Factor analysis (FA) plays a critical role in psychometrics, econometrics, and statistics. Recently, maximum likelihood FA (MLFA) has been applied to direction of arrival (DOA) estimation in unknown nonuniform noise and a variety of iterative approaches have been developed. In particular, the Factor Analysis for Anisotropic Noise (FAAN) method proposed by Stoica and Babu has excellent convergence properties. In this article, the Expectation/Conditional Maximization Either (ECME) algorithm, an extension of the expectation-maximization algorithm, is designed again for MLFA by introducing new complete data, which can thus use two explicit formulas to sequentially update the estimates of parameters at each iteration and have excellent convergence properties. Theoretical analysis shows that the ECME algorithm has almost the same computational complexity at each iteration as the FAAN method. However, numerical results show that the ECME algorithm yields faster stable convergence and the convergence to the global optimum is easier. Importantly, MLFA is not the best choice for the subspace based DOA estimation in unknown nonuniform noise.

翻译：因子分析在心理测量学、计量经济学和统计学中发挥着关键作用。近年来，最大似然因子分析已被应用于未知非均匀噪声环境下的波达方向估计，并发展出多种迭代方法。特别是Stoica和Babu提出的各向异性噪声因子分析方法具有优异的收敛特性。本文通过引入新的完备数据，为最大似然因子分析重新设计了期望/条件最大化替代算法——该算法作为期望最大化算法的扩展，能够利用两个显式公式在每次迭代中顺序更新参数估计，并具备优异的收敛特性。理论分析表明，ECME算法在每次迭代中的计算复杂度与FAAN方法几乎相同。然而，数值结果表明ECME算法能实现更快的稳定收敛，且更容易收敛至全局最优解。需要强调的是，在未知非均匀噪声环境下基于子空间的DOA估计中，最大似然因子分析并非最优选择。