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2. Create height differences between laser altimetry data and reference data (ground control ‘points’). Conditions a, b 
enc of step 1 also apply to this step. The number of height differences from step 1 and step 2 together has to exceed 
three times the number of strips (per strip three parameters are estimated), to ensure redundancy. 
3. Execute an integral least squares adjustment in which correction parameters are estimated from the height differences 
which were determined in step 1 and 2. In this adjustment also height differences with the prescribed cross-strips 
(figure 4b) are taken into account. 
There are two types of observation equations, that are the basis for the adjustment. For the height differences i 
between two laser altimetry strips j and k the equation reads (cf. equation (1)): 
laser P. laser |. - la 
For the height differences i between laser altimetry data in strip j and reference data k (NAP heights, the national 
height system), the observation equation reads: 
HT H, PT a,+b,U,+eV, dm 
4. Analyse the results by investigating the residuals (see below). 
5. Apply the corrections. Strips are fit together in the best possible way by shifting and rotating. 
The inspection of the results (step 4) is done in 
various ways. One of them is analyzing the 
spatial distribution of the height residuals after 
adjustment. Figure 6 shows the locations of the 
50x50 m? areas (tie points). These areas are 
grouped in pairs, so that two profiles of height 
differences in the along overlap can be created: 
one for the right and one for the left part of the 
overlap. Analyzing these profiles of residuals 
before and after adjustment facilitates the 
interpretation of the achieved improvement and 
Occuring errors. 
  
An example is given in figure 7 (‘real’ data). The 
outer black lines are the height differences for 
the two profiles before the adjustment. 
Apparently, the strips cross each other in the 
overlap at a line which is approximately parallel 
to the flightline, because one profile reads positive values, and the other negative values. The inner (colored) lines yield 
the residual height differences after the adjustment. In this example relevant corrections were determined. 
    
Figure 5: Is he doing a strip adjustment? 
The pattern shows random effects that are within the expected noise from error sources 1 and 2 (see section 2). 
Furthermore, the empirical covariance function (ECF) in the lower part of figure 7 indicates, that almost no systematic 
behaviour remains after adjustment for the two profiles. An ECF shows the spatial correlation of the height residuals 
after adjustment. If correlation (systematic effects) between points up to distance s apart from each other exists, the 
function will not go to zero before distance s at the horizontal axis. The value at distance zero reads the quadratic 
standard deviation of the residuals. 
The standard deviation of the residuals after adjustment is small (2-3 cm). The effectiveness of the strip adjustment can 
also be examined by analyzing histograms of residuals before and after adjustment for whole laser blocks. In figure 8 an 
example is given. The figure relates to a large block of strips in the southern part of the Netherlands (more than 300 
strips). The residuals are significantly smaller after the strip adjustment, leading to the conclusion that strip adjustment 
increased the quality of the dataset considerably. GPS-errors (component 2) can be blamed for the remaining residuals. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 233