A Geometric Approach to Time Delay Estimation for Acoustic Localization of Primates

Abstract

Due to the threatened status of multiple howler monkey species, it is important to monitor them for effective conservation. Passive methods such as acoustic localization are becoming increasingly popular for this purpose. This involves recording vocalizations by an array of microphones that are spread over the habitat of the animal and estimating differences in arrival times to triangulate its position. The quality of these time differences therefore largely determines the quality of the position estimate. However, the signal of interest may be significantly obscured by background noise, thereby complicating the accurate estimation of those differences. The state-of-the-art cross-correlation method fails to overcome this difficulty, which calls for more robust methods. This thesis investigates whether techniques from computational geometry may be more successful in this, with the ultimate goal of improving the position estimates. We model the problem of shape matching under one-dimensional translations and propose (multiple variations of) exact or approximation methods for three geometric distance measures: the Hausdorff distance, the Fréchet distance and the Earth Mover's Distance. Experimental results demonstrate that the cross-correlation method is still significantly more robust than our proposed methods. The localization of eight roars captured from the field shows more promising results as the performance of the Hausdorff distance for point sets does not show a statistically significant difference, whereas the other methods lag behind and perform significantly worse. Simulations reveal the limitations and the impact of the microphone geometry on those, which confirm that the largest bottleneck is the scalability.