  This paper presents an efficient method for computing maximum likelihood (ML)
direction of arrival (DOA) estimates assuming unknown sensor noise powers. The
method combines efficient Alternate Projection (AP) procedures with Newton
iterations. The efficiency of the method lies in the fact that all its
intermediate steps have low complexity. The main contribution of this paper is
the method's last step, in which a concentrated cost function is maximized in
both the DOAs and noise powers in a few iterations through a Newton procedure.
This step has low complexity because it employs closed-form expressions of the
cost function's gradients and Hessians, which are presented in the paper. The
method's total computational burden is of just a few mega-flops in typical
cases. We present the method for the deterministic and stochastic ML
estimators. An analysis of the deterministic ML cost function's gradient
reveals an unexpected drawback of its associated estimator: if the noise powers
are unknown, then it is either degenerate or inconsistent. The root-mean-square
(RMS) error performance and computational burden of the method are assessed
numerically.
