Allan variance of time series models for measurement data

Metrologia

Volumn 45, Issue 5, 2008, Pages 549-561

  Zhang, Nien Fan ^a  

^a NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FREQUENCY STANDARDS; MATHEMATICAL MODELS; RANDOM PROCESSES;

1/F NOISES; ALLAN VARIANCES; AUTOCORRELATED MEASUREMENTS; FREQUENCY METROLOGIES; MEASUREMENT DATUMS; NOISE MODELS; POWER LAWS; PROCESS VARIATIONS; RANDOM WALKS; SAMPLE VARIANCES; STATIONARY PROCESSES; TIME DOMAINS; TIME SERIES;

UNCERTAINTY ANALYSIS;

EID: 58149352865     PISSN: 00261394     EISSN: 16817575     Source Type: Journal    
DOI: 10.1088/0026-1394/45/5/009     Document Type: Article

References (30)

1. ISO/IEC 1995 Guide to the Expression of Uncertainty in Measurement (Geneva: International Organization for Standardization)
2. Zhang N F 2006 Calculation of the uncertainty of the mean of autocorrelated measurements Metrologia 43 S276-81
3. Witt T 2007 Using the autocorrelation function to characterize time series of voltage measurements Metrologia 44 201-9
4. Rutman J 1978 Characterization of phase and frequency instabilities in precision frequency sources: fifteen years of progress Proc. IEEE 66 1048-75
5. Barnes J et al 1971 Characterization of frequency stability IEEE Trans. Instrum. Meas. 20 105-20
6. Rutman J and Walls F L 1991 Characterization of frequency stability in precision frequency sources Proc. IEEE 79 952-60
7. Sullivan D B, Allan D W, Howe D A and Walls F L (ed) 1990 Characterization of clocks and oscillators NIST Technical Note 1337
8. Lesage P and Audoin C 1979 Characterization and measurement of time and frequency stability Radio Sci. 4 521-39
9. Wallis F L and Allan D W 1986 Measurements of frequency stability Proc. IEEE 74 162-8
10. Allan D W, Weiss M A and Jespersen J L 1991 A frequency-domain view of time-domain characterization of clocks and time and frequency distribution systems Proc. 45th Annual Freq. Contr. Symp. (Los Angeles) pp 667-78
11. Witt T 2000 Testing for correlations in measurements Advanced Mathematical and Computational Tools in Metrology IV ed P Ciarlini et al (Singapore: World Scientific) pp 273-88
12. Witt T and Reymann D 2000 Using power spectra and Allan variances to characterize the noise of Zener-diode voltage standards IEE Proc.-Sci. Meas. Technol. 147 177-82
13. Witt T and Tang Y 2005 Investigations of noise in measurements of electronic voltage standards IEEE Trans. Instrum. Meas. 54 567-70
14. Priestley M B 1981 Spectral Analysis and Time Series (London: Academic)
15. Zhang N F 1998 Estimating process capability indexes for autocorrelated data J. Appl. Stat. 25 559-74
16. Allan D 1987 Should the classical variance be used as a basic measure in standards metrology? IEEE Trans. Instrum. Meas. 36 646-54
17. Allan D 1966 Statistics of atomic frequency standards Proc. IEEE 54 221-30
18. Yoshimura K 1978 Characterization of frequency stability: uncertainty due to the autocorrelation of the frequency fluctuations IEEE Trans. Instrum. Meas. IM-27 1-7
19. Anderson T W 1971 The Statistical Analysis of Time Series (New York: Wiley)
20. Brockwell P J and Davis A D 1987 Time Series: Theory and Methods (New York: Springer)
21. Box G E P and Jenkins G M 1976 Time Series Analysis: Forecasting and Control (San Francisco: Holden Day)
22. Schmidt L 2003 Atomic clock models using fractionally integrated noise processes Metrologia 40 S305-11
23. Mandelbrot B 1967 Some noises with 1/f spectrum, a bridge between direct current and white noise IEEE Trans. Inform. Theory 13 289-98
24. Granger C W J and Joyeux R 1980 An introduction to long-range time series models and fractional differencing J. Time Series Anal. 1 15-30
25. Hosking J R M 1981 Fractional differencing Biometrika 68 165-76
26. Allan D W and Barnes J A 1990 A modified 'Allan variance' with increased oscillator characterization ability NIST Technical Note 1337 pp TN254-8
27. Andrews L C 1992 Special Functions of Mathematics for Engineers 2nd edn (New York: McGraw-Hill)
28. Brockwell P J, Davis A D and Calder M V 2002 ITSM-2000 Version 7.1 (Fort Collins, CO: B & D Enterprises Inc)
29. Gradshetyn I S and Ryezhik I M 1994 Table of Integrals, Series, and Products 5th edn (San Diego: Academic)
30. Jolley L B W 1961 Summation of Series (New York: Dover)