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It is of course important to reduce the effect of image error on adjusted 
object coordinates (e9) and increase the effect on image residual (r) so that 
it can be easily detected. This can be achieved by improving the geometry, or 
increasing the number of intersecting rays at object points. Table 1 gives 
the values of e4 and r (averaged for all non-control points) for points with 
different numbers of intersecting rays and for different blocks. 
It is clear that improving the geometry, by increasing the number of 
intersecting rays, leads to the desired increase in r and decrease in es (see 
also figure 1). In fact, the average of eq (x) and e9 (y) is always: 
1.5 (9) 
where n is the number of intersecting ays. In any block, the average of 
e» (x) and e) Cy) for all the points, each appearing n times in the block, 
always follows equation (9). This could be due to the fact that 
1.5 points (3 observation) results in zero redundancy and the error appears 
entirely at adjusted coordinates (average e» (x) and e» Cy) = 1.0). 
The above analysis applies when no additional constraints or conditions exist 
between the object coordinates. Now, is it possible to increase the 
redundancy number r and decrease the factor e, through added constraints 
rather than improving the geometric strength of intersecting rays? This is 
the objective of the next sections. 
Effect of Additional Constraints on Gross-Error Detection 
The constraints used in this test are spatial distances and height 
differences. These are probably the most useful terrestrial data for 
inclusion in a combined adjustment and also the easiest to acquire in 
practice. It is expected, as mentioned ín the previous section, that the 
combined adjustment will increase the effect of the gross errors on the 
residuals while their effect on the adjusted object coordinates will decrease. 
This is demonstrated using combined adjustment with distances only and with 
distances and height differences together. The redundancy numbers are 
computed for different cases as shown in tables 2 and 4. An error of 100 um 
is introduced at each of these cases and the effect on the adjusted object 
coordinates is computed with and without terrestrial data (tables 2 and 4). 
Two blocks are used here, the simulated block and the close-range block. All 
the selected points, distances, and height differences were on the perimeter 
of the block (figures 2 and 3). This is of course the area where the 
geometric structure is the weakest, and thus improvement by additional 
constraints is most needed and more noticeable than anywhere else in the 
block. 
Table 2 displays the changes in ry for two different blocks and for different 
combinations of distances for points with different number of intersecting 
rays. When two or more measured distances originate from a point, the 
redundancy number increases to 0.50-0.9 range. One distance only does not 
improve the reliability (case D), also if the distance is in x direction, the 
increase in Ty is small (case B). 
Table 3 shows the effect of an 100 um image error, for the cases of table 2, 
on the adjusted object coordinates, without and with distances. Except for 
case D (one distance only), the effect on adjusted object coordinates is 
reduced substantially when distances are used. In cases E to H, the object 
coordinates are almost unaffected by the error. In cases A and B, where the 
distances are in X-direction, the improvement is mainly in X, with moderate 
improvement in Y, and little or no improvement in Z. These two cases are