Estimation of non-uniquely identifiable parameters via exhaustive modeling and membership set theory

A new methodology for estimating parameters that are not structurally globally identifiable is presented. The set of all the models which have exactly the same input–output behavior is first generated. The influence of the measurement noise and structural error is then taken into account by assuming that upper and lower bounds of the acceptable output error are available. The set of all the models compatible with this hypothesis is characterized, and ranges for the possible values of the estimated parameters are provided. An example is treated involving two real–life model structures used to describe the behavior of an isotopic tracer in a reactor producing methane from carbon monoxide and hydrogen.