NONLINEAR PARAMETER-ESTIMATION BY WEIGHTED LINEAR ASSOCIATIVE MEMORY WITH NONZERO INTERCEPTION

The method of linear associative memory (LAM) has recently been applie d in nonlinear parameter estimation. In the method of LAM. a model res ponse, nonlinear with respect to the parameters, is approximated linea rly by a matrix, which maps inversely from a response vector to a para meter vector, This matrix is determined from a set of initial training parameter vectors and their response vectors according to a given cos t function, and can be updated recursively and adaptively with a pair of newly generated parameter response vector. The advantage of LAM is that it can yield good estimation of the true parameter from a given o bserved response even if the initial training parameter vectors are fa r from the true values. In a previous paper, we have significantly imp roved the LAM method by introducing a weighted linear associative memo ry (WLAM) approach for nonlinear parameter estimation, In the WLAM app roach, the contribution of each pair of parameter-response vector to t he cost function is weighted in a way such that if a response vector i s closer to the observed one then its pair plays more important role i n the cost function, However, in both LAM and WLAM, the linear associa tion is introduced with zero interceptions, which would not give an ex act association even if the model function is linear and so will affec t the efficiency of the estimations, In this paper, we construct a the ory which introduces a linear association memory with a nonzero interc eption (WLAMB). The results of our estimation tests on two quite diffe rent models, Van der Pol equation and somatic shunt cable model, sugge st that WLAMB can still significantly improve on WLAM.