Time Scales Virtual Clocks and Algorithms

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Time ScalesVirtual Clocks and Algorithms

• Ricardo José de Carvalho
• National Observatory
• Time Service Division
• February 06, 2008

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Introduction

• Let us assume that we have an ensemble of atomic
  clocks that are running at the same time and we
  want to build an independent atomic time scale
  from an ensemble of clocks. That scale will be
  used as an internal reference for the generation
  of a local UTC(k) time scale.
• What are the possibilities and the difficulties
  we are facing?
• What are the ingredients necessary to build
  UTC(k) from ensemble of atomic clocks?

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Time Scale from one Clock

• Simple solution
• We can select one of the clocks and we can decide
  that our atomic time scale is identified with the
  output of this clock.
• This solution is valid if the clock exhibits
  qualities superior to the others.

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Time Scale System

• Better Solution
• We can build a time scale system that can enable
  a time laboratory to keep time with stability,
  accuracy, and reliability beyond the performance
  level of the best physical clock in the
  laboratory by combining all the clocks resulting
  in a Virtual Clock.

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Time Scale System
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Time Scale System

• In practice a time scale system can be divided
  into three parts
• The first part is a clock ensemble that will be
  used as a reference for the generation of a local
  UTC time scale
• The second, an automated data acquisition system
  that measures the time differences between the
  clocks
• The third is a time scale algorithm that computes
  the paper time scale.  
•  

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The Clock Ensemble

• Atomic clock are very stable and accurate but
  they may be sensitive to the environmental
  conditions, so they are to be maintained in the
  most stable environment to avoid injecting
  instabilities.

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Automated Data Acquisition

• Because the time of an individual clock can not
  be measured, one must measure time differences
  between clocks. Inside the laboratory the time
  differences are obtained with a high degree of
  accuracy using electronic counter.

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Time Scale Algorithm

• By samplig an ensemble of clocks, an ideal time
  scale algorithm would generate time and frequency
  with more reliability, stability and frequency
  accuracy than one of the individual clocks in the
  ensemble.
• In general a time scale algorithm takes the time
  difference measurements between clocks and
  combines them mathematically to produce an
  average time scale.

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Time Scale Formulation

• The Simplest Time Scale of all is just the
  reading of a single clock, that is
• The condition imposed on the time scale is

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Time Scale Formulation

• To Simple Mean of Two Clocks the time scale is
  defined by
• The condition imposed on the time scale is

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Time Scale Formulation

• The time scale defined by equation (3) will be
  affected by any anomalus behavior that one of the
  clocks present. For example, suppose that the
  clock 1 has jumped by an amount
• Then the time scale is affected by an amount

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Time Scale Formulation

• To Simple Mean of n Clocks, n gt 2 the time scale
  is defined by
• The condition imposed on the time scale is
• Anomalous behavior can thus be detected with
  confidence incresing as n increases.

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Time Scale Formulation

• To Weighted Mean of n Clocks the time scale is
  defined by
• The condition imposed on the time scale is
• Anomalous behavior can thus be detected with
  confidence increasing as n increases.

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Time Scale Formulation

• The time scales considered previously possess a
  disadvantage that, if one the clocks stops or a
  new clock is introduced, a step and a rate change
  will generally occur in the time scale.
• To solve this problem the definition of the time
  scale should be modified, in such a way that, the
  considered average is on the time offset of clock
  with the time scale as reference.

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Time Scale System
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Brazilian Atomic Time Scale

• In the choice of the algorithm to calculated
  TA(ONRJ) we have consider that the optimum
  algorithm with a small group of clocks is not
  obvious and very difficult to find.
• The algorithm that generates TA(ONRJ) follows the
  same steps of the main ensemble algorithm used
  successfully in the NIST and is outlined here
  shortly.

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Brazilian Atomic Time Scale

• A first prediction of the time offset for each
  clock against the ensemble is given by
• The best estimate of the time offset of each
  clock at time given the measurements is

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• Once the are known the average frequency of each
  clock over the last interval can be estimate by
• An exponentially filtered estimate of the current
  average frequency of clock i that will be used in
  the next prediction interval is given by

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• where mi is an exponential time constant
  determined from the relative levels of white
  noise and random walk FM, that is
• The clock weights wi are calculated from

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• The prediction error estimate is given by
• because ensemble time is a weighted average
  of each clock times, the prediction error
  estimate (7) is biased, because each clock is a
  member of the ensemble, so it is necessary to
  correct this biasing by
•  

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• Since the noise characteristics of a cesium clock
  may not be stationary, the current prediction
  error of each clock is exponentially filter where
  the past prediction error are deweighted in the
  process, that is
• the time constant for the filter is typically
  chosen to be 20 days and the initial value of is
  estimated as

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Brazilian National Time Scale System.
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CONCLUSIONS

• We showed that it is possible to generate an
  atomic time scale with a small group of clocks.
• The next step will consist in making the system
  almost fully automated, by implementing the
  automatic detection of clock anomalies and to
  allow for the maintenance, to add or remove clock
  from the system in easily fashion.
• The new UTC(ONRJ) is now inside of the limits
  recommended by the CCIR and by the CCDS. 100ns
  of UTC.