Gaussian mixture noise can model non-Gaussian noise and also be used when outliers are present. 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 direction of arrival (DOA) estimates at each iteration and cannot properly converge under unequal signal powers. In this article, 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 shows that the AECM algorithm has almost the same computational complexity of each iteration as the SAGE algorithm. However, numerical results show that the AECM algorithm yields faster stable convergence and is computationally more efficient.

翻译：高斯混合噪声可建模非高斯噪声，亦可用于存在离群值的情形。针对高斯混合噪声中的确定性最大似然测向问题，Kozick与Sadler二十余年前应用并设计了空间交替广义期望最大化（SAGE）算法——作为期望最大化算法的扩展，该算法在每次迭代中同时更新波达方向（DOA）估计，且在信号功率不等时无法正确收敛。本文应用并设计了交替期望条件最大化（AECM）算法——作为SAGE算法的扩展，该算法利用完整数据的多个低信息量版本及黄金分割搜索方法，在每次迭代中顺序（逐一）更新DOA估计。理论分析表明，AECM算法每次迭代的计算复杂度与SAGE算法几乎相同。然而，数值结果表明，AECM算法实现了更快的稳定收敛，且计算效率更高。