Linear and nonlinear associative memories for parameter estimation

Abstract

This paper proposes the use of associative memories for obtaining preliminary parameter estimates for nonlinear systems. For each parameter vector r i in a selected training set, the system equations are used to determine a vector s i of system outputs. An associative memory matrix M̂ is then constructed which optimally, in the least squares sense, associates each system output vector s i with its corresponding parameter vector r i . Given any observed system output vector s ∗ , an estimate r̂ for the system parameters is obtained by setting r ̂ = M ̂ s ∗ . Numerical experiments are reported which indicate the effectiveness of this approach, especially for the nonlinear associative memory case in which the training vectors s i include not only the system output levels but also products of these levels. Training with noisy output vectors is shown to improve the accuracy of the parameter estimates when the observation vectors s ∗ are noisy. If experimental data are available for use as the training set, the estimation procedure can be carried out without knowing the system equations.