Identification of Nonlinear Input/Output Models Using Non-Gaussian Input Sequences

The results presented here extend our earlier results for the identification of second-order Volterra models from non-Gaussian white noise [1]. Here, we replaced the white noise input sequence with an elliptically distributed sequence having arbitrary correlation structure and constant kurtosis k. These processes generalize stationary Gaussian processes and exhibit many of the characteristics of Gaussian stochastic processes, but they can exhibit arbitrary positive kurtosis values. The results we obtained here were similar in chracter to those obtained in the white noise case. In particular, the input autocorrelation matrix defines a transformation of variables that maps the identification problem into a form similar to that obtained for white input sequences, as seen in equation (29) - as in [1], the diagonal and off-diagonal terms of the transformed matrix A are computed differently in a way that depends on the kurtosis. Future efforts will be aimed at developing "practical, plant-friendly" input sequences for second-order Volterra and other nonlinear process models. The results presented here represent a second step in that direction ad provide us with a mathematically tractable example in which we can explicitly control both the correlation structure and the non-Gaussian nature of the input sequence. The insights gained from this problem have suggested some new avenues of exploration, which will be described in later publications.