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Volterra kernels of bilinear systems have tensor train structure


Despite being able to approximate the outputs of a wide class of (weakly) nonlinear dynamical systems, the finitememory discrete-time Volterra models known as Volterra filters (VF) are notoriously too heavy from a computational point of view, due to the often huge number of parameters needed to fully describe their kernels. This shortcoming has prompted the development of alternative, low-complexity approximate models, among which low-rank tensor-based approaches figure prominently. In this work, we argue that for bilinear (or more generally, linear-analytic) systems, the Volterra kernels in the so-called regular form are naturally structured in the form of a tensortrain decomposition, a property that can be easily exploited for achieving complexity reduction. We compare this proposed approach with other existing tensor-based ones in the case where state-space equations are known but typically hard and/or too costly to realize in discrete-time, which motivates the use of lowcomplexity discrete-time nonlinear filters. Our numerical results illustrate the benefits of our proposal in an example involving a nonlinear loudspeaker of known state-space equations.
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hal-03233382 , version 1 (24-05-2021)


  • HAL Id : hal-03233382 , version 1


José Henrique de M Goulart, Phillip Mark Seymour Burt. Volterra kernels of bilinear systems have tensor train structure. 29th European Signal Processing Conference (EUSIPCO 2021), Aug 2021, Dublin, Ireland. ⟨hal-03233382⟩
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