Nonlinear system identification in impulsive environments

Nonlinear system identification has been studied under the assumption that the noise has finite second and higher order statistics. In many practical applications, impulsive measurement noise severely weakens the effectiveness of conventional methods. In this paper, alpha-stable noise is used as a noise model. In such case, the minimum mean square error (MMSE) criterion is no longer an appropriate metric for estimation error due to the lack of finite second-order statistics of the noise. Therefore, we adopt minimum dispersion criterion, which in turn leads to the adaptive least mean pth power (LMP) algorithm. It is shown that the LMP algorithm under the alpha-stable noise model converges as long as the step size satisfies certain conditions. The effect of p on the performance is also investigated. Compared with conventional methods, the proposed method is more robust to impulsive noise and has better performance.