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The learning speed of an adaptive algorithm can be improved by properlyconstraining the cost function of the adaptive algorithm. Besides, thestabilization of the NCLMF algorithm is more complicated, whose stabilitydepends solely on the input power of the adaptive filter and the NCLMFalgorithm with unbounded repressors is not mean square stability even for asmall value of the step-size. So, in this paper, a noise variance constrainedleast mean absolute third (LMAT) algorithm is investigated. The noiseconstrained LMAT (NCLMAT) algorithm is obtained by constraining the costfunction of the standard LMAT algorithm to the third-order moment of theadditive noise. And it can eliminate a variety of non-Gaussian distribution ofnoise, such as Rayleigh noise, Binary noise and so on. The NCLMAT algorithm isa type of variable step-size LMAT algorithm where the step-size rule arisesnaturally from the constraints. The main aim of this work is first time toderive the NCLMAT adaptive algorithm, analyze its convergence behavior, meansquare error (MSE), mean-square deviation (MSD) and assess its performance indifferent noise environments. Finally, the experimental results in systemidentification applications presented here illustrate the principle andefficiency of the NCLMAT algorithm.

Noise constrained least mean absolute third algorithm