Maximum Likelihood Estimation in Mixed Integer Linear Models

Area of Science:

• Signal Processing
• Statistical Inference
• Optimization

Background:

• Maximum likelihood (ML) parameter estimation is crucial for mixed integer linear models.
• Existing methods face challenges with arbitrary noise covariance.
• Applications include single frequency, phase contrast imaging, and direction of arrival (DoA) estimation.

Purpose of the Study:

• To present a novel lattice basis construction for ML parameter estimation.
• To address the closest lattice point problem inherent in these estimations.
• To demonstrate the method's efficacy in relevant applications.

Main Methods:

• Developed a specific lattice basis construction tailored for ML estimation.
• Formulated the parameter estimation as a closest lattice point problem.
• Utilized simulated data for validation.

Main Results:

• Successfully constructed a lattice basis for ML parameter estimation.
• Demonstrated improved performance in simulated DoA estimation.
• Validated effectiveness in simulated phase contrast imaging scenarios.

Conclusions:

• The proposed lattice basis construction is effective for ML parameter estimation.
• The method offers a viable solution for mixed integer linear models with arbitrary noise covariance.
• Applicable to critical areas like DoA and phase contrast imaging.