross correlation function (CCF) is a powerful tool in time delay estimation and parabola functions are widely used as parametric models of it. However, no study has been done on the accuracy of the parabola approximation of CCF. In this paper we analyze the CCF of multi-sensors and derive the analytic forms of CCF for the stationary processes of exponential auto-correlation function and with respect to two important types of sensor kernels. We demonstrate that the Gaussian function is a better and more robust approximation of CCF than the parabola in these cases. This new approach leads to higher precision in time delay estimation using the CCF peak locating strategy.

Low-frequency oscillations measured in the periphery with near-infrared spectroscopy are strongly correlated with blood oxygen level-dependent functional magnetic resonance imaging signals

“…The RIPTiDe procedure determined two independent quantities: the time delay value between the NIRS and fMRI data, and the contribution of the delayed NIRS signal to the BOLD variance. The time delay was determined by fitting a Gaussian to the cross-correlation calculated in the time domain 38 (which is more robust for determining subTR time shifts in the presence of aliasing than the direct frequency domain method). This cross-correlation was implemented using 181 invocations of film_gls (part of FSL) with differently time-shifted NIRS Δ[tHb] time courses used as a regressor.…”

Binaural Localization and Detection of Speakers in Complex Acoustic Scenes

“…Instead of using the integer time lag directly for ITD estimation, it is possible to refine the fractional peak position by applying parabolic [36] or exponential [84] interpolation strategies. It has been found that the exponential interpolation performs better than the parabolic one, which is in line with results reported by Tervo and Lokki [73].…”

“…In accordance with [79], it has been decided to use 37 histogram bins to cover the azimuth range of [−90, 90 • ] in steps of 5 • , where each individual bin is chosen to represent the time delay of the corresponding anechoic HRTF. To increase the resolution of the final azimuth estimate, exponential interpolation is applied to refine the maximum peak position of the histogram analysis [84].…”

Features for speaker localization in multichannel bilateral hearing aids

“…In order to compute the TDOA features with the required inter-sample accuracy, exponential interpolation [8] has been used to determine the maximum of the cross-correlation function.…”