Dynamic system modeling methods have become a hot topic for stationary and nonstationary signal processing. Nonnegativity is a desired constraint that usually exerts on to be estimated parameters, and its generation usually based on the inherent physical characteristics of unknown system. Moreover, non-Gaussian noise is present in many practical system identification situations. In this paper, an adaptive nonnegative maximum correntropy criterion (NNMCC) algorithm is proposed for system identification under non-negativity constraints. We derive the NNMCC algorithm based on the Karush-Kuhn-Tucker conditions and a fixed-point iteration scheme. The first-order and second-order moments of the NNMCC algorithm adaptive weights are theoretically analyzed. Experimental results validate the theoretical analysis and illustrate the superior performance of NNMCC in non-Gaussian noise environments.

Lncosh function has been used for constructing a cost function for devising an adaptive filter algorithm to provide a desired performance under non-Gaussian noise, naming as least Lncosh algorithm (LLA). However, its transient behavior analysis has not been analyzed and investigated. As an important characteristic for the LLA, the transient behavior affects its performance in real-world applications. Herein, we present the theoretical model for evaluating the mean weight behavior and the transient excess mean square error (EMSE) behavior of the LLA. In addition, the proposed models can also be used to predict the transient behavior of the adaptive filtering algorithms with error nonlinearities {under non-Gaussian noises}. The experiment results have verified the validity of the presented models.