[time-nuts] Best GPS 1PPS Accuracy

[Ulrich Bangert]

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 
>  additional 
> 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? ...
>  
> Thanks for your feedback,
> Said
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