Frequency domain adaptive filters using higher-order statistics with application to adaptive time delay estimation

Novel block-adaptive frequency domain filters based upon higher-order statistics are proposed for estimation of the parameters of a class of errors-in-variables models. The class includes moving average models as well as autoregressive models, The input to the system is restricted to be non-Gaussian with either non-vanishing bispectrum or non-vanishing trispectrum. The noise processes contaminating the input and the output measurements are assumed to be Gaussian if the input bispectrum vanishes, whereas they are allowed to be non-Gaussian with vanishing bispectra if the input has non-vanishing bispectrum. An integrated polyspectrum (bispectrum or trispectrum) of a random process is defined and exploited for adaptive parameter estimation. The integrated polyspectrum is computed as a cross-spectrum leading to substantial computational savings. Consistency of the proposed approaches is proved for the stationary case under certain mild sufficient conditions. The proposed approaches are applied to the problem of adaptive differential time delay estimation for non-Gaussian signals under spatially correlated Gaussian noise environment. Simulation results are presented to illustrate the proposed approaches.