Adaptive Polynomial Filtering using Generalized Variable Step-Size Least Mean pth Power (LMP) Algorithm

Abstract

This correspondence presents the adaptive polynomial filtering using the generalized variable step-size least mean $$p$$ p th power (GVSS-LMP) algorithm for the nonlinear Volterra system identification, under the $$\alpha $$ ? -stable impulsive noise environment. Due to the lack of finite second-order statistics of the impulse noise, we espouse the minimum error dispersion criterion as an appropriate metric for the estimation error, instead of the conventional minimum mean square error criterion. For the convergence of LMP algorithm, the adaptive weights are updated by adjusting $$p\ge 1$$ p ? 1 in the presence of impulsive noise characterized by $$1<\alpha <2$$ 1 < ? < 2 . In many practical applications, the autocorrelation matrix of input signal has the larger eigenvalue spread in the case of nonlinear Volterra filter than in the case of linear finite impulse response filter. In such cases, the time-varying step-size is an appropriate option to mitigate the adverse effects of eigenvalue spread on the convergence of LMP adaptive algorithm. In this paper, the GVSS updating criterion is proposed in combination with the LMP algorithm, to identify the slowly time-varying Volterra kernels, under the non-Gaussian $$\alpha $$ ? -stable impulsive noise scenario. The simulation results are presented to demonstrate that the proposed GVSS-LMP algorithm is more robust to the impulsive noise in comparison to the conventional techniques, when the input signal is correlated or uncorrelated Gaussian sequence, while keeping $$1<p<\alpha <2$$ 1 < p < ? < 2 . It also exhibits flexible design to tackle the slowly time-varying nonlinear system identification problem.