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  4. Fisher information and Cramér-Rao bound for unknown systematic errors
 
Zitierlink DOI
10.26092/elib/3306
Verlagslink DOI
10.1016/j.measurement.2017.08.042

Fisher information and Cramér-Rao bound for unknown systematic errors

Veröffentlichungsdatum
2018-01
Autoren
Fischer, Andreas  
Zusammenfassung
In order to understand the lower bound of achievable measurement uncertainties, the Cramér-Rao inequality is known to be an utmost useful tool. However, the calculation of the Cramér-Rao bound requires a known probability density function that describes the occurring stochastic process. For this reason, the Cramér-Rao bound is applied for determining the lower limit of the measurement uncertainty due to random errors. According to the international guide to the expression of uncertainty in measurement (GUM), unknown systematic errors shall be treated as random errors. This approach is adopted here to enhance the applicability of the Cramér-Rao bound for unknown systematic errors. As a key result, the concept of Fisher information and the Cramér-Rao bound is shown to be applicable also to unknown systematic errors, which is demonstrated for several examples. An unknown offset, an unknown linear drift and successive unknown linear drifts are investigated in detail as systematic errors. Each derived corresponding Fisher information shows a characteristic behavior with respect to the measurement time. In contrast to random errors with a constant variance, the Fisher information can decrease for unknown systematic errors and, thus, the Cramér-Rao bound can increase with an increasing measurement time. For the typically existing case of simultaneously occurring random and unknown systematic errors, an optimal measurement time exists for which the achievable measurement uncertainty becomes minimal. In summary, the examples demonstrate how to determine the Fisher information and the Cramér-Rao bound for unknown systematic errors.
Schlagwörter
Measurement uncertainty limit

; 

Fisher information

; 

Cramér-Rao inequality

; 

Systematic error

; 

Measurement time
Verlag
Elsevier Science
Institution
Universität Bremen  
Fachbereich
Fachbereich 04: Produktionstechnik, Maschinenbau & Verfahrenstechnik (FB 04)  
Institute
Bremer Institut für Messtechnik, Automatisierung und Qualitätswissenschaft (BIMAQ)  
Dokumenttyp
Artikel/Aufsatz
Zeitschrift/Sammelwerk
Measurement  
Band
113
Startseite
131
Endseite
136
Zweitveröffentlichung
Ja
Dokumentversion
Postprint
Lizenz
https://creativecommons.org/licenses/by-nc-nd/4.0/
Sprache
Englisch
Dateien
Lade...
Vorschaubild
Name

Fischer_Fisher information and Cramér-Rao bound for unknown systematic errors_2018_accepted-version.pdf

Size

1.43 MB

Format

Adobe PDF

Checksum

(MD5):cea2fe8681970a12e8dcd50d917f993a

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