ACCURACY OF CLOSE-RANGE ANALYTICAL RESTITUTIONS 369 
And, finally, if RXYZ is the RMS spatial residual estimated from the check points, 
E(RXYZ)  K x E(R'XYZ) 5 (A-4) 
n 
where K= Vian; 
Results for several pairs, for each of the three values 6,7, and 10 of n, are listed in Table A-1. 
In these cases, Equation A-4 becomes 
K-4/—.. 
2n — 9 
SECOND CASE: RESECTIONS IN SPACE OF THE TWO BUNDLES WITH THE DIRECT LINEAR 
TRANSFORMATION METHOD FOLLOWED BY INTERSECTION OF HOMOLOGOUS RAYS. 
  
The same justification as in the first case can be applied. The residuals w; of the observa- 
tion equations are no longer the components of the vector m;, m;. (Figure A-1) but are 
functions of m;, my, i.e., w; 7 f (vj). 
However, in the general case, if the volume depth is not too great, it can be shown that Wi 
is sensibly proportional to v; and that 
wi? minimum €» Y vj? minimum. 
In other words, the two solutions are practically identical. As a consequence: 
E (R'XYZ) » A 5:28. E (RXYZ). 
The results of the tests are given in Table A-2. 
THIRD CASE: RELATIVE ORIENTATION AND LEAST-SQUARE ADJUSTMENT OF THE MODEL TO N 
CONTROL POINTS. 
The same assumptions are made in the third case as were made in the first and second 
cases. The following equation was employed to obtain the results listed in Table A-3: 
E (R'XYZ) «AJ pr 7 E (RXYZ) (A-5) 
  
  
  
  
  
  
TABLE A-1. PROCEDURE WITH RESECTIONS IN TABLE A-2. PROCEDURE WITH RESECTIONS IN 
SPACE (RiGOROUS SOLUTION). TEST OF THE SPACE. (DIRECT LINEAR METHOD). TEST OF THE 
FORMULA: (rIr') - V2n/{2n — 9) FORMULA: (r/r') = V2n/(2n — 11) 
Pair UXYZ rXYZ og 2n Pair rXYZ rXYZ ^r 2n 
reference n contro] check 7 2n—9 reference n control check 7 2n—11 
Ren. 6 7.8 13.3: 1.71 101 7 5.3 7.57 1.43 
Ren. 6 4.2 11.3. 2.69 102 7 4.9 74. 151 
Ren. 6 6.4 108 1.69 106 7 38 109 2.87 
2.03. 9.00 107 7 87. 18.0. 2.08 
101 Tdi 155 8,5 +155 1.97 2.16 
102 7 5.3 Tal 4. 1.34 101 10 4.6 7.1 :.L.66 
106 7 5.6 11.8 2.11 102 10 4.9 7.1: 1.46 
107 7. 130 164 1.26 106 10 5.1 95 .41.87 
l1 7 ‘290 373 129 107 JO. 127 153 12] 
12 7; 192 37.1 1,93 11 10. 319 329 1.03 
1.58 1.67 12 10. 224 346 155 
101 10.< 46 9.8 2.13 146 1.49 
102 10 5.0 6.9 1.38 101 15 5.2 63 1.22 
107 10 15.2 14.3 94 102 15 5.9 73. 1.24 
11 10 382 30.4 ‚80 106 15 5.5 90 165 
12 10 . 29.7 33.6 1.48 107 15: 13.7 153 1.11 
1:35: 0.1.35 11 15° 29.3 997 "1099 
12 15 252 33.2 132 
126 1.26 
101 28 5.5 5.7 103 
102 28 5.8 69 120 
11 28. .268 289 1.08 
12 28 25.0 35.3 140 
118 1.12