Welcome to the repository for the paper "Gohberg-Semencul Toeplitz Covariance Estimation via Autoregressive Parameters"! This repository contains the code to reproduce the main results of our research work.
Source code of the paper
B. Böck, D. Semmler, B. Fesl, M. Baur and W. Utschick, "Gohberg-Semencul Toeplitz Covariance Estimation via Autoregressive Parameters," in IEEE Transactions on Signal Processing, vol. 73, pp. 858-875, 2025, doi: 10.1109/TSP.2025.3536101.
Link to the paper: https://ieeexplore.ieee.org/document/10857370
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.
The script main_example.m contains an exemplary matlab file, in which you can comment in your desired (inverse) covariance estimator. Our code comprises several estimators for Toeplitz structured covariances comprising our proposed estimators PGD and PLS estimator as well as the baselines EM, Circ, Avg, Band, Tape, TSL, ShU, and ShB (see our paper for the acronyms). The script applies any estimator to N P-dimensional samples generated from an AR(3) process with adjustable parameters. The directory our_estimators contains our proposed estimators. The directory cov_generators contains scripts to generate Toeplitz covariance matrices. The baselines directory contains the baselines, and the utils directory stores some auxiliary scripts.
If you are using this code for your research, please cite
@ARTICLE{boeckToep2025,
author={Böck, Benedikt and Semmler, Dominik and Fesl, Benedikt and Baur, Michael and Utschick, Wolfgang},
journal={IEEE Transactions on Signal Processing},
title={Gohberg-Semencul Toeplitz Covariance Estimation via Autoregressive Parameters},
year={2025},
volume={73},
number={},
pages={858-875},
keywords={Estimation;Covariance matrices;Tuning;Matrix decomposition;Vectors;Array signal processing;Standards;Parallel processing;Optimization;Hands;Covariance estimation;autoregressive processes;Gohberg-Semencul;Toeplitz;likelihood estimation},
doi={10.1109/TSP.2025.3536101}}
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