Analysis of the edge-effects in frequency-domain TDOA estimation

Passive estimation of the Time-Difference of Arrival (TDOA) of a common signal at two (or more) sensors is a fundamental problem in signal processing, with applications mainly in emitter localization. A common approach to TDOA estimation is the maximization of the sample cross-correlation between the received signals. For various reasons, this correlation is sometimes computed via the frequency-domain, following a Discrete Fourier Transform (DFT) of the signals - in which case the linear correlation is essentially replaced with a cyclic correlation. Although the two computations differ merely by some relatively short “edge-effects”, these edge-effects can entail more impact than commonly predicted by their relative (usually negligible) effective durations. In this work we analyze the mean square TDOA estimation error resulting from the use of cyclic instead of linear correlations, showing that for some signals the loss can be more severe than what would be predicted by a simple linear dependence on the delay value.

1. INTRODUCTION

Estimation of the Time-Difference of Arrival (TDOA) of a signal intercepted at two sensors is a fundamental, well-studied problem in signal processing. The estimated time difference if often used in the context of localizing the transmitting source, be it in the context of acoustic [5] (or underwater acoustic) signals or electromagnetic signals [2] [3]-but also in other applications (e.g., synchronization). Classical estimation approaches, such as the Generalized Cross-Correlation (GCC) [1] and performance analysis in terms of bounds [3] or small-errors analysis [2] [4] of specific estimators have been proposed and studied over the past three decades.