Time and scale evolutionary EVD and detection

Optimal detection of a known signal in nonstationary noise requires tracking the eigenvalue decomposition (EVD) of the noise data over time. To take advantage of information in the long-term, as well as short-term, correlation lags we turn to EVD over wavelet subspaces. In this paper, we develop a multirate EVD updating method over multiresolution subspaces and find maximum detectability nodes on wavelet binary full-tree structures. We use theoretical analysis to justify the effectiveness of a hyperspectrum for noise based on time and scale evolutionary EVDs. We also show results obtained with simulated 1/ f noise and noise collected by hydrophones of an underwater sonar communication system. Initial results are encouraging as they clearly indicate many subspaces, where detectability is significantly higher than in the original space prior to wavelet decomposition.