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Abstract. Algorithms to treat the maximum likelihood (ML) estimation problem in array localization signal processing are reviewed, including the alternating projection method, the itemtive quadratic maximum likelihood method and the expectation-maximization method. The relationship of ML estimators and the MUSIC algorithm is presented. The Cramer-Rao bounds for the deterministic and stochastic models in array localization are summarized. Finally, the problem of the estimation of the number of sources is discussed.