A constrained anti-Hebbian learning algorithm for totalleast-squares estimation with applications to adaptive FIR and IIRfiltering

摘要

In this paper, a new Hebbian-type learning algorithm for the totalnleast-squares parameter estimation is presented. The algorithm isnderived from the classical Hebbian rule. An asymptotic analysis isncarried out to show that the algorithm allows the weight vector of anlinear neuron unit to converge to the eigenvector associated with thensmallest eigenvalue of the correlation matrix of the input signal. Whennthe algorithm is applied to solve parameter estimation problems, thenconverged weights directly yield the total least-squares solution. Sincenthe process of obtaining the estimate is optimal in the totalnleast-squares sense, its noise rejection capability is superior to thosenof the least-squares-based algorithms. It is shown that thenimplementations of the proposed algorithm have the simplicity of thosenof the LMS algorithm. The applicability and performance of the algorithmnare demonstrated through computer simulations of adaptive FIR and IIRnparameter estimation problems