ABSTRACT
This chapter classifies and dissects the estimation problem into manageable tasks, presents solution strategies, and discusses some of the reasons why computer algorithms tend to fail. Parameter estimation for nonlinear systems is incomparably more complicated than linear regression. The chapter discusses different types of methods, and exemplifies some of them with the estimation of parameters in explicit functions, and discusses parameter estimation for dynamical systems. Using nonlinear regression for parameter estimation, one is often unsure whether the solution is truly the optimum or whether the algorithm might have converged to a local minimum. Gradient methods and genetic algorithms presently dominate the field of search methods for parameter estimation, but there are other alternatives. In the specific application of genetic algorithms to parameter estimation, each individual is a parameter vector. Essentially all principles and techniques of parameter estimation discussed so far are applicable to explicit functions as well as to dynamical systems consisting of sets of differential equations.
