| Higher Order Statistics is a rapidly developing signal processing area with growing applications in science and engineering. There are several motivations behind this. First, higher order cumulants are blind to any kind of Gaussian process. Hence, when the processed signal is non-Gaussian and the additive noise is Gaussian, the noise will vanish in the cumulant domain. Thus, a greater degree of noise immunity is possible. Second, cumulants, are useful for identifying nonminimum phase systems or reconstructing nonminimum phase signals if the input signals are non-Gaussian. That is because cumulants preserve the phase information of the signal. Third, cumulants are useful for detecting and characterizing the properties of nonlinear systems. In this study, the first two properties are exploited.; In this work, we address the problem of estimating the parameters of noncausal nonminimum phase Autoregressive (AR) and Moving Average (MA) systems from estimates of the higher order cumulants of a noisy observed output signal. The algorithms developed here, based on the solution of a generalized non-symmetric eigenproblem, utilize only the third- and fourth-order statistical information of the output sequence in the presence of additive Gaussian process. Consequently, they provide significantly better results at low Signal-to-Noise Ratio (SNR) levels due to the reason given above. In addition, order estimation of the MA models is explored and a relationship is established between the rank of the fourth-order cumulant matrix and the order of the MA system. Furthermore, it is observed that order estimation is not crucial for the AR models. An overestimated order simply leads to multiple solutions with different linear phases. |
