Cumulant based phase estimation for 1-D and 2-D nonminimum phase systems by Fourier series based allpass model

Yang and Chi (se Proc. IEEE Seventh SP Workshop on Statistical Signal and Array Processing, Quebec City, Canada, p.231-34, 1994) proposed a family of 1-D criteria for estimating the phase of a 1-D nonminimum phase linear time-invariant (LTI) system with only non-Gaussian measurements corrupted by additive Gaussian noise. The phase of the LTI system is obtained through an iterative algorithm which processes the given measurements by an ARMA allpass model such that a single absolute Mth-order (M⩾3) cumulant of the allpass model output is maximum. A family of 1-D and 2-D criteria, in which Yang and Chi´s 1-D criteria are included, is proposed for phase estimation using a Fourier series based allpass model. The optimum allpass models for 1-D and 2-D LTI systems are obtained by a 1-D and a 2-D iterative algorithms, respectively. The paper concludes with some simulation results followed by some conclusions