A method of performing cancellation for acoustic or electromagnetic measurement or communications includes receiving an output signal to be applied to a transmit transducer, introducing a delay to the output signal to produce a delayed output signal, applying the delayed output signal to the transmit transducer, receiving an input signal from a receiving transducer, wherein the input signal comprises at least a portion of the delayed output signal, and iteratively solving a Kalman filter problem as a function of the input signal, the output signal, and the delay to produce a first filtered input signal.