A Third-Order Tensor Decomposition Based Linear-In-The-Parameters Nonlinear Adaptive Filter

Linear-in-the-parameters (LIP) nonlinear adaptive filters are widely used for modelling nonlinear systems. However, one major drawback of LIP nonlinear filters is the need to use high expansion orders to achieve accurate modelling, leading to a large number of inactive coefficients, hence overfitting issues and slow convergence. To overcome these issues, in this paper, we propose a third-order tensor (TOT) decomposition based functional link network (FLN) and propose the TOT-decomposition based FLN recursive least-squares algorithm (FLN-RLS-TOT). The decomposition technique significantly reduces the number of adaptive estimation parameters, thus allowing the use of a high expansion order to achieve accurate modelling while avoiding overfitting and convergence issues. Simulation results for nonlinear system identification show improved tracking, with similar or better modelling accuracy compared to existing algorithms.