# New Methods for MLE of Toeplitz Structured Covariance Matrices with Applications to RADAR Problems

arXiv: https://arxiv.org/abs/2307.03923 · HTML: https://mlsanity.com/paper/2307.03923/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2023.

## Built on by (most cited first, 4 of 4)

- [Bit Efficient Toeplitz Covariance Estimation](https://mlsanity.com/paper/2412.12678/) (2024)
- [Self-Supervised Learning for Covariance Estimation](https://mlsanity.com/paper/2403.08662/) (2024)
- [The Optimization Landscape of Carath'eodory Decomposition of Toeplitz Covariances](https://mlsanity.com/paper/2511.01605/) (2025)
- [Compressive Toeplitz Covariance Estimation From Few-Bit Quantized Measurements With Applications to DOA Estimation](https://mlsanity.com/paper/2512.22527/) (2025)

## Abstract (arXiv)

This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced and two iterative algorithms are proposed for the optimization of the equivalent statistical learning framework. Both the strategies are based on the Majorization Minimization (MM) paradigm and hence enjoy nice properties such as monotonicity and ensured convergence to a stationary point of the equivalent MLE problem. The proposed framework is also extended to deal with MLE of other practically relevant covariance structures, namely, the banded Toeplitz, block Toeplitz, and Toeplitz-block-Toeplitz. Through numerical simulations, it is shown that the new methods provide excellent performance levels in terms of both mean square estimation error (which is very close to the benchmark Cram'er-Rao Bound (CRB)) and signal-to-interference-plus-noise ratio, especially in comparison with state of the art strategies.