PARAMETER ESTIMATION IN CHEMICAL DYNAMICS

This thesis deals with parameter estimation in chemistry and physics. Chapter I introduces various sensitivity coefficients of parameters with respect to observables or parameters with respect to model variables where the parameters are estimated with the minimum least square method. In addition it presents an approximation which relates the variance of the parameters to the variance of the observations and the variance in the variables in the model equations if the system has random components. Chapter II contains an adaptation of a method used in nuclear engineering to describe non-linear input-output systems under constraints. The remaining Chapters use stochastic estimation theory to estimate the unknown quantities in physical models. The assumption is that the variables of the physical models under consideration satisfy differential equations and that the observations may be presented as random variables satisfying a diffusion equation. Using stochastic estimation theory an estimate for the unknown quantities in the model can be constructed from a realization of the observational equations. Chapter III introduces a new proof for the Rao-Cramer inequality which is used throughout the remaining Chapters. The inequality is applied to the parameter estimator for the physical model and it is shown that if the model equations are deterministic, the information in the Rao-Cramer lower bound is contained in the sensitivity equations for the physical variables. The fourth Chapter contains applications of stochastic estimation theory to chemical kinetics and laser physics. We show that the filtering method can be used to estimate the unknown reaction rate constants in the kinetics models and how it can be employed to estimate the structural constants of a laser. Several simulations demonstrate the feasibility of the method. Chapter V shows that if the potentials under consideration are of the Rellich type the Kallianpur-Striebel integral equation can be applied to the estimation of unknown parameters residing in the potential or in the initial conditions of the quantal model. The extended Bayes formula can be applied to obtain an analytical form for the a-posteriori density of the unknown time independent parameters. In Chapter VI the quantum model is presented in matrix form and the assumption is that the observations are proportional to the weighted square of the expansion coefficients and some Wiener process. The application of the filtering method to the estimation of the unknown elements in the Hamiltonian matrix is illustrated by some examples. (Abstract shortened with permission of author.)...