Recursive EM and SAGE-inspired algorithms with application to DOA estimation
Recursive EM and SAGE-inspired algorithms with application to DOA estimation
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DOI：
10.1109/tsp.2005.850339
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发表时间：
2005-08
影响因子：
5.4
通讯作者：
Pei-Jung Chung;J. F. Böhme
中科院分区：
文献类型：
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作者：
Pei-Jung Chung;J. F. Böhme
本文讨论增广数据的递推估计问题。我们研究了两个递归程序密切相关的著名的期望和最大化（EM）和空间交替广义EM（SAGE）算法。与迭代方法不同，递归EM和SAGE启发的算法可以快速更新新数据的估计值。在较弱的条件下，这些方法得到的估计是强相合的，且渐近正态分布。这些数学性质对广泛的一类问题是有效的。当应用于波达方向（DOA）估计时，递归EM和SAGE启发的算法导致非常简单和快速的最大似然（ML）方法的实现。每个递归中最复杂的计算是增广信息矩阵的求逆。通过数据扩充，该矩阵是对角矩阵，易于求逆。更重要的是，在这种递归过程中没有搜索。因此，计算时间比现有的数值方法寻找ML估计少得多。这一特性极大地提高了ML方法在实时处理中的潜力。数值实验表明，这两种算法都能以较低的计算代价获得较好的结果。
This paper is concerned with recursive estimation using augmented data. We study two recursive procedures closely linked with the well-known expectation and maximization (EM) and space alternating generalized EM (SAGE) algorithms. Unlike iterative methods, the recursive EM and SAGE-inspired algorithms give a quick update on estimates given new data. Under mild conditions, estimates generated by these procedures are strongly consistent and asymptotically normally distributed. These mathematical properties are valid for a broad class of problems. When applied to direction of arrival (DOA) estimation, the recursive EM and SAGE-inspired algorithms lead to a very simple and fast implementation of the maximum-likelihood (ML) method. The most complicated computation in each recursion is inversion of the augmented information matrix. Through data augmentation, this matrix is diagonal and easy to invert. More importantly, there is no search in such recursive procedures. Consequently, the computational time is much less than that associated with existing numerical methods for finding ML estimates. This feature greatly increases the potential of the ML approach in real-time processing. Numerical experiments show that both algorithms provide good results with low computational cost.