370 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1976 
TABLE A-3. PROCEDURE WITH RELATIVE 
ORIENTATION TEST OF THE FORMULA: 
(rlr') = V3nl(8n - 7) 
  
  
  
Pair T'XYZ rXYZ z 3n 
reference n control check  r' 3n—7 
101 4 10.1 9.3 .92 
102 4 7.1 88 1.24 
106 4 3.6 10.4 2.89 
107 4 27.1 19.6 27 
11 4 15.9 362 2.28 
12 4 18.7 39.8 2.13 
1.70 1.55 
101 4 8.8 8.2 .93 
102 4 5.7 8.6 1.40 
106 4 7.7 11.8 153 
107 4 13.0 196 1.51 
11 4 18.9 38.4 2.03 
Ren. 1 4 10.4 147. 141 
Ren. 2 4 9.3 9.8 1.05 
1.41 1.28 
Tu. 1 3.6 3.6 1.00 
8 
Tu. 2 8 4.6 6.0 1.30 
Tu. 3 8 8.7 108 1.24 
1.18... 1.18 
101 15 8.0 81 LOI 
102 15 8.4 8.0 95 
106 15 9.3 10.0 1.08 
107 15 ‘173 18.3 1.06 
11 15. —337 31.5 .93 
12 15 349 35.0 1.00 
101 1.09 
  
APPENDIX B 
EVOLUTION OF ACCURACY WITH THE NUMBER OF CONTROL POINTS 
One particular computational method will be considered: Resections in space of the two 
bundles with direct linear transformation (collinearity equations and eleven unknown 
parameters per bundle) and then intersection of homologous rays. The resections are 
computed from n control points whose coordinates we assume to be exactly known. It is an 
experimental fact that the final accuracy of the object points depends on the number and 
relative disposition of the n control points. Here we try to determine if there is a simple law 
accounting for the corresponding accuracy variation. 
The theoretical derivation is performed as follows: For each bundle the eleven unknown 
parameters p,, ps, ... , pj are determined from the least-square solutions of the observation 
equations 
_ Pi X; + Pa Y; + ps Z; + pa | ps Xi * ps Yi* ps Zi * ps 
© Pa X; + P10 Ÿ; + Pi Z;* 1 yf = pe Xi+ poY; +p, Z +1 
where X;, Y;, and Z, are the spatial coordinates of the i'^ control point and x; and y; are the 
plate coordinates. 
The precision of the estimations of the eleven parameters is the variance (matrix) 
pi 
pa 
  
  
Xi 
pii 
But this is not the accuracy. Then how is the accuracy estimated?