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We consider the problem of identifying a parallel Wiener-Hammersteinstructure from Volterra kernels. Methods based on Volterra kernels typicallyresort to coupled tensor decompositions of the kernels. However, in the case ofparallel Wiener-Hammerstein systems, such methods require nontrivialconstraints on the factors of the decompositions. In this paper, we propose anentirely different approach: by using special sampling (operating) points forthe Jacobian of the nonlinear map from past inputs to the output, we can showthat the Jacobian matrix becomes a linear projection of a tensor whose rank isequal to the number of branches. This representation allows us to solve theidentification problem as a tensor recovery problem.

Low-rank tensor recovery for Jacobian-based Volterra identification of parallel Wiener-Hammerstein systems