[time-nuts] question about Thunderbolt geo acuracy

[Jim Lux]

On 5/10/12 7:40 AM, Arthur Dent wrote:
> I've found significant altitude errors using a GPS and the following quotes
> found on the internet will explain why. From my experience of hiking
> in the mountains of New Hampshire an aneroid altimeter will vary with
> atmospheric pressure about 200 feet for a change of 0.2" of mercury
> so you have to continually set it at known waypoints, just like setting a
> frequency standard against a known reference, and then it will be
> 'accurate' for some length of time, and then you set it again. GPS altitude
> will be off but it should be fairly consistent in spite of the changing
> atmospheric pressure. The earth neither spins at a constant rate nor is
> it a perfect sphere. Maybe we need to trade it in for a newer model. ;-)
>
> "GPS altitude measures the users' distance from the center of the SVs
> orbits.

Not precisely true.  The SV orbits follow the usual Keplerian things so 
the focus of the ellipse is close to the barycenter of Earth, but of 
course, the moon and non uniform gravity of the Earth affect it too.

GPS fixes are relative to WGS84  coordinate system (x,y,z)   0,0,0 in 
WGS84 is within a few cm of the center of mass of the Earth.  WGS 84 
also defines a datum for the surface (which is not, generally, the 
geoid) as an ellipsoid of revolution.  (compare to the Clarke 1866 
ellipsoid)

These measurements are referenced to geodetic altitude or
> ellipsoidal altitude in some GPS equipment.

This is a bit fuzzy... there are differences between geodetic and 
geocentric altitude for instance.  And then there's the reference 
ellipsoid (e.g. Clarke 1866), or more generally the "geoid"


  Garmin and most equipment
> manufacturers utilize a mathematical model in the GPS software which
> roughly approximates the geodetic model of the earth and reference
> altitude to this model.

Mmm.. I don't know that it "roughly approximates".. WGS84 is precisely 
defined (that's the coordinate system).  The geoid (in terms of the "sea 
surface" is defined in terms of spherical harmonics and varies some 100m 
or thereabouts from the reference datum.

WHether your GPS uses the WGS84 datum (simple ellipsoid) or the fancier 
geoid, is something you'd have to look up.

As with any model, there will be errors as the
> earth is not a simple mathematical shape to represent.  What this
> means is that if you are walking on the seashore,  and see your altitude
> as -15 meters,  you should not be concerned.  First,  the geodetic model
> of the earth can have much more than this amount of error at any specific
> point and second,  you have the GPS error itself to add in.  As a result of
> this combined error,  I am not surprised to be at the seashore and see -40
> meter errors in some spots."
>

Actually, no.. the geodetic model (e.g. the EGM96) should be VERY close 
to the actual sea surface (barring tides and local geographic effects.. 
the Gulf Stream sits several meters higher because it's warmer and less 
dense)

The ellipsoid could easily be off by tens of meters.


> "We have to make some assumptions about the shape of the earth. WGS84
> has defined that shape to be an ellipsoid, with a major and minor axis. The
> particular dimensions chosen are only an approximation to the real shape.
> Ideally, such an ellipsoid would correspond precisely to "sealevel" everywhere
> in the world. As it turns out, there are very few places where the WGS84
> ellipsoid definition coincides with sealevel. On average, the discrepancy is
> zero, but that doesn't help much when you're standing at the water's edge of
> an ocean beach and your GPS is reading -100ft below sealevel. The deviation
> can be as large as 300ft in some isolated locations. When the National Marine
> Electronics Association came up with the NMEA standard, they decreed that
> altitudes reported via NMEA protocol, shall be relative to mean (average) sea
> level. This posed a problem for GPS manufacturers. How to report altitudes
> relative to mean sea level, when they were only calculating altitude relative to
> the WGS84 ellipsoid. Ignoring the discrepancy wasn't likely to make GPS users
> very happy. As it happens, there is actually a model of the difference between
> the WGS84 ellipsoid and mean sea level. This involves harmonic expansions
> at the 360th order. It's a very good model, but rather unusable in a handheld
> device. It was determined that this model could be made into a fairly simple
> lookup table included in the GPS receiver. The table is usually fairly coarse
> lat/lon wise, but the ellipsoid to mean sea level variation, known as geoidal
> separation, varies slowly as you move in lat/lon."


And that is a more accurate description..

The question really is "what does YOUR receiver report".. if it's MSL in 
NMEA strings then I would imagine all modern receivers use some form of 
geoid model with error probably <1 meter. If it's WGS84, then it ignores 
the geoid.