BACKGROUND

Field of the Invention

The present application relates generally to time delay distance estimation.

Description of Related Art

Time delay estimation (TDE) is an important step in the process of source localization. It is known that an emitted signal will travel through a medium and reach one or more spatially distributed sensors or receivers at times that are proportional to the distance traveled. In general, accurate estimates of the relative arrival times will provide accurate estimates of the source location. Conventional approaches to obtaining estimates of arrival times seek to calculate a time delay that maximizes some measure of similarity between received and reference signals. These conventional approaches are often tailored to an assumed noise model (e.g., follow the principle of maximum likelihood) and include maximizing the cross-correlation, minimizing the magnitude of the difference between observed and reference signals, and maximizing the average mutual information function. Each of these approaches, however, assumes that the only difference between the template signal and the observation is the time delay and some noise. But those assumptions lead to an incomplete model because they fail to account for a morphed version of the original signal that occurs when the dynamics of the medium alter the original signal during transit. Examples of such morphing may be seismological vibrations in the Earth, lamb waves moving across a structure, or optical signals propagating through a fiber. Without accounting for morphing of the original signal, the arrival time estimates can be significantly off which leads to an erroneous source location. Moreover, these conventional methods are computationally intensive and require a significant amount of computational time. That limits their ability to be implemented on certain systems. Thus, it would be beneficial to have methods that could account for signal morphing to produce more accurate arrival time estimations while minimizing the computational requirements of an apparatus or system implementing those techniques.

SUMMARY OF THE INVENTION

One or more the above limitations may be diminished by structures and methods described herein.

In one embodiment, a method is provided. A plurality of signals recorded by a plurality of sensors, respectively, are received at a controller. The number of the plurality of sensors is three or more. 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.

In another embodiment, an apparatus is provided. The apparatus includes a controller and a memory communicatively connected to the controller and storing a control program. The controller and memory are configured to: receive a plurality of signals recorded by a plurality of sensors, respectively, wherein a number of the plurality of sensors is three or more, and wherein the plurality of signals recorded by the plurality of sensors are generated in response to a signal emitted by a source; convert the plurality of signals into a plurality of probability density functions; calculate a cumulative distribution transform for each of the plurality of probability density functions; and calculate a time delay for each unique pair of the plurality of sensors by minimizing a Wasserstein distance between two cumulative distribution transforms corresponding to the unique pair of the plurality of sensors.

In yet another embodiment, a system for source localization is provided. The system includes a plurality of sensors each configured to record a signal emitted by a source and a controller. The controller is configured to: receive a plurality of signals recorded by a plurality of sensors, respectively, wherein a number of the plurality of sensors is three or more, and wherein the plurality of signals recorded by the plurality of sensors are generated in response to a signal emitted by a source; convert the plurality of signals into a plurality of probability density functions; calculate a cumulative distribution transform for each of the plurality of probability density functions; and calculate a time delay for each unique pair of the plurality of sensors by minimizing a Wasserstein distance between two cumulative distribution transforms corresponding to the unique pair of the plurality of sensors.

