# [ntp:questions] Timing GPS recommendations

unruh unruh at invalid.ca
Tue Aug 21 19:21:01 UTC 2012

```On 2012-08-21, Chris Albertson <albertson.chris at gmail.com> wrote:
> On Tue, Aug 21, 2012 at 7:33 AM, Brian Utterback <brian.utterback at oracle.com
>> wrote:
>
>> You seemed to have missed the point that unruh was making. Sure you can
>> find the mean of the round trip time, but the accuracy you get setting the
>> clock can never be better than the jitter you get on those times. Say the
>> mean is 50 seconds, but the jitter is +/- 3 seconds. It doesn't help to buy
>> a clock that measures in tenths of a second instead of whole seconds, your
>> accuracy is still going to be +/- 3 seconds.
>>
>>
> I think it comes to +/-3 times the square root of the number of
> measurements.  Or something proportional to that.  You are correct for the
> case were you only do it once.

No. That is maybe true IF the error is gaussian. It is not.
>
> An example is you want to measure the location of a hole 500 feet above the
> ground where someone is droping bird feathers.  You could look straight up
> from where one fell but they flutter randomly as they fall.   But if you
> waut until 1,000 have fallen you can compute a centroid of the scatter.

And it will tell you nothing because the wind blew on one feather and
blew it 10 km away, and that one feather totally dominates the centroid
and the estimate of the standard deviation.

And if you live in the northern USA, the winds tend to be from the west,
meaning that the winds will tend to displace the feathers to the east
and no number of measurements will eliminate that bias.

>  You r estimate of the centriod gets better the more feathers you can
> measure.  Accuracy is pproportional to the square root of the number of
> feathers

Only in certain (often unphysical) conditions.

>
> With a clock once you get the RATE set.  Then we can measure the phase many
> times and find a "mean phase".   You are right in that there is a limit.
>  This is because you can't get the rate set perfect so the number of
> samples in your mean is limited.
>
> I think in the analog world Phase Locked Loops do about the same thing.  A
> PLL can sync two oscillators very well even even with a noisy channel
> between them it's used for "everything" mostly clock recovery in serial
> data.  It in effect figures out the phase by averaging over a great many
> cycles.  I think a PLL is proff that we CAN synchronize phase to much
> better than the jitter in the communicant path.
>
> Chris Albertson
> Redondo Beach, California

```