Roughtly converting DOP to metric error

Hi,

My cave survey freeware connects to a GPS for surface tracking. When I
connect to a Bluetooth GPS, the GGA and GSA NMEA sentences provide
various flavors of DOP values (PDOP, HDOP, VDOP). How can I provide
users with a rough error value in meters (as most GPS units do) from
these unitless numbers?


Luc Le Blanc
http://www.speleo.qc.ca/Auriga

 

DOP is a multiplicative factor, and is used to increase metric errors
calculated by other means; so to evaluate it's effect you would need to know
the reported metric error and whether or not the DOP was already applied to
it. This is a pretty simplistic answer; I'm sure others will weigh in with
more detailed answers

John

 

http://users.erols.com/dlwilson/gpshdop.htm


John

 

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

Estimated Position Error (EPE) and Error Sources
EPE (1-sigma) = HDOP * UERE (1-sigma) (1)

Multiplying the HDOP * UERE * 2 gives EPE (2drms) and is commonly taken as the 95% limit
for the magnitude of the horizontal error. The probability of horizontal error is within
an ellipse of radius 2drms ranges between 0.95 and 0.98 depending on the ratio of the
ellipse semi-axes. User Equivalent Range Error (UERE) is computed in the tables lower on
this page.

EPE (2drms) = 2 * HDOP * SQRT [URE^2 + UEE^2] (2)

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.

URE (User Range Error) is an estimate of "Signals in Space" errors, i.e., ephemeris data,
satellite clocks, ionospheric delay and tropospheric delay. These errors can be greatly
reduced by differential and multiple frequency techniques. Differential correction sources
include user provided reference stations, community base stations, governmental beacon
transmissions, FM sub-carrier transmissions and geosynchronous satellite transmissions.

UEE (User Equipment Errors) includes receiver noise, multipath, antenna orientation,
EMI/RFI. Receiver and antenna design can greatly reduce UEE error sources--usually at
substantial cost.

Position error can range from tens of meters (recreational) to a few millimeters (survey)
depending on equipment, signals and usage. Professional mapping and survey equipment often
includes user-settable minimum thresholds for SNR, mask angle, DOP, number of SVs used, etc.

 

I found such info pages googling for a simple answer, but I can't help
but think that when I turn on my GPS 76, I don't have to input various
parameters to get a position error in meters. Can't I do the same
thing from the NMEA data I get from the GPS, or is the GPS basing its
precision estimation on data the DOP value doesn't convey?


Luc Le Blanc

 

I've never known what algorithm Garmin uses to estimate error.
If the receiver knew its true error... it could correct for the
same.

 

Isn't this reported error a maximum uncertainty around the displayed
position?


Luc Le Blanc

 

Error is usually reported as 1-sigma or 2DRMS oe similar.... it not
in the form of worst case.

 

I seriously doubt that anyone has actually tested one under a variety of
conditions (partially obscured sky, multi-path, wet forest canopy, etc.)
at accurately known locations for extended periods, so I don't think
anyone knows how good the Garmin accuracy estimate is. If you run the
DOP through a random weighting function or one based on astrological
charts to create a nice looking number, I'll bet no one will ever be
able to prove your result isn't as good as Garmin's. And it might just be.

Roy Lewallen

 

Well I now have about 1000 trails up/down the road outside my house
(standard 2 way blacktop, so what, 25-30ft wide?) and while the
=precision= may have something to do with Garmin's number (yes, I AM
more likely to show in the fields instead when the satellite config is
lousy), and while it can show the difference between the two sides of
the road under most circumstances (on the same day), the actual
positional =accuracy= is much worse than the number the GPS (a 60CSX
with external antenna) displays.

So the number Garmin gives may be the +/- sigma or even two sigma, but
it sure as heck isn't 'worse case' (whatever that means). On some
occasions I've been shown as 100m away from where I know damn well I am,
with an indicated error on the handset of 3m. Typically that'll correct
within a few minutes, but sometimes it'll take 15 or 30.

Multipath? Screwed up satellite signal? Bad firmware in the handset??
Not really possible to say, and those are all errors that you can't
figure out from looking at DOP math.

One thing I can deduce is that Garmin scales the 'error' in an averaged
point based on the (sqrt of, I imagine) number of fixes averaged (1 per
second, except when the 60CSX goes into cloud cuckoo land every now and
then). And it'll do that - show increasing precision/accuracy over time,
even when the actual position values it is averaging are getting further
apart (try it while walking along, for instance).

I wish they'd do some stats on the individual results instead. And for
EPE I wish they'd look around all the possible satellites available and
do some stats on the resulting cloud of PVT solutions.

 

In probability distributions like this, that is not possible to state--one
can only state errors in terms of probabilities - like xx percent of the
time within xx meters or some statstic that essentially does that.

 

I've petty-much given up on trying to make sense of variability when
it comes to recreational GPS receivers. The underlying variability is
itself varying all the time, so I'm not even sure if it's reasonable
to assume that the data is normally distributed.

The value of 'accuracy' reported by my eTrex is (I suppose) some sort
of crude indicator of potential precision, but how precision relates
to accuracy is another great mystery to me.

Now, if I want to estimate a position I record fifteen waypoints at
the frequency of one per minute and average them. In places where I
know the true position this seems to produce results good to three or
four metres. Of course, I have no way of knowing what the accuracy is
at places where I don't know the true position.

All good fun.

Regards, N.

 

You can't
DOP is not an indicator of "error" or "accuracy".
Bad DOP does not always mean bad accuracy for example.
Moreover the "accuracy" should not consider only DOP:
Imagine to be indoor (very low signal, a lot of multipath ecc) but
with a good DOP: you may have a very bad accuracy even with a good
DOP... So your indication DOP-based will be wrong.
Unfortunately, if you have only NMEA sentences, you usually don't have
enough data to estimate the accuracy (that can be done internally to
the receiver as it have much more informations inside)

 

Garmin units usually send a proprietary PGRME sentence that reports
horizontal, vertical and overall position error. Other than that, it's
my impression too that the receiver doesn't tell it all.


Luc Le Blanc

 

Forgive me, but I don't think GPS receivers can report errors in
position, to do this they would need to know their true position.

Regards, N.

 

There is a rough indication of signal error sent down from each GPS
satellite - the URA or user range error. It is defined in IS-GPS-200D
available at http://www.navcen.uscg.gov/gps/geninfo/IS-GPS-200D.pdf.
Here's the text describing it:

6.2.1 User Range Accuracy. User range accuracy (URA) is a
statistical indicator of the ranging accuracies
obtainable with a specific SV. URA is a one-sigma estimate of the
user range errors in the navigation data for the
transmitting satellite. It includes all errors for which the Space
and Control Segments are responsible. It does not
include any errors introduced in the user set or the transmission
media. While the URA may vary over a given
subframe fit interval, the URA index (N) reported in the NAV message
corresponds to the maximum value of URA
anticipated over the fit interval.

Currently the URA's smallest value is zero, meaning there is a one-
sigma range error estimate for that fit interval between 0 and 2.4
meters. The URA values increase from there.
When CNAV data begins transmission, the URA will have a different
meaning, and can take on negative values. This gives a much better
precision to the URA estimates. CNAV data will be available on the
new L2C signal.
Ted

 

In fact they should not report error in position, but an estimate of
the error.
If the signal is good, residuals are low, dop is good (and other
params) -> the estimation is good (some meters)
If the signal is low, residuals are very big, dop is bad (and other
params) -> the estimation is bad(maybe hundreds meters)
And you can mix all the situations like bad signal with good
dop...
A complex formula is used for the estimation.
Anyway, GPS receivers that usually have a message for the error
estimation tends to be too much optimistics

 

DOP only includes satellite geometry (not signal strength).

dop...

But may be you knew that.

 

Rigth. DOP only includes satellite geometry. That's why I say that
can't be used for error estimation (at least, not in a reliable
way! ) but you need to consider other parameters.
Anything in my post that let think something else?
Maybe I missed something in my examples of error estimation...

 

Rigtht. DOP only includes satellite geometry. That's why I say that
can't be used for error estimation (at least, not in a reliable
way! ) but you need to consider other parameters.
Anything in my post that let think something else?
Maybe I missed something in my examples of error estimation...

Someone could read your orignal wording as saying that good signal is a
requirement for good DOP but good signals from each satellite (as you are
aware) is not a contributor to good DOP as it only based on the geomentry
not the quality of the signal.