ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002 
If this is done correctly, the overall model test of the least 
squares strip adjustment (F-test) will be approximately equal 
to 1, indicating an appropiate model 
A fully filled covariance matrix for the observations implies a 
much longer processing time for the strip adjustment. From 
several datasets we learned that the resulting standard 
deviations of the strip offsets are about a factor 1.3 higher 
when taking into account the off-diagonal elements. In order 
to save time, the adjustment is therefore done with a diagonal 
covariance matrix for the observations, taking into account 
error component 2 and the sill of error component 3, but 
neglecting the off-diagonal elements (correlations). To 
correct for this, the resulting strip offset standard deviations 
are multiplied by a factor of 1.3. 
In figure 6 strip offset standard deviations are visualised per 
strip. It is apparent that the standard deviations of the offsets 
are smaller in areas with relatively more ground control 
points, see dots, (and also more tie points, not visible in 
figure 6) and in areas with more cross strips. The right part of 
the block has 3 cross strips in opposition to the left strips 
with only a single cross strip. 
  
    
140000 \ 
N au 
150000 ^N a ee et 
ME M 4000050000560) ; 
1 00005200005300005 
RD x (F%% 450000470000480000490000500006% 
RD y [m] 
Figure 6. Standard deviations of strip offsets. 
From the standard deviations of the strip offsets, a single 
standard deviation for the precision of a complete laser 
dataset (entire block) can be calculated by applying the 
propagation law of variances: 
i=n j^! 
N 
2 
26; * 2,000) 
i=1 
2 J=1 (4) 
O dataset — 
n:n 
with: 
iandj = numbers of adjacent strips 
e — standard deviation of offset a of strip i 
Oa, = covariance between offsets of strip i and strip j 
n — total number of strips in the laser dataset 
5. RESULTS OF REAL DATA ANALYSIS 
The Dutch Survey Department is in the fortunate position to 
have laser altimetry data available for almost the complete 
country. Therefore the amplitude of the different error 
components can be calculated for large and numerous data 
sets (approximately the size of a province). Table 1 gives 
typical values for the amplitudes of the different error 
components. Note that outliers occur in practice. 
  
  
  
  
  
  
  
  
error per mean max dimens. | 
1 | point 0.08 0.10 m 
2 | GPS observation: nugget | 0.03 0.05 m 
3a | strip: Jsill 0.04 0.05 m 
3b | strip: range 9 15 km 
4a | block: Ostrip offsets 0.03 0.08 m 
4b | block: strip offsets 0.03 0.10 m 
  
  
  
  
  
Table 1. Typical values for the error components 
6. UTILISATION OF ERROR DESCRIPTION 
The new height error description will be used for two 
purposes. The new quality demands for laser DEMs, 
delivered by laser scanning companies, are based on this 
description. On the other hand, the customers (DEM users) 
will be provided with this extended quality description. 
6.1 Towards the laser scanning companies 
The Dutch Survey Department intends to use the new error 
model with suitable amplitude requirements in the contracts 
with the laser scanning companies. The calculation methods 
described in section 4 enable fast and (nearly) automatic tools 
for the assessing of the data delivered in strips from the 
contractors. 
Table 2 shows the maximal allowed error amplitudes per 
error type. For every error component the mean value and the 
maximal occurring value (max) for an entire dataset (project 
area) has to be below these thresholds. Note that the 
demanded amplitude for error component 4b (strip offsets) is 
quite strict. The reason is that this error (systematic per strip) 
can easily be corrected by strip adjustment. We expect that 
the companies already have executed a strip adjustment. 
  
  
  
  
  
  
  
  
  
  
  
error per mean max dimens. 
1 | point 0.12 0.24 m 
2 | GPS observation: {nugget | 0.03 0.06 m 
3a | strip: sill 0.05 0.08 m 
3b | strip: range 10 30 km 
4a | block: Ostrip offsets 0.05 0.08 m 
4b | block: strip offsets 0.05 0.13 m 
  
  
Table 2. Contract demands for maximal error amplitudes 
6.2 Towards the users 
Moreover, the new height error model will be used for the 
description of the precision of laser altimetry deliveries to 
customers. With the given error amplitudes per laser dataset, 
customers (or DEM users) are able to compute the precision 
of derived products from the laser data, e.g. volumes or mean