A lattice structure for the detection of a non-Gaussian signal in Gaussian AR noise

The estimated parameters of a lattice structure (PARCOR coefficients) can be used to detect an unknown signal in colored Gaussian noise of unknown autocovariance, but the detection performance is poor when the signal and noise spectra are overlapped. In this case, if the signal is not Gaussian, higher-order statistics can be used to improve detectability. To retain the order-recursive nature of the detector, we propose in the paper to employ two lattice filters: a conventional one, and another (in parallel with the first) that uses a set of coefficients computed using fourth-order cross-moments of the residuals at each stage. These parameters are identical with the PARCOR coefficients only under Gaussian assumption, so the differences between both sets of parameters are used to test normality. A study of the proposed statistic is also conducted to check its asymptotic bias and variance