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

Mon Jan 28 17:32:52 CST 2008

Yes, I'm working on a KF.  Coding hasn't started yet (it took me long  
enough just to "get it"), but it's part of my grand scheme:
http://deanandara.com/Argonaut/Sensors/KalmanFilter/

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.

 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

Where "Horizontal" means tangent to the earth's surface; and  
"Vertical" means perpendicular to the surface.
Notice that PDOP is equal to a rounded sqrt(HDOP^2 + VDOP^2).

!!Dean

On Jan 28, 2008, at 16:35 , dpa wrote:

> Dean.
>
> Cool.  Good homework.
>
> You are working on a navigation Kalman Filter?  What are your sensors,
> besides GPS?
>
> I checked my notes but I don't see it right off.  Which NMEA sentence
> has the HDOP parameter?  I wonder if this is how the Garmin GPS
> calculates its "navigation accuracy" display units.  That's usually
> around 10 or 15 feet, though I've seen it as small as 5 feet when
> averaging over 30 minutes or longer.
>
> best regards,
> dpa
>
> ----------------------------------------------------------------------
>
> !!Dean wrote:
>
> Chris Jang, all,
>
> I suggested back in November that using the NumberOfSatellites from
> the NMEA stream of a GPS unit could provide an index into a lookup
> table to get the variance value to use in a Kalman Filter (http://
> list.dprg.org/archive/2007-November/031055.html).
>
> Well, today I stumbled across a better idea.  I was reading through
> this article (http://www.cs.unc.edu/~welch/kalman/Levy1997/ <http:// 
> www.cs.unc.edu/%7Ewelch/kalman/Levy1997/>
> Levy1997_KFWorkhorse.pdf) that suggested on page 8 that pseudoranges
> are preferred outputs to use in the KF.  So I looked again through
> the fields that my SiRFstarIII chip provides... nope, no
> psuedoranges.  However, serendipity befell me and I found the
> Dilution of Precision (DOP) field in the GSA sentence and read up on
> it at http://en.wikipedia.org/wiki/Dilution_of_precision_(GPS  
> <http://en.wikipedia.org/wiki/Dilution_of_precision_%28GPS>)
>
> And there it was, in little black text near the bottom:
>
> The DOP factors are functions of the diagonal elements of the
> covariance matrix of the parameters, expressed either in a global or
> a local geodetic frame.
>
> I followed the reference wikipedia gave, read the article (http://
> www.developerfusion.co.uk/show/4652/2/) and found these two gems:
>
> 	"As a general rule of thumb, an HDOP value of six or less is
> recommended for any application which makes suggestions to the user
> based on the current location."
>
> 	Accuracy of GPS Device * DOP = Maximum Allowable Error
>
> I plan to use the HDOP in my KF.  Also, note that the HDOP is usually
> much smaller (=better) than the VDOP and mean DOP.  Here are real-
> world measurements I made: with 10 sats in view, I got a HDOP of 1.8;
> with 12 sats (max for my GPS), HDOP = 0.9.  Although I cannot confirm
> it, it seems (from measuring and comparing to Google Earth) that *DOP
> values have a unit of meters.  So it looks like the HDOP value will
> provide a nice input to calculate my GPS module's measurement error
> variance.  The downside is that the GSA sentence containing the HDOP
> does not arrive as often as the RMC and VTG sentences in the default
> configuration.
>
> !!Dean
>
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