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A method of estimating frequency drift rate and removing its effect from Allan variance plots is given. When tried on a test of hydrogen masers, the methods gives consistent results. An error in the previous Allan variance computation algorithm is corrected.
Minimum variance estimation requires that the statistics of random observation errors be modeled properly. If measurements are derived through the use of atomic frequency standards, then one source of error affecting the observable is random fluctuation in frequency. This is the case, for example, with range and integrated Doppler measurements from satellites of the Global Positioning and baseline determination for geodynamic applications. An analytic method is presented which approximates the statistics of this random process. The procedure starts with a model of the Allan variance for a particular oscillator and develops the statistics of range and integrated Doppler measurements. A series of five first order Markov processes is used to approximate the power spectral density obtained from the Allan variance.
It is shown how a commercial time interval counter can be used to measure the relative stability of two signals that are offset in frequency and mixed down to a beat note of about 1 Hz. To avoid the dead-time problem, the counter is set up to read the time interval between each beat note upcrossing and the next pulse of a 10 Hz reference pulse train. The actual upcrossing times are recovered by a simple algorithm whose outputs can be used for computing residuals and Allan variance. A noise floor-test yielded a delta f/f Allan deviation of 1.3 times 10 to the minus 9th power/tau relative to the beat frequency.
It is shown how a commercial time interval counter can be used to measure the relative stability of two signals that are offset in frequency and mixed down to a beat note of about 1 Hz. To avoid the dead-time problem, the counter is set up to read the time interval between each beat note upcrossing and the next pulse of a 10 Hz reference pulse train. The actual upcrossing times are recovered by a simple algorithm whose outputs can be used for computing residuals and Allan variance. A noise floor-test yielded a delta f-f Allan deviation of 1.3 times 10 to the minus 9th power/tau relative to the beat frequency.
Measurements of the short-term stability of the Rb-87 maser as a function of the maser power output and the receiver cutoff frequency are reported. The experimental data are compared to theoretical results obtained from an approximate theory. In this theory the transfer function of the maser for thermal noise is derived, and the spectral density of the phase fluctuations is calculated. An analytical expression for the 'Allan variance' is also given. A comparison of the stability of the Rb-87 maser with existing frequency standards shows its superiority for averaging times less than 1 sec.
Preparation is being made by the DSN to monitor the stability of its clocks and frequency standards in the 64 meter net by means of VLBI. Since variations in the earth's rotation rate represent an error source to VLBI clock synchronization, the Allan Variance of the earth rotation was calculated to find that, in a long-term sense at least, these variations do not noticeably increase the differential instability of two clocks as measured by Intercontinental VLBI.
Observations of radio-wave phase scintillation are reported which used the Viking spacecraft having an earth-spacecraft link very similar to that which will be used in very low-frequency (VLF) gravitational-wave searches. The phase power-spectrum level varies by seven orders of magnitude as the sun-earth-spacecraft (elongation) angle changes from 1 to 175 deg. It is noteworthy that a broad minimum in the S-band (2.3 GHz) phase fluctuation occurs in the antisolar direction; the corresponding fractional frequency stability (square root Allan variance) is about 3 x 10 to the -14th for 1000-s integration times. A simultaneous two-frequency two-station observation indicates that the contribution to the phase fluctuation from the ionosphere is significant but dominated by the contribution from the interplanetary medium. Nondispersive tropospheric scintillation was not detected (upper limit to fractional frequency stability about 5 x 10 to the -14th). Evidently, even observations in the antisolar direction will require higher radio frequencies, phase scintillation calibration, and correlation techniques in the data processing, for detection of gravitational bursts at the anticipated strain amplitude levels of no more than 10 to the -15th.
A new generation of frequency standards, the VLG-11 hydrogen maser, has been designed and built at the Smithsonian Astrophysical Observatory (SAO). A comprehensive series of environmental and short-term stability tests on three VLG-11 masers has been completed and evaluated. The test results reported here show substantial improvements over previous hydrogen masers in measured sensitivity to variations in ambient temperature, barometric pressure, and magnetic fields. The maser frequency stability, as represented by the two-sample (Allan) variance, has been measured for averaging times ranging from 1 to 100,00 seconds. The variance is lower than 1 x 10 to the -15th for averaging intervals between 1400 and 20,000 seconds. For times shorter than 4000 seconds, the measured stability data agree remarkably well with theoretical values calculated from thermal noise mechanisms and the 'noise within the linewidth' regime is clearly discernable in the data.
A time domain estimate for the NAVSTAR-4 SV clock offset was obtained for each SV pass over the GPS monitor sites, using a smoothed reference ephemeris, with corrections for ionospheric delay, tropospheric delay, earth rotation and relativistic effects. Conversion from the time domain to the frequency domain was made using the two sample Allan Variance; sigma-tau plots used to identify the noise processes. Estimates of flicker and white frequency noise for the NAVSTAR-4 rubidium frequency standard were obtained. The contribution of the reference ground clocks and other error sources to the frequency stability estimates were also considered.
Four sets of experiments were conducted to measure the relative epoch offsets between atomic clocks in California, Australia, and Spain by means of very long baseline interferometry (VLBI). The experiments were conducted using an incomplete R & D VLBI system with a number of inherent limitations. The results indicate that the measurement objective of epoch offset to 10 nanoseconds will be met. Tables show the measured offset, the residual to fit, and the square root Allan variance. Graphs show the rate change and the rate reset.
An optical fiber communications link was installed for the purpose of evaluating the applicability of optical fiber technology to the distribution of frequency and timing reference signals. It incorporated a 1.5km length of optical fiber cable containing two multimode optical fibers. The two fibers were welded together at one end of the cable to attain a path length of 3km. Preliminary measurements made on this link, including Allan variance and power spectral density of phase noise are reported.
A time and frequency intercomparison experiment conducted using Earth stations in New Delhi, India and Raisting, FRG is described. The NPL clock was placed at New Delhi Earth Station and the Raisting Clock was calibrated with PTB/Primary standard via LORAN-C and travelling clocks. The random uncertainity of time comparisons, represented by two sample Allan Variance sigma (30 seconds), was less than 10 nanoseconds. The relative frequency difference between the NPL and Raisting Clocks, SNPL, RAIS, as measured over the 44 days period was found to be -15.7 x 10 to the -13th power. The relative frequency difference between PTB Primary Standard and Raisting Clock, SPTB, RAIS, during this period, was measured to be -22.8 x 10 to the -13th power. The relative frequency difference between NPL clock and PTB Primary Standard, SNPL, PTB, thus, is +7.1 x 10 to the -13th power. The clock rate (UTC, India) of +7.1 + or - 0.5 x 10 to the -13th power, agrees well with that obtained via VLF phase measurements over one year period and with USNO travelling clock time comparisons made in September, 1980.
Measurements were made of the stability of time transfer by the IRIG-B code over a dedicated telephone link on a microwave system. The short and long term Allan Variance was measured on both types of microwave system, one of which is synchronized, the other having free local oscillators. The results promise a time transfer accuracy of 10 microns. The paper also describes a prototype slave clock designed to detect interference in the IRIG-B code to ensure local time is kept during such interference.
The quality of the frequency standards used in very-long-baseline interferometry (VBLI) limits the coherent integration time and the accuracy of geodetic experiments except in special cases when clock instabilities can be made to cancel out by using differential interferometry. Formulas are derived for estimating the coherence of these interferometers from the Allan variances of the frequency standards. Experiments using extremely high-quality frequency standards, such as hydrogen masers, may be limited by the phase noise that results from atmospheric and ionospheric fluctuations.
The masers were tested for environmental sensitivities (magnetic field, temperature, barometric pressure) and long-term aging. Allan variance runs of 72 days were made in order to attain averaging times from several seconds to 1 million seconds. Auto- and cross-correlation techniques were used to determine the effects of uncontrolled parameters such as humidity. Three-cornered-hat and other data reduction techniques were used to determine the characteristics of the individual masers.
The article presents observations of turbulence-induced tropospheric phase fluctuations measured at 5 GHz on the near-vertical paths relevant to many astronomical and geophysical measurements. The data are summarized as phase power spectra, structure functions, and Allan variances. Comparisons to other microwave observations indicate relatively good agreement in both the level and shape of the power spectrum of these tropospheric phase fluctuations. Implications for precision Doppler tracking of spacecraft and geodesy/radio interferometry are discussed.
The Deep Space Network must maintain time and frequency within specified limits in order to accurately track the spacecraft engaged in deep space exploration. The DSN has three tracking complexes, located approximately equidistantly around the Earth. Various methods are used to coordinate the clocks among the three complexes. These methods include Loran-C, TV Line 10, very long baseline interferometry (VLBI), and the Global Positioning System (GPS). The GPS is becoming increasingly important because of the accuracy, precision, and rapid availability of the data; GPS receivers have been installed at each of the DSN complexes and are used to obtain daily time offsets between the master clock at each site and UTC(USNO/NBS). Calculations are made to obtain frequency offsets and Allan variances. These data are analyzed and used to monitor the performance of the hydrogen masers that provide the reference frequencies for the DSN frequency and timing system (DFT). A brief history of the GPS timing receivers in the DSN, a description of the data and information flow, data on the performance of the DSN master clocks and GPS measurement system, and a description of hydrogen maser frequency steering using these data are presented.
An on-orbit frequency stability performance analysis of the GPS NAVSTAR-1 quartz clock and the NAVSTARs-6 and -8 rubidium clocks is presented. The clock offsets were obtained from measurements taken at the GPS monitor stations which use high performance cesium standards as a reference. Clock performance is characterized through the use of the Allan variance, which is evaluated for sample times of 15 minutes to two hours, and from one day to 10 days. The quartz and rubidium clocks' offsets were corrected for aging rate before computing the frequency stability. The effect of small errors in aging rate is presented for the NAVSTAR-8 rubidium clock's stability analysis. The analysis includes presentation of time and frequency residuals with respect to linear and quadratic models, which aid in obtaining aging rate values and identifying systematic and random effects. The frequency stability values were further processed with a time domain noise process analysis, which is used to classify random noise process and modulation type.