A simple neural learning algorithm for total least-squares adaptive filtering

A Hebbian-type learning algorithm for the total least-squares parameter estimation is presented. An asymptotic analysis is carried out to show that the algorithm allows the weight vector of a linear neuron unit to converge to the eigenvector associated with the smallest eigenvalue of the correlation matrix of the input signal. When the algorithm is applied to solve parameter estimation problems, the converged weights directly yield the total least-squares solution. It is shown that the implementations of the proposed algorithm have the simplicity of those of the LMS algorithm, but its noise rejection capability is much superior to those of the least-squares-based algorithms. The applicability and performance of the algorithm are demonstrated through computer simulations of adaptive FIR and IIR parameter estimation problems