Adaptive System Identification via Low-Rank Tensor Decomposition

Tensor-based estimation has been of particular interest of the scientific community for several years now. While showing promising results on system estimation and other tasks, one big downside is the tremendous amount of computational power and memory required – especially during training – to achieve satisfactory performance. We present a novel framework for different classes of nonlinear systems, that allows to significantly reduce the complexity by introducing a least-mean-squares block before, after, or between tensors to reduce the necessary dimensions and rank required to model a given system. Our simulations show promising results that outperform traditional tensor models, and achieve equal performance to comparable algorithms for all problems considered while requiring significantly less operations per time step than either of the state-of-the-art architectures.