Time Delay Estimation via Wasserstein Distance Minimization
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Solution Overview
Problem
Conventional time delay estimation methods fail to account for signal morphing during transit through mediums, leading to inaccurate source location and high computational requirements, which limits their implementation on certain systems.
Innovation Solution
The method involves converting recorded signals into probability density functions and calculating cumulative distribution transforms to minimize the Wasserstein distance between sensors, allowing for accurate time delay estimation while reducing computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional time delay estimation methods are used, then computational requirements are high, but measurement precision deteriorates due to failure to account for signal morphing
Solution Approach 1:
The patent transforms the time delay estimation problem from the time domain to the frequency domain by applying Fourier transforms. This parameter transformation allows the use of cross-spectral density functions instead of direct time-domain correlation, which accounts for signal morphing effects while providing a more computationally efficient framework for estimation.
Solution Approach 2:
The patent replaces conventional mechanical/computational correlation methods with a spectral analysis approach. By substituting time-domain correlation with frequency-domain cross-spectral density analysis, the method achieves both accuracy in handling signal morphing and reduced computational burden through efficient spectral processing.
2Productivity
If conventional time delay estimation methods are used, then computational time is significant, but productivity improves in terms of source localization capability
Solution Approach 1:
The patent changes the computational parameter domain from time to frequency, enabling the use of fast Fourier transform algorithms. This parameter transformation reduces computational time while maintaining the ability to perform source localization by analyzing the spectral characteristics of signals from multiple sensors.
Solution Approach 2:
The patent introduces cross-spectral density functions as an intermediary between the raw sensor signals and the time delay estimates. This intermediary representation in the frequency domain captures signal morphing effects and enables more efficient computation compared to direct time-domain methods.
3Device complexity
If signal morphing is not accounted for, then device complexity is reduced, but measurement precision deteriorates significantly
Solution Approach 1:
The patent transforms the estimation problem to the frequency domain where signal morphing effects are naturally captured in the cross-spectral density function. This parameter transformation allows the model to account for morphing without requiring complex time-domain signal processing or explicit morphing models.
Solution Approach 2:
The patent moves the analysis from the one-dimensional time domain to the two-dimensional frequency domain (real and imaginary parts of the cross-spectral density). This dimensional change provides a more comprehensive representation of signal characteristics, enabling accurate accounting of morphing effects while maintaining model tractability.
Data Source
AI summary
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.