Stochastic Behavior of the Nonnegative Least Mean Fourth Algorithm for Stationary Gaussian Inputs and Slow Learning
This work addresses the need for theoretical understanding in constrained online estimation for non-Gaussian noise scenarios, but it is incremental as it builds on existing algorithms.
The paper tackled the theoretical analysis of the nonnegative least mean fourth (NNLMF) algorithm for system identification with nonnegativity constraints, focusing on stationary Gaussian inputs and slow learning, and validated the analysis through simulations.
Some system identification problems impose nonnegativity constraints on the parameters to estimate due to inherent physical characteristics of the unknown system. The nonnegative least-mean-square (NNLMS) algorithm and its variants allow 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.