A priori identifiability: An overview on definitions and approaches

For a system, a priori identifiability is a theoretical property depending only on the model and guarantees that its parameters can be uniquely determined from observations. This paper provides a survey of the various and numerous definitions of a priori identifiability given in the literature, for both deterministic continuous and discrete-time models. A classification is done by distinguishing analytical and algebraic definitions as well as local and global ones. Moreover, this paper provides an overview on the distinct methods to test the parameter identifiability. They are classified into the so-called output equality approaches, local state isomorphism approaches and differential algebra approaches. A few examples are detailed to illustrate the methods and complete this survey.