Increasing the Size of Region of Convergence for Parameter Estimation

In the estimation of parameters in systems described by ordinary differential equations Gauss-Newton method is attractive because of the quadratic convergence property. However, the region in the parameter space where convergence is obtained is rather small. As a result, the algorithm has been modified by numerous investigators. However, it is shown that such modifications are really unnecessary if the first few iterations are performed by direct search optimization and then, in the vicinity of the optimum, the Gauss-Newton method used. Viability of such Two-step procedure is discussed and illustrated by two examples.