For many years, the popular minimum variance (MV) adaptive beamformer has b
een well known for not having been derived as a maximum likelihood (ML) est
imator. This paper demonstrates that by use of a judicious decomposition of
the signal and noise, the log-likelihood function of source location is, i
n fact, directly proportional to the adaptive MV beamformer output power In
the proposed model, the measurement consists of an unknown temporal signal
whose spatial wavefront is known as a function of its unknown location, wh
ich is embedded in complex Gaussian noise with unknown but positive definit
e covariance, Further, in cases where the available observation time is ins
ufficient, a constrained ML estimator is derived here that is closely relat
ed to MV beamforming with a diagonally loaded data covariance matrix estima
te. The performance of the constrained ML estimator compares favorably with
robust MV techniques, giving slightly better root-mean-square error (RMSE)
angle-of-arrival estimation of a plane-wave signal in interference. More i
mportantly, however,the fact that such optimal ML techniques are closely re
lated to conventional robust MV methods, such as diagonal loading, lends th
eoretical justification to the use of these practical approaches.