# [ntp:questions] ntp.br project - how to calculate the discrepancy?

Antonio M. Moreiras moreiras at nic.br
Mon Oct 8 21:07:52 UTC 2007

```David Woolley escreveu:

>> A discrepancy of 16ms in a Internet NTP primary server is acceptable?
>
> It would exceed modern expectations, even if not necessary for most
> applications.  People expect this sort of accuracy on end nodes.

I have understood that 16ms is unnaceptable and I will review the project.

But I need help to know, at first, if I calculated this 16ms correctly.

The rubidum clock manufacturer says that:
mensal ageing < 5e-11
anual ageing  < 5e-10

What would be the correct way to calculate the discrepancy in seconds
after a given elapsed time?

I calculated the error as 31,536,000,000 ms (1 year) * 5e-10  =
15.765ms, but I think this is not correct, because the 5e-10 is the
frequency error after 1 year. This calculation would be correct if the
5e-10 were a constant frequency error along all the year, what is not
the case.

Calculating in a mensal basis (but considering 5e-11 as a constant freq
error within the month, what is wrong too but with a smaller
overestimated error):

Month	Accum Ageing	Err(ms)	Tot Error(ms)
1	0,00000000005	0,130	0,130
2	0,00000000010	0,259	0,389
3	0,00000000015	0,389	0,778
4	0,00000000020	0,518	1,296
5	0,00000000025	0,648	1,944
6	0,00000000030	0,778	2,722
7	0,00000000035	0,907	3,629
8	0,00000000040	1,037	4,666
9	0,00000000045	1,166	5,832
10	0,00000000050	1,296	7,128
11	0,00000000055	1,426	8,554
12	0,00000000060	1,555	10,109

If this is correct, it means that whith 3 calibrations per year, it
would be possible to keep the discrepancy < 1ms. And if we calibrate the
system in a monthly basis, the discrepancy would be less than 150us.

We are studying, as suggested by some people, using GPS as time
reference, but one of primary requisites to our project is to have the
servers in sync with the official brazilian time, that is UTC(ONRJ).

Considering that we could completely trust the GPS system (can we? it is
a us military system...) there would be no practical differences, but
yet there would be some legal differences. So we are looking for
alternatives to synchronize to UTC(ONRJ) with an acceptable accuracy.

The studied alternatives include using cesium reference clocks, instead
of rubidium, or calibrate the rubidium ones within shorter periods of time.

>> what is the discrepancy of GPS time from UTC (without
>> considering the leap seconds)?
>
> 50 nano seconds at about the 50 percentile, is the official specification.
> The constellation needs to be in synch with each other to rather better
> than this for GPS to work at all, although it is not strictly necessary
> that they match UTC.  Even if they don't match UTC exactly, the offset
> will be available.
>
> I seem to remember that typical NTP servers can lock to this to
> microsecond accuracies, although typical network delays will degrade
> this to around 1 ms.

Thanks.

[]s
Antonio M. Moreiras

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