Nonlinear parameter estimation by weighted linear associative memory with nonzero interception

摘要

The method of linear associative memory (LAM) has recently been applied in nonlinear parameter estimation. In the method of LAM, a model response, nonlinear with respect to the parameters, is approximated linearly by a matrix, which maps inversely from a response vector to a parameter vector. This matrix is determined from a set of initial training parameter vectors and their response vectors according to a given cost 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 observed response even if the initial training parameter vectors are far from the true values. In a previous paper, we have significantly improved the LAM method by introducing a weighted linear associative memory (WLAM) approach for nonlinear parameter estimation. In the WLAM approach, the contribution of each pair of parameter-response vector to the cost function is weighted in a way such that if a response vector is closer to the observed one then its pair plays more important role in the cost function. However, in both LAM and WLAM, the linear association is introduced with zero interceptions, which would not give an exact association even if the model function is linear and so will affect the efficiency of the estimations. In this paper, we construct a theory which introduces a linear association memory with a nonzero interception (WLAMB). The results of our estimation tests on two quite different models, Van der Pol equation and somatic shunt cable model, suggest that WLAMB can still significantly improve on WLAM.