Program to estimate parameters of linear systems without numerical differentiation.

Abstract

This paper describes a computer program for estimating the parameters of a linear differential equation systen with constant coefficients by use of a nonlinear least-squares method. For minimization the sum of squares of an existing standard program, the Gauss-Newton gradient procedure, is employed. The differential equation system is solved by the Taylor expansion method. The advantage of this approach is that the derivatives with respect to the parameters are available without numerical differentiation. Therefore the inaccuracy inherent in numerical differentiation and the problem of choosing the modification of the parameters are eliminated. The given procedure is applicable for all the first order gradient methods. The presented method was tested with generated data from a four-compartmental model.