Audio signals from any array of microphones are individually filtered, delayed, and scaled in order to form an acoustic beam that focuses the array on a particular region. Nonlinear robust signal estimation processing is applied to the resulting set of audio signals to generate an output signal for the array. The nonlinear robust signal estimation processing may involve dropping or otherwise reducing the magnitude of one or more of the highest and lowest data in each set of values from the resulting audio signals and then selecting the median from or generating an average of the remaining values to produce a representative, central value for the output audio signal. The nonlinear robust signal estimation processing effectively discriminates against noise originating at an unknown location outside of the focal region of the acoustic beam.