# [time-nuts] Best GPS 1PPS Accuracy

bg at lysator.liu.se bg at lysator.liu.se
Thu Dec 14 07:29:43 EST 2006

```Ulrich,

+-3 sigma is 99% on a gaussian distribution.

If you want to look at other algorithms on this topic, here is one:

br,

Björn

On Thu, December 14, 2006 12:55, Ulrich Bangert said:
> Hello Said,
>
> from my own experience in detecting and removal of outliers i can asure
> you that it is a challenging and ambitious task in statistical math. I
> fear you expect too much from a receiver's TRAIM firmware to compute the
> necessary statistic math on a pulse to pulse base. Nevertheless you can
> do it on your own if the microcontroller that compares the LO to the
> GPS's 1pps has enough RAM and processing power.
>
> It involves computing the MEDIAN over a number measurements (say 60) to
> get a reliable estimate of the measurement's MEAN value in that time.
> Note that the normal MEAN computation is susceptible to outliers while
> the MEDIAN is not. On the other hand computing the MEDIAN involves
> sorting the measurements in ascending order, much more stuff than simple
> MEAN adding/dividing. Once you have the MEDIAN of your measurements you
> can compute the distances between the single measurements and the
> median. But in contrast to the simple STANDARD DEVIATION which is
> susceptible to outliers itself, you now compute the MEDIAN over the
> distances between the measurements and their MEDIAN to give you
> something that is called the MAD (MEDIAN ABSOLUTE DEVIATION. As the
> STANDARD DEVIATION the MAD is a measure of the witdh of the
> measurement's distribution in the sense of a 'sigma' but not susceptible
> to outliers. Once you have that number you can easily decide whether the
> last measurement is within or without a range of say +/- 5 * sigma. I
> guess +/- 5 * sigma resembles 99% of normal distributed values, so you
> are on the safe side to throw away anything outside +/- 5 * sigma. Note
> that you have to perform the above steps for every new measurement, i.e.
> every second removing the oldest in your data buffer and adding the
> latest measurement to you data buffer. It can be done and i do so in my
> DIY GPSDO but actually it needs exactly this complexity.
>
> Best regards
> Ulrich Bangert, DF6JB
>
>> -----Ursprüngliche Nachricht-----
>> Von: time-nuts-bounces at febo.com
>> [mailto:time-nuts-bounces at febo.com] Im Auftrag von SAIDJACK at aol.com
>> Gesendet: Donnerstag, 14. Dezember 2006 01:56
>> An: time-nuts at febo.com
>> Betreff: Re: [time-nuts] Best GPS 1PPS Accuracy
>>
>>
>> Hi guys,
>>
>> slightly off-topic, but has anyone done stability tests with
>> the m12+ or
>> M12M when the antenna goes bad in TRAIM-enabled mode (e.g.
>> less than 4 good sats
>> being received by i.e. disconnecting the antenna)?
>>
>> I see that the 1PPS output goes away only after about 5 or so
>> pulses have been generated, so these 5 pulses are  "free-running".
>>
>> These pulses are somewhat inaccurate, and I am wondering if
>> anyone has done
>> a max/min analysis on the errand pulse's offsets?
>>
>> I wonder if the TRAIM limits can be set to say +-50ns
>> effectively to kill
>> these pulses and improve overall accuracy?
>>
>> I know lot's of folks run the M12 TRAIM limits at 1us, that
>> seems excessive
>> on a receiver that is supposed to do 10ns 1-Sigma, doesen't it? ...
>>
>> Said
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>
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