An identifiability criterion in the presence of random nuisance parameters

This paper concerns with the identifiability of an unknown deterministic vector in the presence of random nuisance parameters. In these cases, the classical definition of identifiability, which requires calculation of the Fisher Information Matrix (FIM) and of its rank, is often difficult or impossible to be implemented. Instead, the Modified FIM (MFIM) can be usually computed. We generalize the main results on parameter identifiability to take the presence of random nuisance parameters into account. We provide an alternative definition of identifiability that can be always applied also in the presence of nuisance parameters and we investigate the relationships between the classical and the new identifiability conditions. Finally, the new definition of identifiability is applied to a common estimation problem in netted radar systems: the relative grid-locking problem.