Estimation of Conditional Expected Value for Exponentially Autocorrelated Data

• Autorzy: Kowalczyk A. , Szlachta A. , Hanus R. , Chorzępa R.

Identyfikatory

DOI

10.1515/mms-2017-0005

• Języki publikacji: EN

Abstrakty

EN

Autocorrelation of signals and measurement data makes it difficult to estimate their statistical characteristics. However, the scope of usefulness of autocorrelation functions for statistical description of signal relation is narrowed down to linear processing models. The use of the conditional expected value opens new possibilities in the description of interdependence of stochastic signals for linear and non-linear models. It is described with relatively simple mathematical models with corresponding simple algorithms of their practical implementation. The paper presents a practical model of exponential autocorrelation of measurement data and a theoretical analysis of its impact on the process of conditional averaging of data. Optimization conditions of the process were determined to decrease the variance of a characteristic of the conditional expected value. The obtained theoretical relations were compared with some examples of the experimental results.

Słowa kluczowe

EN

conditional averaging; conditional expected value; auto-correlated data; random signals

• Wydawca: Komitet Metrologii i Aparatury Naukowej PAN
• Czasopismo: Metrology and Measurement Systems
• Rocznik: 2017
• Tom: Vol. 24, nr 1
• Strony: 69--78
• Opis fizyczny: Bibliogr. 18 poz., rys., tab., wykr., wzory

Twórcy

autor

Kowalczyk A.

• Rzeszow University of Technology, Department of Metrology and Diagnostic Systems, Powstańców Warszawy 12, 35-959 Rzeszów, Poland

autor

Szlachta A.

• Rzeszow University of Technology, Department of Metrology and Diagnostic Systems, Powstańców Warszawy 12, 35-959 Rzeszów, Poland

autor

Hanus R.

• Rzeszow University of Technology, Department of Metrology and Diagnostic Systems, Powstańców Warszawy 12, 35-959 Rzeszów, Poland

autor

Chorzępa R.

• Rzeszow University of Technology, Department of Metrology and Diagnostic Systems, Powstańców Warszawy 12, 35-959 Rzeszów, Poland

Bibliografia

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• [4] Evaluation of measurement data. Supplement 2 to the “Guide to the expression of uncertainty in measurement” − Extension to any number of output quantities. (2011). JCGM 102:2011.
• [5] Box, G.E.P., Jenkins, G.M., Reinsel, G.C. (1994). Time series analysis: forecasting and control. Prentice Hall, Englewood Cliffs.
• [6] Bayley, G.V., Hammersley, G.M. (1946). The “effective” number of independent observations in an autocorrelated time-series. J. Roy. Stat. Soc. Suppl. 8, 184-197.
• [7] Zhang, N.F. (2006). Calculation of the uncertainty of the mean of autocorrelated measurements. Metrologia 43, 276-281.
• [8] Dorozhovets, M., Warsza, Z. (2007). Evaluation of the uncertainty type A of autocorrelated measurement observations. Measurement Automation and Monitoring, 53(2), 20-24.
• [9] Witt, T.J. (2007). Using the autocorrelation function to characterize time series of voltage measurements. Metrologia, 44, 201-209.
• [10] Zięba, A. (2010). Effective number of observations and unbiased estimators of variance for autocorrelated data - an overview. Metrol. Meas. Syst., 17(1), 3-16.
• [11] Zięba, A., Ramza P. (2011). Standard deviation of the mean of autocorrelated observations estimated with the use of the autocorrelation function estimated from the data. Metrol. Meas. Syst., 18(4), 529-542.
• [12] Dorozhovets, M. (2009). Influence of lack of a priori knowledge about autocorrelation functions of observations on estimation of their average value standard uncertainty. Measurement Automation and Monitoring, 55(12), 989−992.
• [13] Zhang, N.F. (2008). Allan variance of time series models for measurement data. Metrologia, 45, 549-561.
• [14] Kowalczyk, A., Szlachta, A., Hanus, R. (2012). Standard uncertainty determination of the mean for correlated data using conditional averaging. Metrol. Meas. Syst., 19(4), 787-796.
• [15] Kowalczyk, A. (2015). Measurement applications of conditional signal averaging. Oficyna Wydawnicza Politechniki Rzeszowskiej, Rzeszów.
• [16] Bendat, J.S., Piersol, A.G. (2010). Random data. Analysis and measurement procedures. John Wiley & Sons, New York.
• [17] Kowalczyk, A. (2008). Classical method for determination of linear system dynamic properties using signal conditional averaging. Measurement Automation and Monitoring, 54(12), 820-823.
• [18] Szlachta, A., Kowalczyk, A., Wilk, G. (2009). Accuracy investigations of impulse response estimation obtained by conditional averaging. Measurement Automation and Monitoring, 55(12), 981-984.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).