ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002 
  
mean heights of certain areas. Furthermore, it was not clearly 
formulated. 
The former and the new error description scheme will be 
described in the following paragraphs, together with methods 
to quantify the differently scaled error components. The 
chosen thresholds for every error component, derived from 
real data, will be presented. Finally, the benefit of the error 
description scheme for the AHN user will be illustrated by 
propagating the error components to the height precision of 
derived products. 
Thus, this paper deals with assessing the height precision of 
laser altimetry DEMs and quantifying the effects of the 
different error components on the measured heights. This 
paper does however not aspire to give methods for 
eliminating or minimizing these errors, or for quantifying the 
errors themselves, e.g. roll, pitch and heading errors of the 
INS, such as Schenk [2001] did. 
2. FORMER WAY OF DESCRIBING LASER DEM 
HEIGHT PRECISION 
The demanded height precision for the AHN is strict: 5 cm 
systematic error and 15 cm standard deviation. It turned out 
that these requirements were not always achievable. In 
addition, a fundamental drawback of this formulation is its 
ambiguity: several interpretations are possible. The region 
size, for which the thresholds for bias and standard deviation 
are valid, is missing. Does the 5 cm bias apply for, for 
example, 100 m? areas or for 1 km? or for 10 km? ? Or is this 
maximal bias valid for all these areas? And what about 
controlling this, as such large ground control fields can 
hardly be measured? 
Another disadvantage of this height error description is that 
not all the occurring error types of current laser data are taken 
into account. The error behaviour of laser altimetry data, 
acquired by a complex system of different sensors, cannot be 
expressed by only two parameters: a bias and a standard 
deviation. These two parameters do not suffice for describing 
the height precision of a laser altimetry DEM. 
A more sophisticated approach for comprehensively 
describing the height quality is required. This new approach 
must take into account the specific scale of each error type. 
Some errors are stochastic for a single laser point. Others are 
systematic for a small area or for an entire laser strip, but 
stochastic as we focus on a large number of these small areas 
or strips. In the following paragraph, these different error 
components will be described including their technical 
causes. 
3. NEW HEIGHT ERROR DESCRIPTION MODEL 
In our opinion the total error budget of laser altimetry data 
can be divided into four components with different 
amplitudes and with different spatial resolution [Crombaghs 
et al. 2000]. These errors, which are illustrated in figure 1, 
are: 
1: Error per point. Due to the measuring uncertainty of 
the laser scanner each laser point is affected with a 
random error. This error is also called ‘point noise’. 
2. Error per GPS observation. Every GPS observation as 
well is affected with a random error. This error, 
however, is constant (systematic) for all laser points 
measured during this second. Usually, these points are 
lying in a strip-wide area of about 100 m in length. This 
depends on flying speed and GPS observation interval. 
3. Error per strip. GPS and INS sensors are needed to 
measure the position and orientation of the aircraft 
along the flight path. The GPS/INS-system introduces 
systematic errors in strips, like vertical offsets, tilts in 
along- and across-track direction and periodic effects 
with a period of several kilometres. 
4. Error per block. Terrestrial reference measurements 
(ground control ‘points’) are used to transform blocks 
of laser measurements into the national height system. 
Errors in these control ‘points’ result in height 
deviations which affect entire blocks of laser strips. 
This influence depends on the block configuration 
(position and number of strips, cross strips and control 
‘points’) and on the correction procedure (strip 
adjustment). 
Error per GPS observation — Error per strip (GPS/INS) 
/ 
Ni A | 
e 
  
Error per |laser point 
Error per block 
  
  
  
Figure 1. Different scaled error components. 
At the Survey Department strip adjustment techniques are 
developed to minimize error components 3 and 4 
[Crombaghs et al. 2000] whereas for error components 1 and 
2 it is impossible to correct for. The amplitudes of the four 
error components differ per project and depend on hardware, 
software, measurement setup (block confi-guration) and 
measurement procedures (e.g. calibration). The next 
paragraph describes how the amplitude of the error 
components can be determined. 
4. DETERMINATION OF ERROR COMPONENTS 
In order to quantify the different error amplitudes, various 
methods are used, such as cross correlation techniques, 
analysis of empirical covariance functions and 1d strip 
adjustment. In the following paragraphs these techniques will 
be described. 
4.1 Error per point 
The amplitude of this error cannot be determined by simply 
taking the standard deviation of the laser data because this 
standard deviation covers the total error budget of a single 
laser point. To obtain the pure point noise, cross correlation 
techniques are used. Flat areas of 50m x 50m without 
vegetation and buildings are selected. The height of each