On time delay interpolation for improved acoustic reflector localization

The localization of acoustic reflectors is a fundamental component in various applications, including room acoustics analysis, sound source localization, and acoustic scene analysis. Time delay estimation (TDE) is essential for determining the position of reflectors relative to a sensor array. Traditional TDE algorithms generally yield time delays that are integer multiples of the operating sampling period, potentially lacking sufficient time resolution. To achieve subsample TDE accuracy, various interpolation methods, including parabolic, Gaussian, frequency, and sinc interpolation, have been proposed. This paper presents a comprehensive study on time delay interpolation to achieve subsample accuracy for acoustic reflector localization in reverberant conditions. We derive the Whittaker-Shannon interpolation formula from the previously proposed sinc interpolation in the context of short-time windowed TDE for acoustic reflector localization. Simulations show that sinc and Whittaker-Shannon interpolation outperform existing methods in terms of time delay error and positional error for critically sampled and band limited reflections. Performance is evaluated on real-world measurements from the MYRiAD dataset, showing that sinc and Whittaker-Shannon interpolation consistently provide reliable performance across different sensor-source pairs and loudspeaker positions. These results can enhance the precision of acoustic reflector localization systems, vital for applications, such as room acoustics analysis, sound source localization, and acoustic scene analysis.