Robust and accurate ARX and ARMA model order estimation of non-Gaussian processes

Abstract

The field of higher order statistics is emerging rapidly for analyzing non-Gaussian processes. There are several motivations behind the use of higher order statistics. The emphasis of this paper is based on the property that higher order cumulants are blind to any kind of Gaussian process. Hence, when the processed signal is non-Gaussian stationary and the additive noise is stationary Gaussian, the noise will vanish in the cumulant domain. This paper presents an extension to the results of Liang et al. (1993). This extension is a straightforward generalization of Liang's approach to third-order cumulants (TOCs). The new cumulant-based algorithm provides a higher level of accuracy in the presence of noise than the original second-order algorithm. In addition, the original results of Liang have been extended to the case of colored Gaussian noise. Examples are given to demonstrate the performance of this algorithm even when the observed signal is heavily corrupted by Gaussian noise.