| In parameter estimation of systems described by ordinary differential equations, quasilinearization and Gauss-Newton methods are commonly used because of the quadratic convergence property. Although these methods are often considered to be separate in the literature, in this study it is shown that by means of a simple transformation a redundant set of differential equations can be removed from the quasilinearization method, making it computationally the same as the Gauss-Newton method. It is further shown that quasilinearization and Gauss-Newton methods yield identical results unless there is a nonlinear relationship between the observed and state variables.;The Information Index can also be used as a tool in experimental design to indicate the time interval over which measurements of the output vector should be obtained. Thus, it is ensured that the designed experiment is utilized to its full extent thereby improving the efficiency of sequential design procedures.;Finally, the estimation of parameters in systems with unknown components in the initial state vector is considered and the similarity of this parameter estimation problem to the well-known two point boundary value problem is shown.;The region in the parameter space over which convergence is obtained is usually rather small and, therefore, good initial estimates are required for the parameters. To overcome the problem of the small region of convergence, two different procedures have been developed. First, a two-step procedure is proposed, whereby direct search optimization is used initially to arrive in the vicinity of the optimum, followed by the Gauss-Newton method to yield the optimal parameter estimates. The second procedure is based on the use of the Information Index and of an optimal step size policy. The Information Index is introduced here to provide a measure of the available sensitivity information as a function of time, thereby locating the most appropriate section of data to be used for parameter estimation. If observations are not available in the most appropriate section of data, artificial data can be generated by data smoothing and interpolation. With minor modifications this procedure is especially attractive for systems described by stiff differential equations. |
