On the normalized minimum error-entropy adaptive algorithm: Cost function and update recursion

Information theoretical learning (ITL) has recently been proved to be an efficient tool for developing new adaptive filtering algorithms. The starting point of this approach is the use of an information theoretical cost function. The most widely used family of algorithms in this class is the minimum error entropy (MEE). Linear and nonlinear adaptive filters from MEE family have better overall performance than traditional minimum mean-squared error and least-square filters in environments that include nonlinear models and/or where high-order-statistic noises are present, such as impulsive noises. In this paper, we study a well-known MEE-based algorithm: the normalized minimum error entropy (NMEE).We propose an alternative cost function associated with the current known NMEE update recursion. In addition, we propose a new update recursion related to the original NMEE cost function.