WEIGHTED LINEAR ASSOCIATIVE MEMORY APPROACH TO NONLINEAR PARAMETER-ESTIMATION

The method of linear associative memory (LAM), a notion from the field of artificial neural nets, has been applied recently in nonlinear par ameter estimation. In the LAM method, a model response, nonlinear with respect to the parameters, is approximated linearly by a matrix, whic h maps inversely from a response vector to a parameter vector. This ma trix is determined from a set of initial training parameter vectors an d their response vectors, and can be updated recursively and adaptivel y with a pair of newly generated parameter response vectors. The LAM a dvantage is that it can yield a good estimation of the true parameters from a given observed response, even if the initial training paramete r vectors are far from the true values. In this paper, we present a we ighted linear associative memory (WLAM) for nonlinear parameter estima tion. WLAM improves LAM by taking into account an observed response ve ctor oriented weighting. The basic idea is to weight each pair of para meter response vectors in the cost function such that, if a response v ector is closer to the observed one, then this pair plays a more impor tant role in the cost function. This weighting algorithm improves sign ificantly the accuracy of parameter estimation as compared to a LAM wi thout weighting. In addition, we are able to construct the associative memory matrix recursively, while taking the weighting procedure into account, and simultaneously update the ridge parameter a of the cost f unction further improving the efficiency of the WLAM estimation. These features enable WLAM to be a powerful tool for nonlinear parameter si mulation.