Parameter estimation and unique identifiability

Abstract

One of the fundamental problems in system parameter estimation is the specification of the sufficient conditions (in the absence of noise) for unique estimation of the parameters in process models. We examine what unique identifiability means for parameters in linear and nonlinear process models comprised of algebraic and ordinary differential equations, and discuss related tests for uniqueness for prespecified types of measurements and process inputs. Typical examples encountered in chemical engineering are used to illustrate the tests. No procedure exists that will universally determine whether the parameters in any process model can be uniquely identified, but some of the tests cited have been found useful in numerous practical applications.