Generalized wiener spline adaptive filter for nonlinear system identification

Since online identification of nonlinear system is very important for the active noise control system, a new structure of nonlinear spline adaptive filter (SAF) is presented in this paper. This new filter is composed of a linear IIR filter followed by a series of nonlinear spline adaptive filters (spline filter bank). The IIR filter and the spline filter bank describe the linearity and nonlinearity of the practical system, respectively. This new filter is called the generalized Wiener spline adaptive filter (GWSAF). In GWSAF, the spline filter bank receives the input of the system, the output of the IIR filter and the output of the system as its input signals. All the parameters in IIR filter and spline filter bank are updated by stochastic gradient descent (SGD) method. Compared with the traditional spline adaptive filter, this new structure contains more comprehensive descriptions of nonlinearity, which makes it have superior nonlinear modelling ability. Simulation shows that the proposed GWSAF performs much better than the existing SAF-family algorithms under complex nonlinearity.