This paper considers the joint estimation of the bearing and strength parameters of a noise source, by a uniformly spaced array of sensors in the presence of self‐noise, assumed to be independent between any pair of sensors. Contrary to the analogue systems of processing (i.e., correlation and beamforming), the present scheme, which is based on the maximum‐likelihood (ML) principle, operates on a set of time samples representing the bandlimited output of the array’s elements. The system, as a result, does not require the assumption of long observation time normally used in other schemes and is easily implemented on a digital computer. The resulting ML estimator is not in theory a sufficient one. Nevertheless, when the estimator’s variance is compared with the Cramer–Rao lower bound, the estimator virtually attains its asymptotic sufficiency as the number of array elements exceeds a ’’threshold’’ which is a decreasing function of the signal‐to‐noise ratio (SNR) and the length of the observation time. Except when the SNR is very poor and the observation time is quite short, the ’’threshold’’ is found to be surprisingly small. It is also demonstrated, at least when the error in the bearing estimate is small, that the ML estimator is unbiased.