Adaptive nonlinear filter by ellipsoidal-basis-function networks

An adaptive nonlinear filter, which is based on ellipsoidal-basis-function networks (EBFN) and implements the TSK fuzzy system functionally, is proposed in this paper. An online hybrid algorithm suitable for structure learning and determination of hybrid parameters is presented. The proposed filter has the following salient features: (1) The filter´s structure is identified adaptively, i.e., it is not necessary to determine the initial number of fuzzy rules and input data space clustering in advance. (2) Online learning. The free parameters in the corresponding EBF neurons and the consequent parts are trained simultaneously by an online hybrid algorithm which is global optimal and inherently stable. This feature makes the real-time applications of the proposed filter feasible. (3) Low system resource requirements which means the filter needs lower computation load and less memory. As a basic advantage of the neuro-fuzzy-based system, the fuzzy rules can be extracted to reproduce the filter. The proposed filter is applied to adaptive noise cancellation. Simulation results show that it is capable of tackling nonlinear filtering problem and cancelling the noise signal from the distorted information signal efficiently.