Parametric Signal Estimation Using the Cumulative Distribution Transform.

Area of Science:

• Signal processing
• Statistical estimation
• Mathematical transforms

Background:

• Accurate estimation of signal model parameters is crucial for various scientific and engineering applications.
• Traditional methods often face challenges with nonlinearities and noise in signal data.
• The Wasserstein distance is a powerful metric for comparing probability distributions, but its application in signal estimation is complex.

Purpose of the Study:

• To develop a novel and robust method for estimating signal model parameters.
• To transform a nonlinear estimation problem into a linear one for computational efficiency.
• To enhance the performance of signal parameter estimation in the presence of noise.

Main Methods:

• Utilizing the Cumulative Distribution Transform (CDT) to analyze signal data.
• Minimizing the Wasserstein distance between measured and model signals.
• Deriving properties of the CDT to facilitate a linear least squares estimation in the transform domain.
• Developing a noise mitigation strategy for improved estimation accuracy.

Main Results:

• The Cumulative Distribution Transform (CDT) converts a nonlinear estimation problem into a linear least squares problem.
• The proposed method demonstrates robustness to noise, with a novel approach for impact mitigation.
• Evaluation on a source localization problem shows competitive or superior performance compared to traditional methods.

Conclusions:

• The CDT offers a powerful tool for simplifying complex signal estimation problems.
• The developed method provides a robust and efficient approach for parameter estimation, particularly in noisy conditions.
• This technique has significant potential for applications in areas like source localization and beyond.