A CONSTRAINED ANTI-HEBBIAN LEARNING ALGORITHM FOR TOTAL LEAST-SQUARESESTIMATION WITH APPLICATIONS TO ADAPTIVE FIR AND IIR FILTERING

In this paper, a new Hebbian-type learning algorithm for the total lea st-squares parameter estimation is presented. The algorithm is derived from the classical Hebbian rule. An asymptotic analysis is carried ou t to show that the algorithm allows the weight vector of a linear neur on unit to converge to the eigenvector associated with the smallest ei genvalue of the correlation matrix of the input signal. When the algor ithm is applied to solve parameter estimation problems, the converged weights directly yield the total least-squares solution. Since the pro cess of obtaining the estimate is optimal in the total least-squares s ense, its noise rejection capability is superior to those of the least -squares-based algorithms. It is shown that the implementations of the proposed algorithm have the simplicity of those of the LMS algorithm. The applicability and performance of the algorithm are demonstrated t hrough computer simulations of adaptive FIR and IIR parameter estimati on problems.