Fitting noncasual autoregressive signal plus noise models to noisy non-Gaussian linear processes

The problem of estimating parameters of a noncausal autoregresslve signal from noisy observations is considered. The signal is assumed to be non-Gaussian. The measurement noise is allowed to be non-Gaussian. Two techniques that use both autocorrelations and third-order autocumulants of the data are presented for parameter estimation. Strong consistency of the proposed techniques is proved under certain sufficient conditions. Knowledge of the probability distribution of the driving noise is not required. Simulation examples are presented to illustrate the two methods. The problem of model order selection is also addressed.