Parameter fitting in dynamic models

We consider the numerical approaches for the least squares estimation of the parameter vector p in the initial value problem y′ = g(t, y, p), y(t₀) = y₀(p) when observations are available on some or all components of the vector y(t). Special attention is paid to the development of techniques which, although not global, are less sensitive to initial parameter estimates than the standard approach employing the sensitivity equations. Experience indicates that interactive approaches can be very valuable when good starting parameter approximations are unavailable. We describe the main features of our interactive parameter fitting package PARFIT. This package contains standard techniques employing the sensitivity equations as well as special algorithms designed to improve poor parameter estimates. These special algorithms have been selected and developed with user interaction in mind. We describe in detail one special approach designed for the case when observations are not available on all state variables. An example (using computer generated observations) is presented to illustrate this approach. Finally, the power of an interactive approach is demonstrated with two examples involving attempts to model physically observed phenomena.