Hierarchical learning-based cascaded adaptive filtering for nonlinear system identification

To enhance the dynamic performance of point-wise nonlinear expansion-based filters, such as the functional links artificial neural networks (FLANN) and Legendre neural networks (LNN), a novel cascaded filter in a hierarchical design fashion between FLANN and LNN, has been introduced in this paper. The proposed filter comprises two layers: the first layer consists of small-sized FLANN modules nested in a pipelined fashion to extract features from the input data efficiently; the second layer is an LNN transversal filter whose task is to further process the output data from the first layer. A nonlinear activation function is implemented between the two layers to ensure stability in Legendre functional expansion. The adaptive weights of the layers are updated based on a modified hierarchical learning algorithm to avoid the cost of computing the backpropagation error. Furthermore, the proposed filter is computationally efficient, thanks to small-sized FLANN modules and a parallel processing architecture. Besides, the study has analyzed the stability and convergence conditions of the algorithm. Experimental results have shown that the proposed filter performs better in nonlinear dynamic system identification scenarios than FLANN, LNN, and other cascaded FLANN-LNN filters.