Optimal estimation of clock values and trends from finite data
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clock models↗
Engineering topics
Greenhall, Charles
Publications and source records attributed to Greenhall, Charles.
Optimal Estimation of Clock Values and Trends from Finite Data
We show how to solve two problems of optimal linear estimation from a finite set of phase data. Clock noise is modeled as a stochastic process with stationary dth increments. The covariance properties of such a process are contained in the generalized autocovariance function (GACV). We set up two principles for optimal estimation: with the help of the GACV, these principles lead to a set of linear equations for the regression coefficients and some auxiliary parameters. The mean square errors of the estimators are easily calculated. The method can be used to check the results of other methods and to find good suboptimal estimators based on a small subset of the available data.
stationary increments↗
Progress on a Multichannel, Dual-Mixer Stability Analyzer
Several documents describe aspects of the continuing development of a multichannel, dual-mixer system for simultaneous characterization of the instabilities of multiple precise, low-noise oscillators. One of the oscillators would be deemed to be a reference oscillator, its frequency would be offset by an amount (100 Hz) much greater than the desired data rate, and each of the other oscillators would be compared with the frequency-offset signal by operation of a combination of hardware and software. A high-rate time-tag counter would collect zero-crossing times of the approximately equal 100-Hz beat notes. The system would effect a combination of interpolation and averaging to process the time tags into low-rate phase residuals at the desired grid times. Circuitry that has been developed since the cited prior article includes an eight-channel timer board to replace an obsolete commercial time-tag counter, plus a custom offset generator, cleanup loop, distribution amplifier, zero-crossing detector, and frequency divider.
Kirk, Albert↗
Estimating the Modified Allan Variance
The third-difference approach to modified Allan variance (MVAR) leads to a tractable formula for a measure of MVAR estimator confidence, the equivalent degrees of freedom (edf), in the presence of power-law phase noise. The effect of estimation stride on edf is tabulated. A simple approximation for edf is given, and its errors are tabulated. A theorem allowing conservative estimates of edf in the presence of compound noise processes is given.
Allan Variance↗
Estimating the Modified Allan Variance
A paper at the 1992 FCS showed how to express the modified Allan variance (mvar) in terms of the third difference of the cumulative sum of time residuals. Although this reformulated definition was presented merely as a computational trick for simplifying the calculation of mvar estimates, it has since turned out to be a powerful theoretical tool for deriving the statistical quality of those estimates in terms of their equivalent degrees of freedom (edf), defined for an estimator V by edf V = 2(EV)2/(var V). Confidence intervals for mvar can then be constructed from levels of the appropriate 2 distribution.
Allan Variance↗