ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002 
  
heights of differently sized areas. In the following, some 
examples are given for the determination of the height 
precision of derived entities. The total error budget for the 
height of a single laser point is: 
  
= i J 2 O24 02 2 2 
laserpoint — 0j *05 t O34 * O4, t O4) 
All error components are present in a single laser point. The 
total error budget for the mean height of an area of 25m x 
25m is: 
  
m 2 2 2 2 2 
O25mx25m = Joi /40 +07 + 034 + O4a + Tab 
It is assumed that there are 40 laser points in this area. The 
point noise is reduced by the averaging process. The total 
error budget for the mean height of an area of 500m x 500m 
is: 
  
2 2 2 2 2 
O 500m x 500m — Joi /15,000 +02 /5 +03, +044 +04) 
In this case the point noise is almost vanishing due to 
averaging such a large number of laser points. It is assumed 
that the data in this area is covered by 5 GPS observations. 
Error component 2 is therefore reduced by factor 5. The area 
of interest is still lying within a single strip. The total error 
budget for the mean height of an area of 5km x 5km is: 
  
sk x Bh = Jo? /1,500,000 + 03 /4,000 + 03 /20 + 63, + 03) 
It is assumed that the data in this area covers 4000 GPS 
observations and 20 strips (overlap has to be taken into 
account). Error components 1 and 2 are averaged out 
(almost) completely, and error component 3a is reduced by 
factor 20. 
For simplification purposes we assume that error components 
4 are constant within a block (even though there are varying 
errors 4a and 4b per strip). Therefore for error components 4 
cannot be reduced by averaging, except if the mean height of 
several blocks is determined. The larger the area of interest, 
the more dominant this error component becomes. The 
averaging effect of the error components for different sized 
areas is visualised in figure 7. 
Error 1 2 3a 4a 4b 
   
  
  
5mx 5m 
25mx25m | | | EE LIB88PMN... 
500m x 500m . | IER . 
5km x 5 km 1 1] els 
Figure 7. Averaging out of error components 
Note that the total error budget refers to the absolute height 
precision with respect to the national height system. For some 
applications of laser data the relative error between mean 
heights of neighbouring regions are more important. These 
relative errors are smaller than the absolute errors. 
7. CONCLUSIONS 
Describing height precision of laser altimetry DEMs with 
solely two parameters, a bias and a standard deviation, is 
ambiguous and, above all, not sufficient. Due to the 
integration of different sensors (GPS, INS, laser scanner) in a 
complex measuring system, the height error budget of single 
laser points or regions of a certain size is a combination of 
several error components. These errors can be 
characteristized by amplitude and spatial resolution. With 
regard to the affected area, these errors can roughly be 
divided into four components: an error per point, strip section 
(covered during one GPS observation), strip and entire block. 
Deriving typical values for the error amplitudes from 
numerous datasets enabled the Survey Department to 
formulate new demands for maximal error amplitudes with 
regard to the contractors (laser scanning companies). Besides, 
the new height error description model and the developed 
tools for determining the amplitude of each error component 
from a specific dataset provide a useful instrument to get a 
thorough insight into the height quality of the delivered 
datasets. Finally, the knowledge of such a comprehensive 
height error description per dataset is very useful to the users. 
They are enabled to determine height precision of derived 
products in a reliable way. 
Up to now, the usual strip adjustment is 1d (height 
adjustment). A complete 3d strip adjustment, such as 
proposed in Burman [2000] or Vosselman and Maas [2001] 
could increase the height precision of laser altimetry DEMs 
due to a better modelling of the occurring errors. It is 
desirable to use a 3d strip adjustment in the near future. 
REFERENCES 
Brügelmann, R., 2000. Automatic breakline detection from 
airborne laser range data. In: International Archives of 
Photogrammetry and Remote Sensing, vol. 33, part B3/1, pp. 
109-115. 
Burman, H., 2000. Adjustment of Laserscanner Data for 
Correction of Orientation Errors. In: International Archives 
of Photogrammetry and Remote Sensing, vol. 33, part B3/1, 
pp. 125-132. 
Crombaghs, M.J.E., Brügelmann, R., de Min, E.J., 2000. On 
the adjustment of overlapping strips of laseraltimeter height 
data. In: International Archives of Photogrammetry and 
Remote Sensing, vol. 33, part B3/1, pp. 224-231. 
Huising, E.J., Gomes Pereira, L.M., 1998. Errors and 
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scanning systems for topographic applications. ISPRS 
Journal of Photogrammetry and Remote Sensing 53 (5) 245- 
261. 
Schenk, T., 2001. Modeling and recovering systematic errors 
in airborne laser scanners. In: Proceedings OEEPE workshop 
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Detailed Digital Elevation Models. OEEPE Publication no. 
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Vosselman, G. and H.-G. Maas, 2001. Adjustment and 
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SAR for Detailed Digital Elevation Models. OEEPE 
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