DPRG mailing list archives: [DPRG] Using GPS HDOP for KF purposes

Tue Jan 29 22:51:42 CST 2008

One thing to keep in mind is that there are really
three different covariance matrices with a Kalman
filter.

1. error in the process model (prior)
2. error in the measurement model
3. error in the current best estimate (posterior)

The one people really want to know is number 3. That
characterizes what the probability distribution looks
like around the mean (current best estimate).

I just googled for "HDOP gps" and this page:

http://www.edu-observatory.org/gps/gps_accuracy.html

says:

"HDOP (Horizontal Geometric Dilution of Precision),
GDOP, PDOP and VDOP are determined by the geometry of
the current satellites visible above the receiver's
mask angle with respect to user receiver's antenna.
DOPs can be degraded (made larger) by signal
obstruction due to terrain, foliage, building, vehicle
structure, etc."

I read that as implying the DOP may be a dimensionless
aggregate characterization of error in the measurement
model. It may not reflect the posterior error (for the
latest position estimate).

--- Kenneth Maxon <kmaxon at qwest.net> wrote:

> 
> 
> Yes, so here would be the magic bullet that would
> ensure that data set
> continued enough information to pull out with a very
> simple filter.
> 
> Imagine that along with plotting every point during
> a capture if one drew
> the error circle as indicated by a value such as
> HDOP around that point.
> Over a X-minute range, then all of the error circles
> should overlap at at
> least one point which happens to be the true
> position.   Of course it
> doesn't.
> 
> My observation and comment back to Dean then about
> the perceived lack of
> correlation was that not only is the above
> preposterous, that when one
> actually runs those plots and looks at them
> graphically over any significant
> sampling the size of the HDOP error circles further
> away from the actual
> position are not larger and those closer are not
> smaller in any manner of
> consistent fashion.   Additionally, at some of the
> extremes when the
> reported position wanders quite far away and then
> later repeats the quite
> far wandering the reported HDOP does not repeat
> either...
> 
> -Just data for consideration.   It was quite a
> disheartening observation,
> sigh...
> 
> -Kenneth
> 
> -----Original Message-----
> From: dprglist-bounces at dprg.org
> [mailto:dprglist-bounces at dprg.org]On
> Behalf Of Kipton Moravec
> Sent: Tuesday, January 29, 2008 5:08 PM
> To: dpa
> Cc: dprglist
> Subject: Re: [DPRG] Using GPS HDOP for KF purposes
> 
> 
> Since I am working on a GPS system, I'm very
> interested in this also. I
> am wondering if the jump with the HDOP corresponded
> with a satellite
> being added or being lost.
> 
> Did you collect satellite numbers also? They usually
> are reported less
> often, like every 5 seconds. (When I get position
> every second.)
> 
> Kip
> 
> On Tue, 2008-01-29 at 16:00 -0600, dpa wrote:
> > Howdy,
> >
> > !!Dean wrote:
> >
> >
> > > > Yes, I'm working on a KF.  Coding hasn't
> started yet (it took melong
> > > > enough just to "get it"), but it's part of my
> grand scheme:
> > > >
> http://deanandara.com/Argonaut/Sensors/KalmanFilter/
> > >
> >
> > Great!
> >
> > I have not "got it" but I'd like to.  Perhaps if
> you can make the
> > DPRG spring event you might be prevailed upon to
> give a presentation?
> >
> >
> > > > I will be estimating 4 state variables using 3
> or 4 low-dimensional
> > > > filters: heading, velocity, positionX and
> positionY.  The inputs for
> > > > heading are: GPS heading, magnetic compass and
> turn-servo*velocity.
> > > > The inputs for velocity are: GPS velocity,
> motor encoder and PID set-
> > > > value.  The inputs for positionX,Y are: the
> GPS position and the
> > > > calculated new position using velocity and
> heading.
> > >
> >
> > That looks like it might be generally applicable
> to other robots as
> > well, thanks for the web page.
> >
> > > >
> > > > From SiRF NMEA Manual, Rev 1.3, the GPGSA
> sentence contains, PDOP,
> > > > HDOP and VDOP as the last 3 fields of the
> sentence before the
> > > > checksum.  Not all GPS chipsets are going to
> give a GPGSA sentence.
> > > > Example from the manual:
> > > >
> > > > $GPGSA,A,3,07,02,26,27,09,04,15, , , , ,
> ,1.8,1.0,1.5*33
> > > >
> > > > PDOP = 1.8    // Position Dilution of
> Precision
> > > > HDOP = 1.0    // Horizontal Dilution of
> Precision
> > > > VDOP = 1.5    // Vertical Dilution of
> Precision
> > >
> >
> > Ok, found it.  That record is indeed one of the
> NMEA sentences included
> > in the Garmin paragraph.  The HDOP parameters for
> the 40 minutes of
> > data collected yesterday were extracted and
> plotted here:
> >
> >
>
<http://geology.heroy.smu.edu/~dpa-www/gps/gps_garmin_28jan08_hdop.png>
> >
> > Here's the plot of the locations again:
> >
> >
>
<http://geology.heroy.smu.edu/~dpa-www/gps/gps_garmin_28jan08_dec_3b.png>
> >
> > I can't see any particular correlation between the
> HDOP over time and the
> > location errors.  The HDOP range is pretty small. 
> I believe there were
> > 10 or 12 satellites locked in over the whole 40
> minutes, so maybe this
> > is not a good test of the correlation.
> >
> > I went ahead and put the Garmin GPS data itself
> from yesterday afternoon
> > on the webserver for Kenneth or anyone else who
> might like to play with
> it.
> > The Garmin connects at 4800 baud and sends a
> paragraph of NMEA sentences
> > every two seconds.  So for 40 minutes that's 1200
> total records:
> >
> >
>
<http://geology.heroy.smu.edu/~dpa-www/gps/gps_garmin_28jan08.dat>
> >
> > Notice if you look at the locations in time order
> they are highly
> > correlated, as John observes.
> >
> > dpa
> >
> >
> >
> >
> >
> > _______________________________________________
> > DPRGlist mailing list
> > DPRGlist at dprg.org
> > http://list.dprg.org/mailman/listinfo/dprglist
> >
> --
> Kipton Moravec KE5NGX
> "Always do right; this will gratify some people and
> astonish the rest."
> --Mark Twain
> 
> 
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> 
> 
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