International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004 
Sb Nba heb 
SAR azimuth direction 
  
Figure 2: Contour map generated from the calibrated D- 
InSAR height change measurements (cm). Coordinates 
are expressed in pixels with a size of 40 by 40 m. 
are given in figures 3(a — c). These show that the number 
of outside values of errors decreases following calibration, 
whereas symmetry increases. Directional variograms of 
the discrepancies (figures 4(a-c)) show a trend contained 
in the discrepancies of the original D-InSAR. measure- 
ments since the variograms are unbounded, particularly 
in the SAR range direction (azimuth=90). This trend is 
not present in the other two approaches. For the original 
data, the mean error equals 2.1, which reduces for the 
detrended and the integrated results to 0.0. Meanwhile, 
the root mean square error (RMSE) is equal to 2.8 for the 
original data, 1.1 for the detrended measurements and 0.8 
for the integrated results. Notice that these values are not 
directly comparable, as the data are of a different type. 
Data detrending removes the trend part of the system- 
atic distortions and decreases the RMSE value, but the 
spatially correlated errors still remain. The correlation 
length is approximately 180 pixels ( 7 km). By remov- 
ing the spatially correlated errors predicted using kriging, 
both the RMSE and the correlation length decrease. 
4 Conclusion 
This paper describes a geostatistical approach of combin- 
ing D-InSAR with in situ leveling measurements. This 
approach allows a reduction of the RMSE provided that 
high enough coherence of the associated images is ensured 
and a number of in situ leveling measurements are avail- 
able. It also allows a considerable reduction of the amount 
of leveling benchmarks particularly in a large area. 
  
  
    
  
  
  
  
(a) (b) (c) 
Figure 3: Box plots of the discrepancies of leveling mea- 
surements with (a) original D-InSAR measurements, (b) 
error-detrended measurements, and (c) integrated mea- 
surements. 
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