On frequency domain models for TDOA estimation

Abstract

Time-difference-of-arrival (TDOA) estimation is an important problem in many microphone signal processing applications. Traditionally, this problem is solved by using a cross-correlation method, but in this paper we show that the cross-correlation method is actually a restricted special case of a much more general method. In this connection, we establish the conditions under which the crosscorrelation method is a statistically efficient estimator. One of the conditions is that the source signal is periodic with a known fundamental frequency of 2π/N radians per sample, where N is the number of data points, and a known number of harmonics. The more general method only relies on that the source signal is periodic and is, therefore, able to outperform the cross-correlation method in terms of estimation accuracy on both synthetic data and artificially delayed speech data. The simulation code is available online.

Real-time loudspeaker distance estimation with stereo audio

“…Consequently, the delay parameter can be separated out analytically from the source signal and modelled as a continuous parameter. For finite length signals, however, a delay in the time domain only corresponds to a phase shift in the frequency domain if the signal is periodic with fundamental frequency 2π/N radians per sample (or an integer multiple thereof) [11]. Since we here consider very long segments compared to the delay, we wish to estimate, we do not make an inappropriate error by assuming that the source signals are periodic.…”

“…This is necessary to ensure that the decomposition of s i (η) is real-valued for non-integer values of η [11].…”

“…This increases the robustness of the estimator. Inspired by the recent work in [11], we also formulate the signal model so that the estimator produces estimates from a continuous set without resorting to any heuristic interpolation method. This is in contrast to many of the proposed localisation methods whose resolution is bounded to the sampling grid (see, e.g., [4,5,7]).…”

Grid size selection for nonlinear least-squares optimisation in spectral estimation and array processing

“…where fs is the sampling frequency in Hz and c is the propagation speed in meters/second. As we have recently detailed in [20], an often implicit assumption on a broadband source signal is that it is periodic in N so that a time-shift becomes a phase-shift in the frequency domain. That is,…”

DOA estimation of audio sources in reverberant environments

“…It is important to note that this has the widely used broadband model for DOA estimation as a special case if we chose ω0 = 2π/N and L = N [19], and the used model is therefore less restrictive than it might seem at first glance. Regarding the array structure, we assume a uniform linear array (ULA) as a proof-of-concept, but the methods developed in the following could just as well be derived or generalized to other array structures.…”