Guidelines for the use of GNSS in surveying and mapping

steps used in generating the local grid coordinates.
This will ensure that any future survey
work is totally compatible with that previously
carried out.
6.3.4 Height transformations
There is a special treatment required to calculate
the heights of points observed by GNSS. It is
simpler to envisage the reverse transformation from
levelled orthometric heights, to those observed by
GNSS. Before any co-ordinate transformations take
place, the elevation height of the control point in
the national datum (e.g. to mean sea level (MSL))
must first be converted from an orthometric height
to an ellipsoidal height. Before any datum
transformation, this orthometric height is the height
of the control point above the geoid in that area,
usually given the symbol H.
However, what is required is the ellipsoidal height
relative to that ellipsoid used in the national datum.
For example, in Great Britain Ordnance Datum,
Newlyn height (H) must be converted into the Airy
ellipsoidal height (h). The difference between the
two heights is the height of the geoid above the
ellipsoid, or geoid-local ellipsoid separation, N. This
is shown in Figure 6.3 with an exaggerated
separation for clarity.
Figure 6.3: Height relationships
Thus the general equation to relate heights can be
written as: h = H+N
Where:
+ h is the ellipsoidal height
+ H is the orthometric height
+ N is the geoid-ellipsoid separation (undulation
or geoidal height).
The ellipsoid used for a local datum was selected
when the datum was defined, and is usually the
best-fitting ellipsoid to the geoid in that part of the
globe. In the local datum the value for N is
therefore typically small; in Great Britain for
example the maximum separation between the Airy
ellipsoid and the geoid (MSL Newlyn) is only 2.5m
over the whole of the country.
However, with a global geocentric ellipsoid such as
ITRS89, the separation can vary dramatically. In
Great Britain the geoidal height is approximately
50m, whilst in areas of the Middle East it is -10m;
i.e. the ellipsoid is 10m above the geoid. Thus,
height corrections for the geoid/ellipsoid separation
are extremely important when transforming ITRS89
geodetic latitude, longitude and ellipsoidal heights
to co-ordinates with a local orthometric height.
There are many different geoid models published
and these provide the basic look-up table for
orthometric /ellipsoid separation values over a
given area. Both global and country models exist,
and most give the values between the global or
local geoid and the ITRS89 ellipsoid. The models
are incorporated differently into GNSS
manufacturers’ software and it is good practice to
check which model, and associated accuracy, is
being used.
In practice, the reverse of the procedure is carried
out. GNSS observed heights are transformed from
cartesian to ellipsoidal co-ordinates, then by an
application of the orthometric/ellipsoid separation
model, the resultant ortho heights are produced.
Depending on the local situation, best practice
differs:
+ use GNSS plus the orthometric/ellipsoid
separation model to bring orthometric height
onto a site. Traditional spirit levelling should
then be used to promulgate the orthometric
height around the site
+ include at least three or four height control
points in a survey network which have reliable
orthometric heights. These orthometric heights
can then be compared with the computed
values from the national control and the
application of the geoid model. The figures may
show up a bias in the model, especially if it is
to a large grid global geoid model. They can be
held fixed in any final adjustment if required.
GUIDELINES FOR THE USE OF GNSS IN LAND SURVEYING AND MAPPING |47