  The learning speed of an adaptive algorithm can be improved by properly
constraining the cost function of the adaptive algorithm. Besides, the
stabilization of the NCLMF algorithm is more complicated, whose stability
depends solely on the input power of the adaptive filter and the NCLMF
algorithm with unbounded repressors is not mean square stability even for a
small value of the step-size. So, in this paper, a noise variance constrained
least mean absolute third (LMAT) algorithm is investigated. The noise
constrained LMAT (NCLMAT) algorithm is obtained by constraining the cost
function of the standard LMAT algorithm to the third-order moment of the
additive noise. And it can eliminate a variety of non-Gaussian distribution of
noise, such as Rayleigh noise, Binary noise and so on. The NCLMAT algorithm is
a type of variable step-size LMAT algorithm where the step-size rule arises
naturally from the constraints. The main aim of this work is first time to
derive the NCLMAT adaptive algorithm, analyze its convergence behavior, mean
square error (MSE), mean-square deviation (MSD) and assess its performance in
different noise environments. Finally, the experimental results in system
identification applications presented here illustrate the principle and
efficiency of the NCLMAT algorithm.
