Approaches To F.I.R. System Identification With Noisy Data Using Higher-order Statistics

In this paper we address the problem of estimating the parameters of a moving average (MA) model given the noisy observations of the system output. The system is &lven by an i.i.d. (indefx?ndent and identically distributed) non-Gaussian sequence that is not observed. The noise is additive, i.i.d. and possibly non-Gaussiarr. We first briefly review the existing linear parametric approaches to tfds problem. Chief among these are: the linear least-sqmwes solution due to Giannakis and Mendel (GM) (ICA$SP 1987), the ARMA modeling approach due to Nikias (IEEE Trans. ASSP, April 1988), and the solution due to Giannakis (IEEE Proc,, Sept. 1987). We observe that in the presence of the non-Gaussian measurement noise the Nikias' solution may be biased. In the presence of any measurement noise the GM approach yields biased solutions. Both the Nikias' and the Giannakis' solutions neglect the second-order statistics, The Giannakis' solution yields high-variance estimates, and is unstable under order mismatch. We focus on the GM approach and show that following their basic approach, sevemf other useful linear relations maybe obtained between the system parameters and the output statistics. Using these relations we modify the GM solution to obmin consistent parameter estimates in measurement noise. Fhmfly, we investigate the dkcct, nonlinear least-squares solution to the simultaneous second- and highcrorder cumulant matching problem. Simulations show that this approach yields the most accurate estimates.