Roughtly converting DOP to metric error

Discussion in 'General GPS Discussion' started by speleoluc, Mar 1, 2009.

  1. speleoluc

    speleoluc Guest


    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
    speleoluc, Mar 1, 2009
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  2. speleoluc

    John Tyson Guest

    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 Tyson, Mar 1, 2009
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  3. speleoluc

    jaf Guest

  4. speleoluc

    Sam Wormley Guest


    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.
    Sam Wormley, Mar 1, 2009
  5. speleoluc

    speleoluc Guest

    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
    speleoluc, Mar 2, 2009
  6. speleoluc

    Sam Wormley Guest

    I've never known what algorithm Garmin uses to estimate error.
    If the receiver knew its true error... it could correct for the
    Sam Wormley, Mar 2, 2009
  7. speleoluc

    speleoluc Guest

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

    Luc Le Blanc
    speleoluc, Mar 2, 2009
  8. speleoluc

    Sam Wormley Guest

    Error is usually reported as 1-sigma or 2DRMS oe similar.... it not
    in the form of worst case.
    Sam Wormley, Mar 2, 2009
  9. speleoluc

    Roy Lewallen Guest

    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
    Roy Lewallen, Mar 2, 2009
  10. 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.
    GSV Three Minds in a Can, Mar 2, 2009
  11. 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.
    David L. Wilson, Mar 2, 2009
  12. speleoluc

    Nick Guest

    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.
    Nick, Mar 2, 2009
  13. speleoluc

    claudegps Guest

    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)
    claudegps, Mar 4, 2009
  14. speleoluc

    speleoluc Guest

    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
    speleoluc, Mar 4, 2009
  15. speleoluc

    Nick Guest

    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.
    Nick, Mar 5, 2009
  16. speleoluc

    T Driver Guest

    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
    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.
    T Driver, Mar 5, 2009
  17. speleoluc

    claudegps Guest

    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 :)
    claudegps, Mar 6, 2009
  18. DOP only includes satellite geometry (not signal strength).
    dop... :)

    But may be you knew that.
    David L. Wilson, Mar 6, 2009
  19. speleoluc

    claudegps Guest

    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...
    claudegps, Mar 8, 2009
  20. 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.
    David L. Wilson, Mar 8, 2009
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