Gohberg-Semencul Estimation of Toeplitz Structured Covariance Matrices and Their Inverses

Welcome to the (preliminary) repository for the paper "Gohberg-Semencul Estimation of Toeplitz Structured Covariance Matrices and Their Inverses"! This repository contains the code to reproduce the main results of our research work. As the paper is still undergoing the review process, the code, as well as the paper, may change continuously.

Abstract

In our work, we introduce a class of Toeplitz Covariance Matrix Estimators and their inverses based on the so-called Gohberg-Semencul decomposition, which is closely related to autoregressive parameters.

Usage

Currently, only the real-valued projected least squares estimator (denoted as PLS in our work) is available. By running the script "main_example.m", you apply the PLS estimator with hyperparameter tuning to samples generated from an AR(3) process.

Citation

If you are using this code for your research, please cite

@misc{boeck2023toep,
      title={{G}ohberg-{S}emencul Estimation of {T}oeplitz Structured Covariance Matrices and Their Inverses}, 
      author={Benedikt B\"ock and Dominik Semmler and Benedikt Fesl and Michael Baur and Wolfgang Utschick},
      year={2023},
      eprint={2311.14995},
      archivePrefix={arXiv},
      primaryClass={eess.SP},
      note={arXiv:2311.14995},
}

Licence of Contributions

This code is covered by the BSD 3-Clause License:

BSD 3-Clause License

Copyright (c) 2023 Benedikt Böck. All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

• Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

• Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

• Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

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