New Methods for MLE of Toeplitz Structured Covariance Matrices with Applications to RADAR Problems
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915280589946880 |
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| author | Aubry, Augusto Babu, Prabhu De Maio, Antonio Rosamilia, Massimo |
| author_facet | Aubry, Augusto Babu, Prabhu De Maio, Antonio Rosamilia, Massimo |
| contents | 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 Cramér-Rao Bound (CRB)) and signal-to-interference-plus-noise ratio, especially in comparison with state of the art strategies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_03923 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | New Methods for MLE of Toeplitz Structured Covariance Matrices with Applications to RADAR Problems Aubry, Augusto Babu, Prabhu De Maio, Antonio Rosamilia, Massimo Signal Processing 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 Cramér-Rao Bound (CRB)) and signal-to-interference-plus-noise ratio, especially in comparison with state of the art strategies. |
| title | New Methods for MLE of Toeplitz Structured Covariance Matrices with Applications to RADAR Problems |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2307.03923 |