The identification of non-causal and non-minimum phase signals based on second and fourth order cumulant

A method is presented to identify the non-causal and non-minimum phase signals based on second and fourth order statistics. The algorithm is an extension algorithm of the two-step method, that is, a spectrally equivalent causal minimum phase model is estimated by using second order statistics of observations at first, and then the suitable criterion is exploited to resolve the true location of the signal poles and zeros. According to the concept of minimum entropy, partial 4-th order cumulant functions of the noisy observation is used to estimate the standardized 4-th order cumulant of the innovation sequence, which serves as a criterion for choosing the appropriate location of signal poles and zeros, and which provides a parameter estimation rule for a non-causal and non-minimum phase system. The consistency of the proposed algorithm is proved. The aspects of the structure being completely non-identifiable under the assumption of causal minimum phase can be resolved under certain conditions