Non-stationary analysis of the convergence of the Non-Negative Least-Mean-Square algorithm

Non-negativity is a widely used constraint in parameter estimation procedures due to physical characteristics of systems under investigation. In this paper, we consider an LMS-type algorithm for system identification subject to non-negativity constraints, called Non-Negative Least-Mean-Square algorithm, and its normalized variant. An important contribution of this paper is that we study the stochastic behavior of these algorithms in a non-stationary environment, where the unconstrained solution is characterized by a time-variant mean and is affected by random perturbations. Convergence analysis of these algorithms in a stationary environment can be viewed as a particular case of the convergence model derived in this paper. Simulation results are presented to illustrate the performance of the algorithm and the accuracy of the derived models.