[time-nuts] Modified Total Deviation measurement

[Dick Moore]

Hi Magnus -- Any possibility that there is some math package subroutine error of some kind? In yours or theirs?

Best,
Dick Moore

> 
> Message: 3
> Date: Mon, 18 Jan 2010 03:29:49 +0100
> From: Magnus Danielson <magnus at rubidium.dyndns.org>
> Subject: [time-nuts] Modified Total Deviation calculation
> To: Discussion of precise time and frequency measurement
> 	<time-nuts at febo.com>
> Message-ID: <4B53C79D.5000403 at rubidium.dyndns.org>
> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
> 
> Dear fellow time-nuts,
> 
> In my effort to implement the suite of ADEV and friends, I have been 
> implementing various forms of them along with the 1000 frequency sample 
> test sequence out of NIST SP1065:
> http://tf.nist.gov/timefreq/general/pdf/2220.pdf
> 
> However, I seem to be unable to perfectly match the numbers for the MTotDev.
> 
> My numbers so far:
> 
>         m = 1        m = 10       m = 100
> Max     0.9957452943 0.7003371204 0.5489367785
> Min     0.0013717599 0.2545924150 0.4533354120
> Avg     0.4897744629 0.4897744629 0.4897744629
> Sdev    0.2884663647 0.0929635201 0.0320665644
> NAdev   0.2922318781 0.0996573606 0.0389780433
> OSAdev  0.2922318781 0.0915995342 0.0324134303
> OAdev   0.2922318781 0.0915995342 0.0324134303
> MAdev   0.2922318781 0.0617237638 0.0217092091
> Tdev    0.1687201535 0.3563623166 1.2533817739
> Hdev    0.2943883291 0.1052754194 0.0391086056
> OHdev   0.2943883291 0.0958108317 0.0323763825
> MHdev   0.2942275231 0.0621023549 0.0213087110
> TOTdev  0.2922318781 0.0913474326 0.0340653025
> MTOTdev 0.2303857898 0.0555288598 0.0195467513
> 
> The MTOTdev numbers according to page 118 (of PDF, page number 108 
> according to the printed pagenumbers) should be
> 
> Modified Total Dev 2.418528e-01 6.499161e-02 2.287774e-02
> 
> Do anyone happend to have an implementation (in source) of MTOTdev at 
> hand giving the NIST SP1065 numbers?
> 
> Please note that W. Riley has about the same document in his Handbook, 
> and it reflects the same number. I would also suspect that a STABLE32 
> run would give those numbers.
> 
> I have been using both SP1065 and the original article as reference:
> http://tf.nist.gov/general/pdf/1369.pdf
> 
> I've put care into ensuring that I implement it as close to these as 
> possible, but with no luck in fixing the numbers.
> 
> I use the averaging of the two half-ranges of the 3*m block tecnique 
> rather than the minimum square estimator as recommended. The formulation 
> given may seem strange, but it is the 3/2*m sample average of the
> 
> f(i)=(x[n+3/2*m+i)-x[n+i])/ (3/2*m)
> 
> frequency estimation where i varies from 0 to 3/2*m-1.
> 
> I have already verified my test-sequence and the numbers produced by the 
> other algorithms have been able to match after removing various bugs. An 
> independent implementation may be a good clue.
> 
> An alternative may be that the published numbers is incorrect for some 
> reason, but I don't have sufficient proof for that.
> 
> I have however made two different implementation variants that crunch 
> out the same numbers.
> 
> Cheers,
> Magnus