5.4. Frequency and Time Standards

Vessot, R. F. C.

doi:10.1016/s0076-695x(08)60710-3

Cited by 14 publications

(5 citation statements)

References 12 publications

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“…frequency‐dependent) noise dominates the low‐frequency part. This spectral behaviour of coordinate time‐series is common‐although on a different scale of frequencies—to other, physically different processes where time‐series are involved, and is crucial in assessing the stability of a time‐series, that is the property of resisting changes in its rate (Vessot 1976, ch. 5.4).…”

Section: Power Spectral Densities Of Time‐series and Velocity Uncertamentioning

confidence: 99%

“…Hence the variance of the average rate of change depends on the autocorrelation R x () of the coordinate jitter x ( t ). Using the Wiener–Khinchin Fourier transform relationship between the one‐sided spectral density of a random signal and its autocorrelation function (ω= 2π f ): we finally obtain the expression of the two‐sample Allan variance of a time‐series with spectrum S x , as a function of the time T : For a band‐limited process with high frequency f h it can be shown that the relation between the two‐sample Allan variance and the components of the spectral density described in () is (Spilker 1977; Vessot 1976):…”

Section: Power Spectral Densities Of Time‐series and Velocity Uncertamentioning

confidence: 99%

“…For a band-limited process with high frequency f h it can be shown that the relation between the two-sample Allan variance and the components of the spectral density described in (eq. 2) is (Spilker 1977;Vessot 1976):…”

Section: P O W E R S P E C T R a L D E N S I T I E S O F T I M E -S Ementioning

confidence: 99%

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Average strain rate in the Italian crust inferred from a permanent GPS network - I. Statistical analysis of the time-series of permanent GPS stations

Caporali¹

2003

Geophysical Journal International

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SUMMARY Time‐series of the horizontal coordinates of 21 GPS stations of the EUREF Permanent Network in the Alpine Mediterranean area with three or more years of continuous tracking have been computed with the intent of estimating velocities and their uncertainties, taking into account the detailed structure of their noise. The power spectral densities demonstrate that coloured noise, mostly flicker (1/f) noise, can be present at frequencies below 6 cycle yr−1, while at higher frequencies the spectrum tends to a regime of white (i.e. frequency‐independent) noise. This statistical information is used to obtain more accurate estimates of station velocities and of their uncertainties than by the standard least‐squares method. Following an approach well known in the analysis of time‐series of frequency standards, the stability of each time‐series is computed as a function of time, in the sense of a two‐sample Allan variance. The power spectral density of the time‐series is used to infer the variance of the change in the slope, with 1σ probability, of two consecutive, equal‐length batches of a given time‐series, and this as a function of the length of the batch. The power spectral density of each time‐series is then converted into an autocorrelation function. Taking into account the correct correlations of pairs of samples as a function of their lag, the slope of each time‐series is estimated by the least‐squares method, with a non‐diagonal weight‐matrix. We show that in all the examined cases the uncertainties in the velocities computed taking into account the detailed noise spectrum are larger by a factor of 4 ± 1 than the formal uncertainties obtained by the least‐squares method under the assumption of pure white noise. Estimating the slope of a time‐series taking into account the autocorrelation of the samples yields velocities not significantly different from those obtained assuming uncorrelated samples. We conclude that the reason for the velocity uncertainty estimated by the standard least‐squares method being unrealistically small is the neglect of the cumulative effect of uncorrelated and correlated noise. Neglecting the correlated noise does not, however, affect the velocity. Earlier investigations based on more limited (<3 yr) data sets have resulted in non‐unique conclusions as to the time decrease of the velocity uncertainty with time, and the noise spectrum of the time‐series. We find that the velocity uncertainty does decrease as the time‐series increases, and the value of the velocity uncertainty can be predicted from the power spectral density, as the length of the time‐series increases. The time‐series are finally analysed in the space domain. After removal of common errors, typically represented by sinusoids of annual period, correlation coefficients are computed for pairs of stations and plotted as a function of their distance. We find that the time‐series already decorrelate at very short distances (<100 km). This suggests that random errors affecting the coordinates of clusters of stations such as...

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Section: Power Spectral Densities Of Time‐series and Velocity Uncertamentioning

confidence: 99%

Section: Power Spectral Densities Of Time‐series and Velocity Uncertamentioning

confidence: 99%

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Average strain rate in the Italian crust inferred from a permanent GPS network - I. Statistical analysis of the time-series of permanent GPS stations

Caporali¹

2003

Geophysical Journal International

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“…Since the signal s(t) is real valued, one can write (see e.g. also in Barnes et al 1971;Vessot 1976):…”

Section: The Role Of the Minimummentioning

confidence: 99%

Optimization of heterodyne observations using Allan variance measurements

Schieder

Krämer

2001

A&A

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Abstract. Stability tests based on the Allan variance method have become a standard procedure for the evaluation of the quality of radio-astronomical instrumentation. They are very simple and simulate the situation when detecting weak signals buried in large noise fluctuations. For the special conditions during observations an outline of the basic properties of the Allan variance is given, and some guidelines how to interpret the results of the measurements are presented. Based on a rather simple mathematical treatment clear rules for observations in "Position-Switch", "Beam-" or "Frequency-Switch", "On-The-Fly-" and "Raster-Mapping" mode are derived. Also, a simple "rule of the thumb" for an estimate of the optimum timing for the observations is found. The analysis leads to a conclusive strategy how to plan radio-astronomical observations. Particularly for air-and space-borne observatories it is very important to determine, how the extremely precious observing time can be used with maximum efficiency. The analysis should help to increase the scientific yield in such cases significantly.

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“…[17] The Allan standard deviation s y (t) is a measure of the phase fluctuations on the time scales of interest, which is widely used in the characterization of devices such as atomic clocks and ultrastable oscillators [Vessot, 1976]. It is closely related to the structure function of the fractional frequency fluctuations, y = df/f X , as shown below…”

Section: Rs6004mentioning

confidence: 99%

Spectral broadening and phase scintillation measurements using interplanetary spacecraft radio links during the peak of solar cycle 23

Morabito

2009

Radio Science

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[1] When an interplanetary spacecraft is in a solar superior conjunction configuration, the received radio signals are degraded by several effects that generally increase in magnitude as the angle between the spacecraft and the Sun (Sun-Earth-Probe or SEP angle) decreases as viewed by a terrestrial tracking station. During periods of quiescent solar activity, phase scintillation and spectral broadening follow well-defined trends as a function of solar impact distance (SEP angle) and link frequency. During active solar periods, the magnitudes of these effects increase above background levels predicted by the quiet period models. Several such events were observed during the solar superior conjunction of the Cassini spacecraft during the peak of solar cycle 23 in May 2000. Pronounced features in the spectral broadening data above the quiet background appear to be associated with Coronal Mass Ejections (CMEs), and last for extended periods of time ranging from $30 min to $4 h. These features are coincident with periods of increased activity seen in the region of the spacecraft signal source on coronal white light images, and tend to be related or matched with EIT flare events and possibly long-duration flare events seen in satellite X-ray data. Several such features were captured in the May 2000 Cassini solar conjunction phase scintillation and spectral broadening data at X band (8.4 GHz) and Ka band (32 GHz) radio frequencies, and are presented here. Such characterizations are beneficial in understanding the impact of such events in future interplanetary communication scenarios during solar conjunction periods.

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5.4. Frequency and Time Standards

Cited by 14 publications

References 12 publications

Average strain rate in the Italian crust inferred from a permanent GPS network - I. Statistical analysis of the time-series of permanent GPS stations

Average strain rate in the Italian crust inferred from a permanent GPS network - I. Statistical analysis of the time-series of permanent GPS stations

Optimization of heterodyne observations using Allan variance measurements

Spectral broadening and phase scintillation measurements using interplanetary spacecraft radio links during the peak of solar cycle 23

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