The AECM Algorithm for Deterministic Maximum Likelihood Direction Finding in the Presence of Gaussian Mixture Noise
Abstract
Gaussian mixture noise can model non-Gaussian noise and also be used when outliers are present in measurements. For deterministic maximum likelihood direction finding in Gaussian mixture noise, the Space-Alternating Generalized Expectation-maximization (SAGE) algorithm, an extension of the expectation-maximization algorithm, was applied and designed by Kozick and Sadler twenty odd years ago, which simultaneously updates DOA estimates at each iteration and cannot properly converge under unequal signal powers. In this paper, the Alternating Expectation-Conditional Maximization (AECM) algorithm, an extension of the SAGE algorithm, is applied and designed, which utilizes multiple less informative versions of the complete data and the golden section search method to update DOA estimates at each iteration sequentially (one by one). Theoretical analysis reveals that the AECM algorithm possesses nearly the same computational complexity of each iteration as the SAGE algorithm. However, simulation results prove that the AECM algorithm exhibits faster stable convergence and is more attractive in computation. Importantly, the AECM algorithm, unlike existing subspace based robust DOA estimation methods, can still be used when signals are coherent.
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BibTeX
@misc{gong2026aecm,
title = {{The AECM Algorithm for Deterministic Maximum Likelihood Direction Finding in the Presence of Gaussian Mixture Noise}},
author = {Mingyan Gong and Bin Lyu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.02309},
eprint = {2605.02309},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.02309},
}
RIS
TY - UNPB
TI - The AECM Algorithm for Deterministic Maximum Likelihood Direction Finding in the Presence of Gaussian Mixture Noise
AU - Mingyan Gong
AU - Bin Lyu
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2605.02309
UR - https://arxiv.org/abs/2605.02309
AB - Gaussian mixture noise can model non-Gaussian noise and also be used when outliers are present in measurements. For deterministic maximum likelihood direction finding in Gaussian mixture noise, the Space-Alternating Generalized Expectation-maximization (SAGE) algorithm, an extension of the expectation-maximization algorithm, was applied and designed by Kozick and Sadler twenty odd years ago, which simultaneously updates DOA estimates at each iteration and cannot properly converge under unequal signal powers. In this paper, the Alternating Expectation-Conditional Maximization (AECM) algorithm, an extension of the SAGE algorithm, is applied and designed, which utilizes multiple less informative versions of the complete data and the golden section search method to update DOA estimates at each iteration sequentially (one by one). Theoretical analysis reveals that the AECM algorithm possesses nearly the same computational complexity of each iteration as the SAGE algorithm. However, simulation results prove that the AECM algorithm exhibits faster stable convergence and is more attractive in computation. Importantly, the AECM algorithm, unlike existing subspace based robust DOA estimation methods, can still be used when signals are coherent.
ER -