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Maximum Likelihood Estimation in Mixed Integer Linear Models.

David Tucker1, Shen Zhao2, Lee C Potter1

  • 1Department of Electrical & Computer Engineering, Ohio State University, Columbus, OH 43210.

IEEE Signal Processing Letters
|November 20, 2023
PubMed
Summary
This summary is machine-generated.

We developed a new lattice basis construction for maximum likelihood (ML) parameter estimation in mixed integer linear models. This method improves accuracy for applications like direction of arrival estimation.

Keywords:
Chinese remainder theoremHermite normal formPhase unwrappinglatticessphere decoding

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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.