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The existing expectation maximization (EM) and space-alternating generalized EM (SAGE) algorithms are only applied to direction of arrival (DOA) estimation in known noise. In this paper, the two algorithms are designed for DOA estimation in unknown uniform noise. Both the deterministic and random signal models are considered. In addition, a new modified EM (MEM) algorithm applicable to the noise assumption is also proposed. Next, these EM-type algorithms are improved to ensure the stability when the powers of sources are not equal. After being improved, simulation results illustrate that the EM algorithm has similar convergence with the MEM algorithm, the SAGE algorithm outperforms the EM and MEM algorithms for the deterministic signal model, and the SAGE algorithm cannot always outperform the EM and MEM algorithms for the random signal model. Furthermore, simulation results show that processing the same snapshots from the random signal model, the SAGE algorithm for the deterministic signal model can require the fewest computations. [ABSTRACT FROM AUTHOR]

The maximum likelihood (ML) technique plays an important role in direction-of-arrival (DOA) estimation. In this paper, we employ and design the expectation–conditional maximization either (ECME) algorithm, a generalization of the expectation–maximization algorithm, for solving the ML direction finding problem of stochastic sources, which may be correlated, in unknown nonuniform noise. Unlike alternating maximization, the ECME algorithm updates both the source and noise covariance matrix estimates by explicit formulas, and can guarantee that both estimates are positive semi-definite and definite, respectively. Thus, the ECME algorithm is computationally efficient and operationally stable. Simulation results confirm that the ECME algorithm can efficiently obtain the ML based DOA estimate of each stochastic source. [ABSTRACT FROM AUTHOR]

The classic expectation-maximization (EM) algorithm in maximum-likelihood direction finding updates the complete-data sufficient statistics by finding their conditional expectations. Besides, from the perspective of alternating maximization (AM) these sufficient statistics can also be updated by maximizing the complete-data log-likelihood function with respect to only the complete data, based on which both deterministic and stochastic signal models are considered. Theoretical analysis indicates that the proposed AM algorithm is equivalent to the EM algorithm for the deterministic signal model while outperforming the EM algorithm for the stochastic signal model. On this foundation, a sequential AM (SAM) algorithm and two iterative weighting schemes are proposed to improve the convergence of the AM algorithm. Numerical results show that the SAM algorithm yields faster convergence and the two iterative weighting schemes can be used to avoid the convergence of the EM and AM algorithms to an unwanted limit point efficiently. [ABSTRACT FROM AUTHOR]