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- a nd auto-cumulants, we extend the well-known Steiglitz-McBride identifi cation method to cumulant domains, and show that it is consistent unde r a certain ''third-order'' persistency of excitation condition. By co mparison, the Steiglitz-McBride method is not consistent when either i nput noise is present or when the output noise is colored. For an empi rical assessment, we provide simulations that demonstrate the proposed method's usefulness.