Table 2: RMS values of checkpoint residuals in planimetry (S,, and height (S 
  
z! for 
adjustments of forward- and backward-looking channels only (image mensuration at ETH 
Zurich) for three control (Cl) point configurations. Units are metres. 
  
  
  
  
  
  
  
  
  
  
Number | Order of Lagrange Cl Pts. | .Ck Pts. Ci Pts. . Ck Pts. Cl Pts. | Ck Pts. 
of OIs | polynomial 4 44 12 36 20 28 
Position Attitude Sxy Sz Sxy Sz Sxy Sz 
1 1 9.2 91.5 7.141 10.7 7.4 10.8 
8 2 2 8.8 51.2 6.6 6.3 6.8 2.1 
3 3 8.9 4.9 6.6 5.8 6.8 7.0 
3 1 8.7 4.6 7.2 6.3 6.9 6.9 
Ty T $3.1 9.0 9.7 14.0 9.8 15.0 
6 2 2 10.6 546 7.7 Bil 8.2 7.9 
3 3 10.6 57 2557 5 4 6.3 617 
3 1 9.2 49 7.4 6-5 Ji 7.0 
  
  
  
  
Table 3: RMS values of checkpoint residuals in planimetry (S,,) and height (S,) for 
triangulation adjustments of 3-fold stereo imagery (image mensuration Melbourne 
University) for three control (Cl) point configurations. Units are metres. 
  
  
  
  
  
  
  
  
Number | Order of Lagrange CI bte. ] Ck Pts. Q1 Pts. Ck Pts. Cl Pts. Ck Pts. 
of OIs | polynomial 4 58 12 50 20 42 
Position Attitude Sxy Sz Sxy Sz Sxy Sz 
1 1 12525 12.1 11.6 13.08 11.3 13.4 
8 2 2 10.8 8.8 10.7 9 9 11.1 11.0 
3 3 12.3 8.3 11.2 9.9 11.2 11.0 
3 1 1411.2 7:4 11.4 8.0 11.3 10.0 
T T 15.4 12.2 13.9 14.8 12.9 1845 
6 2 2 20.6 9.4 10.2 9.8 1015 10.4 
3 3 10.5 9:2 10.1 9.8 10.5 10.2 
3 1 9:9 9.2 10.0 9177 10.4 10.3 
  
  
  
  
  
  
From Tables 2 and 3 it can be seen that 
there is reasonable agreement between the 
measures of precision and external 
accuracy for height determination, at 
least in the “cases ‘of “12 ''or more control 
points and second- or third-order 
Lagrange polynomials. Tn planimetry, 
however, the checkpoint discrepancy 
values are larger than the corresponding 
standard errors by'a factor. of at least 
1:5...The.scorresponding factor for, the 
three-fold stereo case is 2.5 or more. 
The cause of this. difference can be 
largely attributed to the control point 
identification problem, and is likely 
also to be a consequence of uncompensated 
systematic error in the sensor system. 
The apparent presence of residual 
systematic error, coupled with the 
control point identification problems, 
limited an in depth evaluation of the 
212 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
impact upon triangulation accuracy of 
control ipoint. «distribution, ;number<iof 
OIs, and order of the Lagrange 
interpolation functions. The results 
listed in Tables 2 and 3 nevertheless 
provide some insight into these aspects. 
5.2 Order of Lagrange Polynomials 
Third-order Lagrange polynomials have 
found favour for the interpolation of 
position and attitude parameters for 
MOMS-02 (e.g. Ebner et al, 1992; Kornus 
et al, . 1995Yy..-In "the. course. . of: the 
present investigation it was decided to 
examine the impact of other orders for 
the polynomials. The 2-D transformation 
stage had indicated that second- and 
third-order functions might be most 
appropriate, yet analysis of the 
recovered attitude parameters suggested 
that their temporal variation was locally 
       
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