Blind system identification using second, third and fourth order cumulants

Parametric modelling methods using second order statistics are theoretically well founded and frequently practiced. The use of higher order statistics in this field adds a further dimension, allowing non-minimum phase systems to be identified and modelled in this way. Recent papers published in this area dealing with moving average filters use mixed second and third, or second and fourth, order methods. This paper uses a novel technique to integrate the use of second, third and fourth order cumulants in one algorithm thus enabling symmetrically distributed input functions to be modelled successfully. The method, based on results reported in (1), has been developed and used in conjunction with an extremely simple model order selection criterion and found to produce stable and accurate results over a wide signal-to-noise ratio (SNR) range. Results for commonly quoted filters are given and compared with a currently available version of the Giannakis-Mendel method with the Tugnait fix (1, 2) (referred to as the GMT method) and those of (3) and (4).