The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
A mathematical model for the atomic clock error
Open accessAbstract
A mathematical model for the clock phase and frequency deviation based on the theory of stochastic differential equations (SDEs) is discussed. In particular, we consider a model that includes what are called the `white and random walk frequency noises' in time metrology, which give rise in a mathematical context to a Wiener and an integrated Wiener process on the clock phase. Due to the particular simple expression of the functions involved an exact solution exists, and we determine it by considering the model in a wider theoretical context, which is suitable for generalizations to more complex instances. Moreover, we determine an iterative form for the solution, useful for simulation and further processing of clock data, such as filtering and prediction. The Euler method, generally applied in literature to approximate the solution of SDEs, is examined and compared to the exact solution, and the magnitude of the approximation is evaluated. The possible extension of the model to other noise sources, such as the flicker and white phase noises, is also sketched.
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“Although many kinds of random noises affect OAC signals [53], the most prominent components are white frequency modulation and random walk frequency modulation [54].”
From Unification of a Global Height System at the Centimeter-Level Using Precise Clock Frequency Signal Links (2023) · cites this paper as [54]
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“The frequency model mainly includes a fixed frequency and a small disturbance term, which can be expressed as [37] f (t) = f 0 + r(t)(4)”
From Performance Evaluation and Requirement Analysis for Chronometric Leveling with High-Accuracy Optical Clocks (2022) · cites this paper as [37]
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“In addition, the frequency statistical error of the optical clock may be caused by outliers, drift, and noise characteristic of the output frequency [37].”
From Performance Evaluation and Requirement Analysis for Chronometric Leveling with High-Accuracy Optical Clocks (2022) · cites this paper as [37]
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“The noise model of an atomic clock could be described by five kinds of independent energy spectrum noises, and the total noise model is the linear superposition of five kinds of noise.The basic model has been widely accepted internationally and can be expressed as [37,41]”
From Performance Evaluation and Requirement Analysis for Chronometric Leveling with High-Accuracy Optical Clocks (2022) · cites this paper as [37]
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Citations
Cites
Numerical solution of stochastic differential equations
Kloeden, P. E. 1., & Platen, E. (2016) · doi:10.5194/gmd-2016-45-rc1 · Cited by 5,119
On the Theory of the Brownian Motion
Uhlenbeck, G. E., & Ornstein, L. S. (1930) · Physical Review · doi:10.1103/physrev.36.823 · Cited by 4,713
Allan, D. W. (1987) · IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control · doi:10.1109/t-uffc.1987.26997 · Cited by 856
Chaffee, J. W. (1987) · IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control · doi:10.1109/t-uffc.1987.26998 · Cited by 59
Uncertainties of drift coefficients and extrapolation errors: application to clock error prediction
Vernotte, F., Delporte, J., Brunet, M., et al. (2001) · Metrologia · doi:10.1088/0026-1394/38/4/6 · Cited by 49
Atomic clock models using fractionally integrated noise processes
Schmidt, L. (2003) · Metrologia · doi:10.1088/0026-1394/40/3/309 · Cited by 41
Stochastic models and statistical analysis for clock noise
Percival, D. B. (2003) · Metrologia · doi:10.1088/0026-1394/40/3/308 · Cited by 26
Stochastic models of stable frequency and time sources and their relationship
Audoin, C., & Dimarcq, N. (1993) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/19.231590 · Cited by 7
Cited by
Sorted by citations
Shen, Z., Shen, W.-B., & Zhang, S. (2017) · Surveys in Geophysics · doi:10.1007/s10712-017-9414-6 · Cited by 25
Shen, Z., Shen, W., Zhang, S., Shum, C. K., Zhang, T., He, L., Cai, Z., Xiong, S., & Wang, L. (2023) · Remote Sensing · doi:10.3390/rs15123020 · Cited by 9
Xiong, C., Liu, D., Wu, L., Bao, L., & Zhang, P. (2022) · Remote Sensing · doi:10.3390/rs14174141 · Cited by 3
Metadata
- Authors
- Galleani, L., Sacerdote, L., Tavella, P., & Zucca, C.
- Affiliations
- University of Turin (IT)
- Venue
- Metrologia
- Publisher
- IOP Publishing
- Published
- 2003-06
- Volume
- 40
- Issue
- 3
- Pages
- S257-S264
- ISSN
- 0026-1394 (ISSN-L)
- 1681-7575
- OpenAlex
- W2047239488
- Cited by
- 113
- References
- 8
- Citations by year
- 2026: 5 · 2025: 6 · 2024: 3 · 2023: 15 · 2022: 3 · 2021: 4 · 2020: 8 · 2019: 5 · 2018: 5 · 2017: 3 · 2016: 6 · 2015: 3 · 2014: 8 · 2013: 4 · 2012: 4
- FWCI
- 1.06
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Metrologia (publishedVersion)
- CINECA IRIS Institutional Research Information System (IRIS Istituto Nazionale di Ricerca Metrologica) (submittedVersion)
- PORTO@Iris (submittedVersion)
- PORTO Publications Open Repository TOrino (Politecnico di Torino) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Frequency and Time Standards
- Physical Sciences › Computer Science › Computer Networks and Communications › Network Time Synchronization Technologies
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advancements in PLL and VCO Technologies
- Keywords
- frequency deviation, stochastic differential equations, white noise, Brownian motion, exact solutions, Euler method, 1/f noise, white phase noise, time metrology
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- Galleani, L., Sacerdote, L., Tavella, P., & Zucca, C. (2003). A mathematical model for the atomic clock error. Metrologia. https://doi.org/10.1088/0026-1394/40/3/305
