Variants of non-negative least-mean-square algorithm and convergence analysis
Résumé
Due to the inherent physical characteristics of systems under investigation, non-negativity is one of the most interesting constraints that can usually be imposed on the parameters to estimate. The Non-Negative Least-Mean-Square algorithm (NNLMS) was proposed to adaptively find solutions of a typical Wiener filtering problem but with the side constraint that the resulting weights need to be non-negative. It has been shown to have good convergence properties. Nevertheless, certain practical applications may benefit from the use of modified versions of this algorithm. In this paper, we derive three variants of NNLMS. Each variant aims at improving the NNLMS performance regarding one of the following aspects: sensitivity of input power, unbalance of convergence rates for different weights and computational cost. We study the stochastic behavior of the adaptive weights for these three new algorithms for non-stationary environments. This study leads to analytical models to predict the first and second order moment behaviors of the weights for Gaussian inputs. Simulation results are presented to illustrate the performance of the new algorithms and the accuracy of the derived models.
Mots clés
non-negativity
adaptive filtering
least mean squares methods
stochastic processes
Wiener filters
nonnegative least-mean-square algorithm
convergence analysis
parameter estimation
NNLMS
Wiener filtering problem
computational cost
stochastic behavior
adaptive weights
nonstationary environments
Gaussian inputs
Signal processing algorithms
Convergence
Algorithm design and analysis
Prediction algorithms
Vectors
Equations
Estimation
Adaptive signal processing
exponential algorithm
least-mean-square algorithms
non-negativity constraints
normalized algorithm
sign-sign algorithm
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