Use of selected HOS information for low-variance estimation of bandlimited systems with short data records

Although reconstruction of a nonminimum-phase system excited by a stationary non-Gaussian white input is only possible using higher-order statistics (HOS) of the system output, there has been a lot of criticism in the literature against the amount of data required for keeping estimation errors low, and the complexity involved. Recently several attempts for reducing the variance of the HOS estimates have appeared. In the case of bandlimited signals, we have demonstrated via simulations that the estimation variance can be reduced if “good” slices, instead of the whole bispectrum, are used. This suggests a potential reduction of variance in the system estimates, without having to resort to long observations. In this paper we justify theoretically the dependence of the system estimate variance on the bispectrum slice, and the criterion of slice selection. We also present simulation results, where the selected-slices approach appears to result in much lower estimation variance, as compared to other entire-bispectrum based approaches, for data lengths as low as 64 samples.