Subspace SNR Maximization: The Constrained Stochastic Matched Filter

In this paper, we propose a novel approach to perform detection of stochastic signals embedded in an additive random noise. Both signal and noise are considered to be realizations of zero mean random processes of which only second-order statistics are known (their covariance matrices). The method proposed, called constrained stochastic matched filter (CSMF), is an extension of the stochastic matched filter itself derived from the matched filter. The CSMF is optimal in the sense that it maximizes the signal-to-noise ratio in a subspace whose dimension is fixed a priori. In this paper, after giving the reasons for our approach, we show that there is neither an obvious nor analytic solution to the problem expressed. Then an algorithm, which is proved to converge, is proposed to obtain the optimal solution. Evaluation of the algorithm's performance is completed through estimation of receiver operating characteristic curves. Experiments on real signals show the improvement brought about by this method and thus its significance.