Abstract
Described is the proposal of evaluation the standard deviation of the stationary random component of measured signal from its regularly sampled observations when they are auto-correlated. As, the first step is the identification and removing the regularly variable components from the raw sample data. Then formulas for standard deviation of the sample and of the mean value are expressed with use the correction coefficients or the so-called ”effective number” of observations. These quantities depend on number of observations and on the autocorrelation function of the sample cleaned from regular components. How to estimate the autocorrelation function for the sample data is also described. Few numerical examples to illustrate problems are included.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Dorozhovetz, M., Warsza, Z.: Methods of upgrading the uncertainty…, Part 2 Elimination of the influence of autocorrelation of observations and choosing the adequate distribution. In: Proceedings of 15th IMEKO TC4 Symposium, Part 1, Iasi Romania, pp. 199–204 (September 2007)
Warsza, Z.L., Dorozhovets, M.: Uncertainty type A evaluation of autocorrelated measurement observations. Biuletyn WAT (Military Technical Academy) LVII(2), 2143–2152 (2008)
Warsza, Z.L., Dorozhovets, M., Korczynski, M.J.: Methods of upgrading the uncertainty of type A evaluation (1). Elimination the influence of unknown drift and harmonic components. In: Proceedings of 15th IMEKO TC4 Symposium, Part 1, Iasi Romania, pp. 1193–1198 (September 2007)
Zięba, A.: Effective number of observations and unbiased estimators of variance for autocorrelated data – an overview. Metrology & Measurement Systems 17, 3–16 (2010)
Zięba, A., Ramza, P.: Standard deviation of the mean of autocorrelated observations estimated with the use of the autocorrelation function estimated from the data. Metrology & Measurement Systems 18, 529–542 (2011)
Warsza, Z.L., Zięba, A.: Niepewność typu A pomiaru o obserwacjach samoskorelowanych (Uncertainty type A in measurements of autocorrelated observations). Pomiary Automatyka Kontrola 58(2), 157–161 (2012)
Warsza, Z.L.: Evaluation of the type A uncertainty in measurements with autocorrelated observations. In: Proceedings of Jointed TC 1 - TC 7 Imeko Symposium, Genua (2013) (in print)
Guide to the Expression of Uncertainty in Measurement, revised and corrected, BIPM 2008 (2008)
Dorozhovets, M., Warsza, Z.L.: Propozycje rozszerzenia metod wyznaczania niepewności wyniku pomiarów wg Przewodnika GUM (1) Uwzględnianie wpływu autokorelacji i nieadekwatności rozkładu wyników obserwacji w niepewności typu A. Pomiary Automatyka Robotyka 11(1), 6–15 (2007) (in Polish)
Dorozhovets, M., Warsza, Z.L.: Propozycje rozszerzenia metod wyznaczania niepewności wyniku pomiarów wg Przewodnika GUM (2) Uściślenie metod obliczeń niepewności typu B. Pomiary Automatyka Robotyka 11(2), 45–52 (2007) (in Polish)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Warsza, Z.L. (2014). Evaluation of the Standard Deviation of the Random Component of the Measured Signal from Its Autocorrelated Observations. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds) Recent Advances in Automation, Robotics and Measuring Techniques. Advances in Intelligent Systems and Computing, vol 267. Springer, Cham. https://doi.org/10.1007/978-3-319-05353-0_69
Download citation
DOI: https://doi.org/10.1007/978-3-319-05353-0_69
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05352-3
Online ISBN: 978-3-319-05353-0
eBook Packages: EngineeringEngineering (R0)