Noisy input/output system identification using cumulants and the Steiglitz-McBride algorithm

We consider the problem of 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. Using third-order cross- and auto-cumulants, we extend the well-known Steiglitz-McBride (1965) identification method to cumulant domains, and show that it is consistent under a certain “third-order” persistency of excitation condition. By comparison, the Steiglitz-McBride method is not consistent when either input noise is present or when the output noise is colored. For an empirical assessment, we provide simulations that demonstrate the proposed method´s usefulness