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

Mon Jan 28 21:27:30 CST 2008

This is a philosophical observation.

One thing I've seen with lately statistical models is
a dichotomy between filtering and classification.

A filter tries to come up with a best estimate of the
true state based on measurement. It may work in the
frequency or time domain, be linear or non-linear.
It's trying to reject noise and find the hidden
signal.

A classifier tries to sort states into discrete
categories. One way this is used is to switch between
several models which hopefully reflect reality. A
system may really behave completely differently
depending on what mode it is in.

These methods can intersect with sampling based
approaches (e.g particle filter) which can support
multi-modal probability distributions. Multiple
hypotheses can be considered without hard
classification. In general though - sampling based
approaches to represent distributions are
computationally expensive. That's why single modal
methods like the KF are popular. The KF is very
efficient.

Computer science people seem to really like
classifiers because they are conceptually more suited
to discrete, algorithmic thinking. I'm not an EE but I
would guess that EEs prefer filters because they are
continuous. I'm kind of new to all of this and am
trying to be agnostic. Both ways are necessary in a
real system.

So why am I saying all of this?

At some point, you may work on your filter and find
that despite best efforts, it sometimes doesn't work
very well in the full system. Then you will see some
variable and think, hmm, these tuning factors can be
adjusted depending on whether some variable is higher
or lower than a threshold. Now you are down the road
to classification. Sophisticated approaches will use
machine learning to compute optimal thresholds to
classify different modes.

>From what I have seen, going down this path can be a
rabbit hole with no end. You may have to jump down the
hole. But I wouldn't do it until concluding there is
no other way.

--- Dean Hall <dwhall256 at gmail.com> wrote:

> 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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> 
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