Article: 90139 of sci.geo.satellite-nav
Message-ID: <36B0E450.8C1434E3@illgen.com>
From: Jeff Valine <jvaline@illgen.com>
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Subject: Re: EPE / DOP: How are they calculated.
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I'm not sure about the Garmin EPE, but DOP (Dilution of Precision) can
be a purely geometrical calculation.  It depends only on how many
satellites are visible, and where they are in relation to you.  You can
calculate the various DOPs (GDOP, PDOP, HDOP, VDOP, TDOP) knowing only
the azimuth & elevation angles to each satellite currently visible.  The
DOPs are obtained from the trace of the covariance matrix:

First fill a n by 4 geometry matrix, where n is the number of sats:

for (i=0; i<num_sats; i++)
{
  G[i,0] = sin(az[i])*cos(el[i]);
  G[i,1] = cos(az[i])*cos(el[i]);
  G[i,2] = sin(el[i]);
  G[i,3] = 1.0;
}

Now compute the covariance matrix [matrix inverse & transpose code is
left to the reader ;-) ]:

COV = inverse(G*transpose(G));

Finally, get the DOPs:

gdop = sqrt(COV[0,0]+COV[1,1]+COV[2,2]+COV[3,3]);
pdop = sqrt(COV[0,0]+COV[1,1]+COV[2,2]);
hdop = sqrt(COV[0,0]+COV[1,1]);
vdop = sqrt(COV[2,2]);
tdop = sqrt(COV[3,3]);
 
The following link uses ECEF user & sat positions instead of az & el,
but it tells the same story:
http://www.utexas.edu/depts/grg/gcraft/notes/gps/gif/gdop.gif

Your low DOP is an indication of excellent geometry, and that makes
sense given you had 12 sats visible.
-- 

Jeff
jvaline@illgen.com

Mike Simmonds wrote:
> 
> I was sitting in a traffic queue last night, watching the satellites swing
> across the display (I was held up for 3 1/4 hours!) when I noticed that my
> Garmin GIII was showing an EPE (Estimated Positional Error) of 36 Feet, and
> a DOP of 0.8.
> 
> Was SA turned off for a while?
> 
> How are these figures calculated / do they make sense ?
> 
> Mike
> 
> P.S. most of the time, 12 SV's were visible to the GPS (Via an external
> ant.)