Wednesday, October 30, 2013

GPS altitude introduction

The global positioning system  is not usually included in the basic topics about air data measurement, nonetheless this instrument is useful to some auxiliary operations that should be carried during normal instruments operation.
Common approach is to log the altitude as above ground level, the departure runway is set then as the reference zero altitude above ground level. Same approach is used with barometer altimeters.
Sometimes this procedure is carried out in an inaccurate way and both the GPS and the barometer are unable to provide mean sea level altitude, not to mention the heavy impact on barometer measures accuracy that can be caused by a coarse, or absent, local weather compensation.

GPS works natively with a ECEF reference frame, the chipset converts this coordinate system to those of a selected ellipsoid. As example I will use a Venus638flpx GPS chipset by Skytraq, get the datasheet here , at page three you can read that GPS datum is by default WGS-84 . This application note at page 44 , indicates that Venus chipset can manage many reference ellipsoids.

WGS-84 provides an approximate model of earth surface, that is modelled as an ellipsoid. Returning to altitude measurements they are refered to the geoid datum. This reference system define a zero elevation surface, the geoid, that would coincide with the mean ocean surface of the Earth if the oceans and atmosphere were in equilibrium. Consider the following figure that depict current altitude reference systems as introduced until now.
Figure F19.1 Altitude datum representation for a flying platform.
H GPS altitude, h altitude , N undulation, AGL above ground level altitude, MSL mean sea level altitude

In the figure H represents graphically the altitude measure provided by the example GPS unit, h is the altitude as globally defined. Deviation between H and h is N or undulation, such deviations are caused by the natural variations of gravity field that as shown \(\epsilon\) can also deviate the gravity vector. Note that geoid surface can either be over or under the WGS-84 surface.

By figure inspection mean sea level altitude can be calculated as \(h=H-N\) therefore there is a need for an accurate knowledge of the geoid altitude.

This information is available through gravity models as EGM 2008 edition by U.S. National Geospatial-Intelligence Agency, on their site there is freely downloadable software in theSoftware and Coefficients for WGS 84 Geoid Undulation Computations by Harmonic Synthesis” section of this page. This software can calculate for us the undulation N in meters.

Is to be noted that the value of altitude supplied by  GPS units can be of different types.
The altitude can be referred to selected ellipsoid, in our example WGS-84, this value don't need to be elaborated further. On the other side, by default on Venus units, altitude reading is compensated for the deviation from ellipsoid, this altitude reading is defined on the manual as MSL. Refer to this document page 8 for typical NMEA $GPGGA position fix message format.
The heigh above WSG-84 geoid H is needed so if our fix message is as follow
                                                                                   ^         ^
GPS altitude H is then 57,2+40,3=97,5 m
Using the coordinates of my RC Group airfield into the EGM08 model I get the following output “45.231386 9.882303 40.488”
First two rows are decimal latitude and longitude and the last is N in meters.
If my GPS altitude reading at the same coordinates is 97,5 m then the altitude, or at last elevation,
is 97,5-40,488=57,012 m MSL.
As alternative you can also use this online calculator, note that this calculator is implementing an older EGM96.
With the same coordinates the output is the following

<<Your Input Coordinates and GPS Height:

Latitude = 45.2313861111111° N = 45° 13' 52.99" N
Longitude = 9.88230277777778° E = 9° 52' 56.29" E
GPS ellipsoidal height = 97.500 (meters)
Geoid height = 40.137 (meters)
Orthometric height (height above mean sea level) =57.363 (meters)
(note: orthometric height = GPS ellipsoidal height - geoid height) >>
There is a difference of 0,351m due to different N value between the two calculations.

Overall measure accuracy is obtained by the sum of accuracy of ellipsoid model, geoid model and GPS measurement itself. Accuracy of WGS-84 and EGM08 are related to the geographic coordinates.

A strong conservative value for EGM08 accuracy is 0,7m at 99% of confidence. A full compilation of documents with accuracy considerations for different geographical areas can be found at this link, for example refer to table 4 page 143.
Returning to our example, the datasheet of Venus GPS page three indicates an accuracy of 2,5m CEP radius; that is an indication of 2D precision of the unit.
Using CEP and some assumptions on error distribution is possible to calculate spherical accuracy SEP. SEP is defined as the radius of sphere centered at the true position estimate in 3D with probability 50%.
Assuming a typical VDOP / HDOP 2, PDOP / HDOP = 2 lead to approximate SEP=5m, similar results here at page 4-5
Probability of 50% is a low value, since half of the measurements will lie outside this radius. The 99% Spherical Accuracy Standard is then calculated as \(SAS_{90}=2,2SEP=11m\)
In a worst case scenario and with a confidence level of 99% the uncertainty is \(u_{t}=11+0,7=11,7m\)
So with the cited GPS unit, with no particular measurement methods, the altitude should be reported as  \(57,0 (\pm 11,7)m\) with 99% confidence level; 94% of total altitude deviation comes from the GPS unit uncertainty.

Is good practice to check our instruments readings against well know referral points, they can be mainly of two kinds.
Landmarks altitude accuracy is variable, but usually they are easy to use. Most commons landmarks are airports or main city squares, is to note that every, even if really small, airports have a good indication of altitude since it is a useful information for aircraft altimeter calibration.
Geodetic networks can also be used for calibration, this kind of networks are used also for cadastral purposes and can reach a really good, let's say impressive, degree of accuracy. In Italy, for example, there is a network called IGM95,Italian counter part of EUREF89 or ETRF89,  by IGM , the approximative location of points can be found on the IGM website ; a non official compilation of IGM 95 points can be found here.
If you test your unit against a referral point you will have a clear feedback about your GPS units degree of accuracy. Note that the geoid deviation calculated internally by your unit is not necessarily equal to the here above calculated deviation, anyway the measurement will be off with both corrections. You should find instead that your measurements fall into the uncertainty interval calculated above.
If you plan to record flight altitudes at your flying site, for the best results, setup a referral point of  altitude. Is a good practice to record both, GPS altitude and GPS corrected altitude, in such a way you can correct your past measurements as soon as another more accurate referral point is available.
These are the premises needed to result interpretation of a next to come example on GPS measurements, of course I will use also a Venus GPS unit.

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