Linear identification of non-Gaussian noncausal autoregressive signal-in-noise processes

A method is presented for estimating the parameters of a stationary non-Gaussian noncausal autoregressive (AR) process that is observed in additive, possibly non-Gaussian noise. The method consists of two linear least-squares estimation steps. First, a spectrally equivalent causal AR signal-in-noise model is fitted to the observation sequence via the extended Yule-Walker equations. This model is then used to filter the observation sequence. Second, an acausal (purely noncausal) all-pass autoregressive moving average (ARMA) model is fitted to the filtered observation sequence by estimating its poles via linear least-squares by using an equation error approach and the higher-order statistics of the filtered sequence. The final noncausal AR model estimate is obtained by cascading the two estimates: the spectrally equivalent causal AR model and the acausal all-pass ARMA model.<>