Detection of weak signals using adaptive stochastic resonance

We present a novel nonlinear filtering approach for detecting weak signals in heavy noise from short data records. Such detection problems arise in many applications including communications, radar, sonar, medical imaging, seismology, industrial measurements, etc. The performance of a matched filter detector of a weak signal in heavy noise is directly proportional to the observation time. We discuss an alternative detection approach that relies on a nonlinear filtering of the input signal using a bistable system. We show that by adaptively selecting the parameters of the system, it is possible to increase the ratio of the square of the amplitude of a sinusoid to that of the noise intensity around the frequency of the sinusoid (stochastic resonance). The sinusoid can then be reliably detected at the output of the nonlinear system using a suitable matched filter even when the data record is short.