System identification with noisy input-output data using a cumulant-based Steiglitz-McBride algorithm

In this brief, we propose a cumulant-based, iterative method for identifying a linear time-invariant system from its noisy input/output data. The input and output are assumed to be non-Gaussian, while the input and output noises are assumed to be mutually correlated, colored, and Gaussian. At each iteration, the proposed method minimizes an objective function that asymptotically is equal to a scalar multiple of Steiglitz and McBride´s (1965) (ensemble average version) objective function for noise-free data. Unlike Steiglitz and McBride´s method, the proposed one is consistent for inputs that are persistently exciting of sufficient order