Parameter estimation for nonlinear models - convergence, data and parameter uncertainty, and constraints on parameter changes (Q1119217)

This paper is concerned with the use of the Gauss-Newton (also called ``quasilinearization'') version of the Newton-Raphson minimization algorithm for estimating the parameters in a possibly nonlinear model. Specifically, the models parameters are determined by minimizing with respect to the following criterion \[ f(p)=[Y-Y_ m(p)]^ TW_ 1[Y- Y_ m(p)]+(p-p^ 0)^ TW_ 2(p-p^ 0) \] where p denotes the vector of unknown parameters, Y is a vector containing the measured values of system output, the vector \(Y_ m(p)\) contains the corresponding values of the model output, \(p^ 0\) is an initial guess for the parameter vector, and \(W_ 1\) and \(W_ 2\) are positive definite weighting matrices. The bulk of the paper makes use of a theoretical model of a 2 degree-of-freedom linear dynamic system to study the influence of \(p_ 0\), \(W_ 1\) and \(W_ 2\) on the convergence properties of the Gauss- Newton algorithm.