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Nonlinear system identification using deterministic multilevel sequences. (English) Zbl 1136.93329
Summary: A new exact method of measuring the Volterra kernels of finite-order discrete nonlinear systems is presented. The kernels are rearranged in terms of multivariate cross-products in vector form. The one-, two-, $$\dots$$ , and $$l$$-dimensional kernel vectors are determined using a deterministic multilevel sequence with $$l$$ distinct levels at the input of the system. It is shown that the defined multilevel sequence with $$l$$ distinct levels is persistently exciting for a truncated Volterra filter with nonlinearities of polynomial degree $$l$$. Examples demonstrating the rearrangement of the Volterra kernels and a novel method for estimation of the kernels are presented. Simulation results are given to illustrate the effectiveness of the proposed method.
##### MSC:
 93B30 System identification 90C10 Integer programming
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