Erik de Min
The corrections can be described by equation (2) (cf. equation (1)):
AH(U,V) — ae hU kal YU 372 D V (2)
gz2
Let's look at an example. Strip 15 from figure 10 is now compared with TOPhoogteMD. At every location of a point in
TOPhoogteMD a laser altimetry value is interpolated. The height differences that can be created this way are shown in
figure 12a. A wave effect in along-track direction is clearly visible in this picture. To assess the significance of all
possible corrections from (2), several consecutive steps are performed. First the strip adjustment parameters offset,
along-track tilt and across-track tilt are estimated and applied. Thereafter a parabola in across-track direction is
estimated (figure 12b) and corrected for. Finally, a periodic function in length direction is fitted to te height values
(figure 12c). Note that the data beyond -1 and +1 comes from zero-differences, that were added to stabilize the
polynomial fit at the borders of the strips avoiding undesired effects.
Figure 12a: Laser vs TOPhoogteMD: sideview of strip 15 Figure 12b: Estimated parabola in across-track direction
Figure 12c: Estimated wave in along-track direction Figure 12d: Empirical covariance functions of residuals
4 ACHIEVABLE HEIGHT PRECISION WITH EXTRA EFFORT
Beside the analysis of real laserdata, some simulation computations were done in order to investigate the maximal
achievable theoretical precision of mean heights in case of adding much more ground control points and extra cross laser
strips. With *mean heights' the over a certain area averaged heights are denoted. In the experience of the Survey
Department, height precision achieved by airborne laserscanning must be considered and analyzed for different sized
regions (e.g. 0.01 km^or 1 km?) and not per single height value to describe the quality of a resulting DEM in a sensible
manner.
From the parameters a, b and c (estimated for every strip, see section 3.1), the precision of the mean height of the entire
strip and, furthermore, of regions extending over more than one strip were determined by means of error propagation.
The standard deviation of a regions mean height depends - beside the error influences as GPS/INS-error and noise - on
the size of the region, its position within the entire block and the configuration of the block. For the simulation computa-
tions starting point was a standard block configuration with 50 strips and one cross strip, every strip being 30 km long
and 400 m wide, with an overlap between neighbouring strips of 100 m. A tie *point' error of 0.8 cm is assumed, GPS-
noise of 2.5 cm and an error of 1 cm of the ground control *points'. For the test computations, the control points always
lay at the begin and at the end of every strip.
236 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
