A first set of signals from an array of one or more microphones, and a second signal from a reference microphone are used to calibrate a set of filter parameters such that the filter parameters minimize a difference between the second signal and a beamformer output signal that is based on the first set of signals. Once calibrated, the filter parameters are used to form a beamformer output signal that is filtered using a non-linear adaptive filter that is adapted based on portions of a signal that do not contain speech, as determined by a speech detection sensor.