[time-nuts] Paper by Allan on weighted average of clocks

Tom Van Baak tvb at leapsecond.com
Fri Mar 11 12:26:44 EST 2005

```Bill,

David Allan's publication list is at:
http://www.allanstime.com/Publications/DWA/

Also, you'll get 100+ hits if you search for Allan as
author at the NIST library:
http://www.boulder.nist.gov/timefreq/general/publications.htm

The basic ensemble concept is to take N clocks,
measure the pair-wise phase among all of them,
and then compute a paper clock that is the average
of them all. If you do it right, the paper clock will
have greater stability than any individual constituent
clock. Most gov't timing labs implement such a
scheme. UTC itself is an example of an ensemble.

If the clocks are not all equal you can get clever
and assign different weights to reward the clocks
that seem to do well compared to the group mean
and punish clocks that seem to deviate from the
mean more than others. One implementation is to
base the weighting of each clock on its ADEV (as
computed against the mean paper clock).

There are a host of details, of course, and papers
about steering, time scales, and clock ensembles
have probably been written every year for decades.

A nice one is Allan's "In Search of the Best Clock"
http://www.boulder.nist.gov/timefreq/general/pdf/815.pdf

See also the Allan paper "The National Bureau of
Standards Atomic Time Scale: Generation, Stability,
Accuracy and Accessibility" which was printed as
part of NBS Monograph 140 (you can find these on
eBay now and then), or online at:
http://www.boulder.nist.gov/timefreq/general/pdf/194.pdf

/tvb

----- Original Message -----
From: "Bill Janssen" <billj at ieee.org>
To: "Discussion of precise time and frequency measurement"
<time-nuts at febo.com>
Sent: Friday, March 11, 2005 08:06
Subject: [time-nuts] Paper by Allan on weighted average of clocks

> Doctor Allan when at NIST did a paper on using a weighted average of an
> ensemble of clocks to get a more accurate and stable clock.
>
> Does anyone have a copy of that paper? I was in a meeting with Dr. Allan
> and he mentioned
> a paper but I don't remember where (or if) it was published.
>
> I think it would be of interest to the group.
>
> Bill K7NOM

```