Robust set-membership filtering algorithms against impulsive noise

In this paper, we propose robust set-membership filtering algorithms against impulsive noise. Firstly, we introduce set-membership normalized least absolute difference algorithm (SM-NLAD). This algorithm provides robustness against impulsive noise through pricing the absolute error instead of the square. Then, in order to achieve comparable convergence performance in the impulse-free noise environments, we propose the set-membership normalized least logarithmic absolute difference algorithm (SM-NLLAD) through the logarithmic cost framework. Logarithmic cost function involves the absolute value of the error for large error values and the square of the error for small error values intrinsically. Finally, in the numerical examples, we show the robustness of our algorithms against impulsive noise and their comparable performance in the impulse-free noise environments.