On the identifiability problem in the presence of random nuisance parameters

This paper concerns with the identifiability of a vector of unknown deterministic parameters. In many practical applications, the data model is affected by additional random parameters whose estimation is not strictly required, the so-called nuisance parameters. In these cases, the classical definit...

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Bibliographic Details
Published in:Signal processing 2012-10, Vol.92 (10), p.2545-2551
Main Authors: Fortunati, Stefano, Gini, Fulvio, Greco, Maria S., Farina, Alfonso, Graziano, Antonio, Giompapa, Sofia
Format: Article
Language:English
Subjects:
Applied sciences
Computation
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
Fisher information matrix
Identifiability
Information, signal and communications theory
Mathematical analysis
Mathematical models
Modified FIM
Nuisance
Nuisance parameters
Parameter estimation
Radar
Signal and communications theory
Signal processing
Signal, noise
Telecommunications and information theory
Vectors (mathematics)
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Summary:This paper concerns with the identifiability of a vector of unknown deterministic parameters. In many practical applications, the data model is affected by additional random parameters whose estimation is not strictly required, the so-called nuisance parameters. In these cases, the classical definition of identifiability, which requires the calculation of the Fisher Information Matrix (FIM) and of its rank, is often difficult or impossible to perform. Instead, the Modified Fisher Information Matrix (MFIM) can be computed. We generalize the main results on the identifiability problem to take the presence of random nuisance parameters into account. We provide an alternative definition of identifiability that can be always applied but that is weaker than the classical definition, and we investigate the relationships between the identifiability condition and the MFIM. Finally, we apply the obtained results to the identifiability in presence of nuisance parameters to the relative grid-locking problem for netted radar system. ► This paper concerns the identifiability problem in the presence of random nuisance parameters. ► We generalize results on the identifiability to take the random nuisance parameters into account. ► Classical definition of identifiability is often difficult or impossible to apply. ► We provide an alternative definition of identifiability, that can be always applied. ► We apply this new definition to the relative grid-locking problem for netted radar systems.
ISSN:0165-1684
1872-7557
DOI:10.1016/j.sigpro.2012.04.004