Abstract: Methods, apparatuses, and systems for calculating time delays by a Wasserstein approach are provided. A plurality of signals are recorded by a plurality of sensors (three or more), respectively, and received at a controller. The plurality of signals recorded by the plurality of sensors are generated in response to a signal emitted by a source. The plurality of signals are converted into a plurality of probability density functions. A cumulative distribution transform for each of the plurality of probability density functions is calculated. A time delay for each unique pair of the plurality of sensors is calculated by minimizing a Wasserstein distance between two cumulative distribution transforms corresponding to the unique pair of the plurality of sensors.

Abstract: Methods, apparatuses, and systems for calculating time delays by a Wasserstein approach are provided. A plurality of signals are recorded by a plurality of sensors (three or more), respectively, and received at a controller. The plurality of signals recorded by the plurality of sensors are generated in response to a signal emitted by a source. The plurality of signals are converted into a plurality of probability density functions. A cumulative distribution transform for each of the plurality of probability density functions is calculated.