Stochastic behavior of the nonnegative least mean fourth algorithm for stationary Gaussian inputs and slow learning

•The nonnegative least mean fourth algorithm is proposed for the online estimation.•This paper analyzes the stochastic behavior of the nonnegative least mean fourth algorithm.•The stochastic behavior analysis is presented by using new approximations.•Simulation results illustrate the accuracy of the proposed analysis.

Some system identification problems impose nonnegativity constraints on the parameters to be estimated due to inherent physical characteristics of the unknown system. The nonnegative least-mean-square (NNLMS) algorithm and its variants allow one to address this problem in an online manner. A nonnegative least mean fourth (NNLMF) algorithm has been recently proposed to improve the performance of these algorithms in cases where the measurement noise is not Gaussian. This paper provides a first theoretical analysis of the stochastic behavior of the NNLMF algorithm for stationary Gaussian inputs and slow learning. Simulation results illustrate the accuracy of the proposed analysis.