In this paper, the problem of identifying linear discrete-time systems from noisy input and output data is addressed. Several existing methods based on higher-order statistics are presented. it is shown that they stem from the same set of equations and can thus be united from the viewpoint of extended instrumental variable methods. A numerical example is presented which confirms the theoretical results. Some possible extensions of the methods are then given. (C) 2009 Elsevier Ltd. All rights reserved.