Correntropy Based Matched Filtering

In this paper a non-linear extension to the matched filter is proposed and applied to signal detection. The decision statistic used in this novel method is derived from ideas on kernel-based learning theory and in fact, is a generalization of the correlation statistic used in the matched filter. The optimality of the matched filter is merely based on second order statistics and hence leaves room for improvement, especially when the assumption of Gaussianity is no longer valid. The proposed method incorporates higher order moments in the decision statistic and shows different behavior than the matched filter and improvement in the detection rate for non-Gaussian noise. Moreover, unlike kernel based approaches, this method is still computationally tractable and can easily be implemented in real-time