A mathematical model for the atomic clock error

Galleani, Lorenzo; Sacerdote, Laura; Tavella, P.; Zucca, Cristina

doi:10.1088/0026-1394/40/3/305

Cited by 100 publications

(83 citation statements)

References 8 publications

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“…Therefore, the abnormal values and blunders in the observations should be eliminated before the model has been established [27][28][29][30][31][32][33]. In this paper, the median absolute deviation (MAD) method was used to detect the phase and frequency jumps which exist in the clock offset sequence.…”

Section: Preprocessing Of Satellite Clock Offsetsmentioning

confidence: 99%

An Improved Predicted Model for BDS Ultra-Rapid Satellite Clock Offsets

et al. 2018

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Abstract:The satellite clocks used in the BeiDou-2 satellite navigation System (BDS) are Chinese self-developed Rb atomic clocks, and their performances and stabilities are worse than GPS and Galileo satellite clocks. Due to special periodic noises and nonlinear system errors existing in the BDS clock offset series, the GPS ultra-rapid clock model, which uses a simple quadratic polynomial plus one periodic is not suitable for BDS. Therefore, an improved prediction model for BDS satellite clocks is proposed in order to enhance the precision of ultra-rapid predicted clock offsets. First, a basic quadratic polynomial model which is fit for the rubidium (Rb) clock is constructed for BDS. Second, the main cyclic terms are detected and identified by the Fast Fourier Transform (FFT) method according to every satellite clock offset series. The detected results show that most BDS clocks have special cyclic terms which are different from the orbit periods. Therefore, two main cyclic terms are added to absorb the periodic effects. Third, after the quadratic polynomial plus two periodic fitting, some evident nonlinear system errors also exist in the model residual, and the Back Propagation (BP) neural network model is chosen to compensate for these nonlinear system errors. The simulation results show that the performance and precision using the improved model are better than that of China iGMAS ultra-rapid prediction (ISU-P) products and the Deutsches GeoForschungsZentrum GFZ BDS ultra-rapid prediction (GBU-P) products. Comparing to ISU-P products, the average improvements using the proposed model in 3 h, 6 h, 12 h and 24 h are 23.1%, 21.3%, 20.2%, and 19.8%, respectively. Meanwhile the accuracy improvements of the proposed model are 9.9%, 13.9%, 17.3%, and 21.2% compared to GBU-P products. In addition, the kinematic Precise Point Positioning (PPP) example using 8 Multi-GNSS Experiment MGEX stations shows that the precision based on the proposed clock model has improved about 16%, 14%, and 38% in the North (N), East (E) and Height (H) components.

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Section: Preprocessing Of Satellite Clock Offsetsmentioning

confidence: 99%

An Improved Predicted Model for BDS Ultra-Rapid Satellite Clock Offsets

et al. 2018

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“…The one based on stochastic differential equations [9] is particularly useful for the evaluation of the impact of clock noise on complex systems and for the implementation and simulation of synchronization protocols based on recursive filtering techniques [10], such as the Kalman filtering.…”

Section: Clock Skew Modelmentioning

confidence: 99%

A servo design for slave clock in IEEE 1588 synchronization networks

Fan

Liu

et al. 2013

Int J Communication

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SUMMARYClock synchronization is critical for a variety of applications in communication networks. In this paper, we design a clock servo named VI_PID-K, which consists of a variable integral PID controller and a Kalman filter. It is a pre-correction mechanism for the skew based on feedback principle to compensate for the poor stability of local clocks in IEEE 1588 networks. Our contribution is establishing discrete differential equation models, bringing in a variable integral PID controller to adjust the skew error and a Kalman filter to act as a skew estimator to predict the skew during one synchronization interval. Simulation results demonstrate that VI_PID-K provides a more stable disciplined clock, improves the speed of skew convergence, and reduces Allan variance in a large time scale when compared to PI method or Fixed_Integral method.VI_PID-K can improve the stability of slave clock and reduce the frequency that master clock sends Sync messages, so the network overhead for clock synchronization can be reduced.

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“…They are also used in metrology as a model of errors of atomic clocks with variable accuracy and synchronization [27].…”

Section: Theoremmentioning

confidence: 99%

Asymptotics of small deviations of the Bogoliubov processes with respect to a quadratic norm

Pusev

2010

Theor Math Phys

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We obtain results on small deviations of Bogoliubov's Gaussian measure occurring in the theory of the statistical equilibrium of quantum systems. For some random processes related to Bogoliubov processes, we find the exact asymptotic probability of their small deviations with respect to a Hilbert norm.The Bogoliubov measure, introduced in [1], [2], plays an important role in the theory of the statistical equilibrium of quantum systems. It occurs in representing Gibbs equilibrium means of Bose operators in the form of functional integrals using Bogoliubov's method of T -products (see [3]).We define the Bogoliubov process ξ(t), t ∈ [0, 1], as a Gaussian process with a zero mean and the covarianceIt follows from the general results of the theory of random processes that trajectories of a Bogoliubov process are almost certainly (a.c.) continuous. From definition (1), we obtain E ξ(1) − ξ(0) 2 = 0 and hencealmost all the trajectories of a Bogoliubov process belong to the space C 0 [0, 1] of continuous functions x(t) defined on the segment [0, 1] and satisfying the condition x(0) = x(1). The distribution of the process ξ(t) in the space C 0 [0, 1] endowed with a uniform metric is called the Bogoliubov measure μ B . Properties of the Bogoliubov measure, of functional integrals over this measure, and of the Bogoliubov process trajectories were studied in [2], [4], [5]. Approximate formulas constructed in [2] for functional integrals over a Bogoliubov measure are exact for functional polynomials. It was established in [4]that similarly to the case of Wiener processes, almost all trajectories of a Bogoliubov process do not satisfy the Hölder condition with the index γ > 1/2 and are therefore nondifferentiable. Some asymptotic formulas for functional integrals with respect to a Bogoliubov measure were obtained in [5], where the asymptotic form of the probability of large deviations of Bogoliubov processes in L p -norms, which is important in many problems in probability theory and mathematical physics, was also derived.Another fundamental characteristic of random processes (used, e.g., to estimate the accuracy of approximations of random process and to calculate the metric entropy of different sets) is the asymptotic form of their small deviations in one norm or another. The theory of small deviations for the norm of Gaussian processes has been rapidly developing in the last decade (see, e.g., [6], [7]). A connection was recently established between small deviations and problems in mathematical statistics: functional analysis of data and nonparametric Bayes estimates [8]- [10].In the majority of cases, it is possible to find a rough (logarithmic) asymptotic expression for the probabilities of small deviations for Gaussian processes. Calculating the exact asymptotic form is a much more complicated problem, whose solution is known for only a few processes [11]-[16].

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A mathematical model for the atomic clock error

Cited by 100 publications

References 8 publications

An Improved Predicted Model for BDS Ultra-Rapid Satellite Clock Offsets

An Improved Predicted Model for BDS Ultra-Rapid Satellite Clock Offsets

A servo design for slave clock in IEEE 1588 synchronization networks

Asymptotics of small deviations of the Bogoliubov processes with respect to a quadratic norm

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