A New Technique for ARMA-System Identification Based on QR-Decomposition of Third Order Cumulants Matrix

In this paper a new technique to estimate the coefficients of a general Autoregressive Moving Average (ARMA) (p, q) model is proposed. The ARMA system is excited by an un-observable independently identically distributed (i.i.d) non-Gaussian process. The proposed ARMA coefficients estimation method uses the QR-Decomposition (QRD) of a special matrix built with entries of third order cumulants (TOC) of the available output data only. The observed output may be corrupted with additive colored or white Gaussian noise of unknown power spectral density. The proposed technique was compared with several good methods such as the residual time series (RTS) and the Q-slice algorithm (QSA) methods. Simulations for several examples were tested. The results for these examples confirm the good performance of the proposed technique with respect to existing well-known methods.