Function approximation from input and output data is one of the most investigated problems in signal processing. This problem has been tackled with various signal processing and machine learning methods. Although tensors have a rich history upon numerous disciplines, tensor-based estimation has recently become of particular interest in system identification. In this paper we focus on the problem of adaptive nonlinear system identification solved with interpolated tensor methods. We introduce three novel approaches where we combine the existing tensor-based estimation techniques with multidimensional linear interpolation. To keep the reduced complexity, we stick to the concept where the algorithms employ a Wiener or Hammerstein structure and the tensors are combined with the well-known LMS algorithm. The update of the tensor is based on a stochastic gradient decent concept. Moreover, an appropriate step size normalization for the update of the tensors and the LMS supports the convergence. Finally, in several experiments we show that the proposed algorithms almost always clearly outperform the state-of-the-art methods with lower or comparable complexity.

翻译：从输入和输出数据中进行函数逼近是信号处理领域中研究最为广泛的问题之一。这一问题已通过多种信号处理与机器学习方法得到解决。尽管张量在众多学科中具有悠久历史，但基于张量的估计方法近年来在系统辨识领域引起了特别关注。本文聚焦于采用插值张量方法解决自适应非线性系统辨识问题。我们提出了三种新型方法，将现有的基于张量的估计技术与多维线性插值相结合。为保持较低的复杂度，我们遵循了算法采用Wiener或Hammerstein结构，并将张量与著名的LMS算法相结合的设计理念。张量的更新基于随机梯度下降概念。此外，针对张量更新与LMS算法采用了适当的步长归一化策略以支持收敛。最后，通过多项实验表明，所提算法在复杂度相当或更低的情况下，几乎始终显著优于现有先进方法。