Noise constrained least mean absolute third algorithm

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.