[time-nuts] GPS orthodontics: sawteeth & hanging bridges - theeffect of time averaging

Dr Bruce Griffiths bruce.griffiths at xtra.co.nz
Fri Dec 22 22:13:06 UTC 2006


Brooke Clarke wrote:
> Hi Ulrich:
>
> Your M12+T plot ends at a little over a day (100k seconds) and the 
> stability is on the order of 4E-13.
> But Cesium and other oscillators can be better than this.  So how do you 
> check them, use longer averaging time?
>
> Have Fun,
>
> Brooke Clarke
>
> w/Java http://www.PRC68.com
> w/o Java http://www.pacificsites.com/~brooke/PRC68COM.shtml
> http://www.precisionclock.com
>
>
>
> Ulrich Bangert wrote:
>
>   
>> Brooks,
>>
>>  
>>
>>     
>>> Excel computed that the unaveraged correction data had a 
>>> standard deviation 
>>> of 8.4 nsec, which is consistent with the actual measured 9.5 
>>> nsec rms 
>>> jitter reported by Rich Hambly (Dec 06, PTTI paper by Clark 
>>> and Hambly, p. 
>>> 15).
>>>    
>>>
>>>       
>> Even if this scientifical improvement has not found its way into Excel:
>> A certain Mr. Allan has shown that the standard deviaton is NOT the
>> appropiate measure for noise processes in oscillators. Therefore he had
>> to find a new statitistics on its own. If you don't own a software to
>> calculate ADEV and other relevant statistical measures with you may
>> download one for free from my homepage:
>>
>> http://www.ulrich-bangert.de/plotter.zip
>>
>>  
>>
>>     
>>> But the question remains "what time averaging is needed to reduce the 
>>> sawtooth/bridge jitter from a typical +/-15 nsec to something 
>>> negligible, 
>>> perhaps +/-1 nsec?
>>>    
>>>
>>>       
>> Have a look to
>>
>> http://www.ulrich-bangert.de/html/photo_gallery_44.html
>>
>> If you can read it it will immediatly give you the answer to your
>> questions: in order to get to a certain precision draw a horizontal line
>> at this precisision on the vertical axis and at the two crossing points
>> read the necessary time for SAW corrected and uncorrected data on the
>> horizontal axis.
>>
>> Nevertheless, pardon to contradict you: One simply has NO choice to
>> average this long or to average that long. You have to set the
>> regulation loop time constant up to exactly where the OCXO's
>> tau-sigma-diagram meets the receiver's tau-sigma. Every loop time
>> constant different from that is a faulty design and nothing else. The
>> regulation loop dynamics may be improved a bit by pre-averaging the
>> phase data before they are fed into the loop but not by computing the
>> arithmetic mean over a time but by a gliding exponential average as is
>> explained in detail in the PRS-10's handbook. Due to stability reasons
>> even this time constant of this pre-filter is more or less fixed to abt.
>> 1/3 the main loop's time constant. 
>>
>> Regards
>> Ulrich Bangert,DF6JB  
>>
>>
>>  
>>
>>     
>>> -----Ursprüngliche Nachricht-----
>>> Von: time-nuts-bounces at febo.com 
>>> [mailto:time-nuts-bounces at febo.com] Im Auftrag von Brooks Shera
>>> Gesendet: Donnerstag, 21. Dezember 2006 18:50
>>> An: Discussion of precise time and frequency measurement
>>> Betreff: [time-nuts] GPS orthodontics: sawteeth & hanging 
>>> bridges - theeffect of time averaging
>>>
>>>
>>> Recently there has been some mention of the influence of 1pps 
>>> sawtooth and 
>>> hanging bridges jitter on the performance of a GPSDO.
>>>
>>> It would seem to me that the jitter must average to zero in 
>>> the long run, 
>>> for if it did not the 1pps signal would drift away from its 
>>> relation to UTC.
>>>
>>> But the question remains "what time averaging is needed to reduce the 
>>> sawtooth/bridge jitter from a typical +/-15 nsec to something 
>>> negligible, 
>>> perhaps +/-1 nsec?"
>>>
>>> To explore this I used TAC32 to record the 1 pps sawtooth 
>>> correction message 
>>>       
>> >from a Motorola M12+ receiver for about 1 hour, during which 
>>     
>>> time many 
>>> bridges occurred (1).  Excel's statistical toolbox was then 
>>> used to examine 
>>> the data.
>>>
>>> Excel computed that the unaveraged correction data had a 
>>> standard deviation 
>>> of 8.4 nsec, which is consistent with the actual measured 9.5 
>>> nsec rms 
>>> jitter reported by Rich Hambly (Dec 06, PTTI paper by Clark 
>>> and Hambly, p. 
>>> 15).
>>>
>>> Averaging the sawtooth/bridge correction data for several 
>>> averaging times 
>>> produced the following results (2):
>>>
>>> Avg Time    Standard Deviation     Residual Jitter
>>> none           8.4 nsec                     +/- 15 nsec
>>> 30 sec        1.53                            +/- 4.3
>>> 100 sec      0.79                            +/- 2.2
>>> 300 sec      0.33                            +/- 0.7
>>>
>>> It is evident that jitter is greatly reduced with a bit of 
>>> time-averaging. 
>>> In addition, the hanging bridges quickly disappeared into the 
>>> residual 
>>> jitter of the smoothed data.
>>>
>>> It appears to me that a typical GPSDO, which has an 
>>> integration time in the 
>>> range of 100's to many 1000's of sec is not likely to be 
>>> impaired by the 
>>> sawtooth/bridge noise of a GPS rcvr.  A GPS-based clock is a 
>>> different story 
>>> since a precise 1pps timing signal without time averaging would be 
>>> desirable.
>>>
>>> In summary, it appears that 1pps sawtooth/bridge noise can be 
>>> ignored for a 
>>> GPSDO.  In some designs it may even be helpful by introducing further 
>>> deterministic randomness to the phase measurement process.
>>>
>>> Regards,  Brooks
>>>
>>> (1) the M12+ correction-message resolution is 1 nsec and this 
>>> seems adequate 
>>> for a jitter statistics investigation.  But as a check, I 
>>> compared the 
>>> correction message data with the actual 1 pps jitter measured 
>>> with a 5370B 
>>> TIC, a PRS10 and a M12+ .  This approach has higher 
>>> resolution but does not 
>>> change the conclusions.
>>>
>>> (2)  I choose 30 sec as the shortest averaging time because 
>>> 30 sec is the 
>>> summation time of the phase-measuring circuit of my GPSDO 
>>> design and hence 
>>> the shortest integration time available.  Of course, the PLL filter 
>>> configuration switches can extend the integration to many 
>>> hours if desired.
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>> _______________________________________________
>>> time-nuts mailing list
>>> time-nuts at febo.com 
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>>>
>>>    
>>>
>>>       
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>   
Brooke

The GPS system has a frequency noise floor with an Allan deviation of 
about 5E-14 for averaging periods of a day or more.
If you need more accuracy than this one has to use techniques like 
Common view, All in view and related time transfer techniques to compare 
one's frequency standards with more accurate standards located elsewhere.

Bruce




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