A mathematical model for the atomic clock error in case of jumps

Zucca, Cristina; Tavella, P.

doi:10.1088/0026-1394/52/4/514

Cited by 26 publications

(20 citation statements)

References 18 publications

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“…where A is the amplitude, ] 0 is the central frequency of the oscillation, and φ(t) represents the random fluctuation in phase. e phase variations φ(t) is given as a summation of seven terms [35,36]:…”

Section: The Oscillator Modelmentioning

confidence: 99%

Characterization of Nonstationary Phase Noise Using the Wigner–Ville Distribution

Levy

Pinchas

Pinhasi

2020

Mathematical Problems in Engineering

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Oscillators and atomic clocks, as well as lasers and masers, are affected by physical mechanisms causing amplitude fluctuations, phase noise, and frequency instabilities. The physical properties of the elements composing the oscillator as well as external environmental conditions play a role in the coherence of the oscillatory signal produced by the device. Such instabilities demonstrate frequency drifts, modulation, and spectrum broadening and are observed to be nonstationary processes in nature. Most of the tools which are being used to measure and characterize oscillator stability are based on signal processing techniques, assuming time invariance within a temporal window, during which the signal is assumed to be stationary. This letter proposes a new time-frequency approach for the characterization of frequency sources. Our technique is based on the Wigner–Ville time-frequency distribution, which extends the spectral measures to include the temporal nonstationary behavior of the processes affecting the coherence of the oscillator and the accuracy of the clock. We demonstrate the use of the technique in the characterization of nonstationary phase noise in oscillators.

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Section: The Oscillator Modelmentioning

confidence: 99%

Characterization of Nonstationary Phase Noise Using the Wigner–Ville Distribution

Levy

Pinchas

Pinhasi

2020

Mathematical Problems in Engineering

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“…Due to influences of intrinsic physical characteristics and outside environments, the SCB series will show non-stable characteristics (Heo et al, 2010). In addition, the on board atomic clocks are generally caesium or rubidium atomic clocks, and the frequency drift over an extended period of time is usually nonlinear (Galleani et al, 2003; Zucca and Tavella, 2015). The factors above will influence stability and accuracy of satellite clocks, and lead to clock offset.…”

Section: Fusion-based Scb Prediction Methodsmentioning

confidence: 99%

Fusion-based Satellite Clock Bias Prediction Considering Characteristics and Fitted Residue

Zhang

Zheng

et al. 2018

J. Navigation

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As Satellite Clock Bias (SCB) prediction may be affected by various factors such as periodic items, sampling length, and stochastic items, a fusion-based prediction method is proposed by considering characteristics of SCB and fitted residue. On this basis, an instance algorithm is presented by fusing four typical prediction models. First, we use Empirical Mode Decomposition (EMD) to pre-process and decompose the SCB series into multiple components with various characteristics. Then, we analyse the fitting performance of each model for different components and prediction length, namely short-, mid- and long-term prediction, and select models with the best performance. Next, we analyse fitted residue of the reconstructed SCB, and select the model with the best fitting results. Finally, we fuse the multiple selected models for SCB prediction. The method is tested using Global Positioning System (GPS) precise clock products provided by the International Global Navigation Satellite System Service (IGS). Experimental results show that, compared with single prediction models and existing combination models, the proposed fusion-based prediction method improves accuracy and stability. In particular, the proposed method is more stable and has better performance for mid- and long-term prediction.

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“…The initial ambiguity of phase measurement is set to an integer number of cycle constant for each continuous arc, and cycle slips are also introduced at some epochs for certain satellites. The satellite clock offsets are obtained from CODE precise clock products, and the receiver clock offsets are simulated by stochastic differential equations (SDEs) [41], which are described in the next subsection. Moreover, some errors, such as the ocean tide loading displacement, PCOs, and PCVs, need to be included in the observation errors to ensure that the simulated observation data are as close to real data as possible.…”

Section: A Simulation Of Gnss Observations Connected With Ground Stamentioning

confidence: 99%

“…These random noises vary according to the type of clock. Previous studies have reported that WFM and RWFM are the predominant noises in high-precise atomic clocks [41], [44]. Accordingly, the mathematical model of the clock offset can be formulated as [41]:…”

Section: B Mathematical Model Of Clock Offsetmentioning

confidence: 99%

Geopotential Determination Based on Precise Point Positioning Time Comparison: A Case Study Using Simulated Observation

Cai

Shen

et al. 2020

IEEE Access

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According to general relativity theory (GRT), the geopotential difference (GD) can be determined by comparing the change in time difference between precise clocks using the precise point positioning (PPP) time transfer technique, referred to as the relativistic PPP time comparison approach. We focused on high-precision time comparison between two precise clocks for determining the GD using the relativistic PPP time transfer,and conducted simulation experiments to validate the approach. In the experiments, we consider three cases to evaluate the performance of the approach using clocks with different stabilities, namely, the frequency stabilities of the clocks equipped at three selected ground stations are respectively (Case 1), (Case 2), and (Case 3) at time period . Conclusions are drawn from the experimental results. First, high-precision clocks can significantly improve the accuracy for PPP time transfer, but the improvement is limited by measurement noises. Compared to Case 1, the long-term stabilities of OPMT-BRUX as well as PTBB-BRUX are improved in Cases 2 and 3. The frequency stabilities of Cases 1-3 are approximately 4.28 × 10 -16 , 4.00 × 10 -17 , and 3.22 × 10 -17 at 10-day averaging time for OPMT-BRUX, respectively, and for PTBB-BRUX, these values are approximately 3.73 × 10 -16 , 8.17 × 10 -17 , and 4.64 × 10 -17 . Second, the geopotential difference between any two stations can be 13 tdetermined at the decimeter level, with its accuracy being consistent with the stabilities of the time links in Cases 1-3. In Case 3, the determined geopotential differences between OPMT and BRUX deviate from the EIGEN-6C4 model values by -0.64 m 2 /s 2 with an uncertainty of 1.11 m 2 /s 2 , whereas the deviation error between PTBB and BRUX is 0.76 m 2 /s 2 with an uncertainty of 1.79 m 2 /s 2 . The approach prosed in this study can be also applied to testing GRT.

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A mathematical model for the atomic clock error in case of jumps

Cited by 26 publications

References 18 publications

Characterization of Nonstationary Phase Noise Using the Wigner–Ville Distribution

Characterization of Nonstationary Phase Noise Using the Wigner–Ville Distribution

Fusion-based Satellite Clock Bias Prediction Considering Characteristics and Fitted Residue

Geopotential Determination Based on Precise Point Positioning Time Comparison: A Case Study Using Simulated Observation

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