Jmm. Anderson et Gb. Giannakis, NOISY INPUT OUTPUT SYSTEM-IDENTIFICATION USING CUMULANTS AND THE STEIGLITZ-MCBRIDE ALGORITHM/, IEEE transactions on signal processing, 44(4), 1996, pp. 1021-1024
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.