New effective analytic representation based on the time-varying Schur coefficients for underwater signals analysis

The paper proposes a new effective analytic signal representation dedicated to underwater signal analysis. The proposed approach is based on the recursive normalized exact least-square ladder estimation algorithm because of its excellent convergence behaviour, extremely fast start-up performance and its capability to quickly track parameter changes. The linear orthogonal parameterization procedure considered in this paper is numerically efficient and stable and follows from the celebrated Schur algorithm. The generalized Schur filter at each time-step calculates optimal orthogonal signal representation using second-order statistics which results in a set of time-varying Schur coefficients. The filter transforms a one dimensional signal (time-series) to a multidimensional sequence of the time-varying Schur coefficients. The second-order signal description based on the generalized Schur filter is efficient and robust. The model parameters such as the forward prediction error or the Schur coefficients can be used for detection and segmentation or for deducing parametric joint time-frequency signal representation. These are common stages in signal estimation and analysis. Moreover, in the future we envisage using the time-varying Schur coefficients to classify and identify different events in the analyzed time-series. The results performed by applying the proposed method to simulated and real-world signals are shown to verify its high performance.