Erik de Min
3 APPROACH FOR CORRECTION OF HEIGHT ERRORS
The Survey Department has developed strip based adjustment methods to determine the above described systematic
height errors and to correct for them (de Min et. al. 1999). The strip adjustment only comprises the height (z-co-
ordinate) in opposition to approaches of (Kilian et.al., 1996) and (Fritsch and Kilian, 1994). It turned out that focussing
on only the heights already results in so many different error aspects that the feasibility of the three dimensional
adjustment is doubted. Besides, it was necessary to quickly get a tool to improve and check the delivered laser data.
Height control points were much more easier to generate than planimetric control points.
In a first step, a height strip adjustment is performed, assuming strips to be stiff and flat boards. Since this did not always
suffice, further correction tools have been created to correct for possible cross strip parabolic effects and to handle strip
torsions or other periodic effects. In the following sections, these methods will be described.
3.1 Strip adjustment (hammering boards together)
Height differences in overlapping areas of neighbouring strips (tie ‘points’) and height differences of laserdata and
reference measurements (ground control ‘points’) are used for the determination and correction of offsets and tilts. This
method can be imagined as hammering boards together like a carpenter. Every individual strip gets corrections for offset
(a) and for along-track (^) and across-track (c) tilts. This means that to all heights the correction-function (1) is applied:
AH(U,V)- a bU * cV (1)
In this formula U en V are coordinates in a local strip-system, as indicated in figure 4a. RD is the Dutch national grid.
Strip adjustment can only be carried out when the laser altimetry data is available per individual strip.
RD-Y RD-Y
Along-oferlap
RD-X
Figure 4a: Local strip system Figure 4b: Along-overlap and across-overlap
The principle of strip adjustment can be described in five steps:
l. Create height differences between two laser altimetry strips in overlapping areas (height differences in tie ‘points’).
A number of conditions have to be fulfilled in order to ensure a correct adjustment:
a) The tie points must not lie on a straight line in order to avoid singularities
b) The differences must not be computed for individual points because of the point noise of about 10-15 cm.
Therefore, differences are computed as mean differences for groups of minimal 100 points in areas of 50x50 m°.
In this case, a point noise of 12 cm results in (12*V2)/V100=1,7 cm for the averaged height differences. This way,
an offset of for example 6 cm can be found in spite of the original point noise of 12 cm.
c) The tie ‘point’ areas of 50x50 m^ have to be flat and smooth. Otherwise small planimetric errors might have a
large impact on the mean difference for this area. The smoothness is checked by cross validation computations.
Interpolation errors are taken into account in the adjustment.
232 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
