A family of robust adaptive filtering algorithms based on sigmoid cost

In this paper, a new framework of cost function for designing robust adaptive filtering algorithms is developed. This new cost framework, called sigmoid cost function, results from imbedding the conventional cost function into the sigmoid framework. Utilizing this proposed sigmoid cost framework, several important members (e.g., the sigmoid least mean square, sigmoid least absolute difference, sigmoid least mean fourth, sigmoid least mean logarithmic square, sigmoid least logarithmic absolute difference algorithms) of this family of robust adaptive filtering algorithms are proposed. In the proposed sigmoid cost framework with a steepness parameter α, a greater (smaller) value of α results in a slower (faster) convergence. Thus, an adaptive α is proposed which is based on an exponential function with respect to the L1-norm of the system error. In addition, the mean-square deviation analysis of the proposed algorithms is also carried out and their accuracies are verified via system identification experiment. Simulations in system identification and acoustic echo-cancellation scenarios have demonstrated that the proposed algorithms outperform the corresponding order's generalized maximum correntropy criterion, normalized least mean square using step-size scaler, sign algorithm and least logarithmic absolute difference algorithms.