2 
mow 
i 
     
corresponding photo coordinates in the left and 
right photographs is listed in ‚table i. The 
‘calculated photo coordinates conform to the 
‘normal case‘ in terrestrial and close range 
photogrammetry. 
Table i:True object space and photo cenrds, imm) 
10.000 10,000 -10,000 
2 20,000 140.000 0.000 
13 20,000 2,020 5,2900 2.000 
2 
£2 
d 1200 3840 0200 
0.000 -10,.0200 0.000 -10,000 12 
00 3840 -500 
15 10,000 -10,000 -10,055 - 
10,0020  &00 3842 -500 
1& 0.000 -10.000 -20.000 -10.000 000 39840 -600 
17 0.000 0.000 -20.020 0.2000 020 3840 O00 
i8 2.000 10.002 -20.0020 10,000 O00 3840 5040 
19 10,222 2.000 -12,020 0.000  &00 3840 000 
21 7,914 7.934 -07,.,934 7.934 E00 48320 8500 
22 15.848 7,934 6.000 7.934 1202 43830 AOD 
23 15.8858 0.0020 0,2000 0.000 12200 4830 2020 
7& 15,868 —7,934 0.000  -7.934 1200 48480 -520 
25 7.938 -7.234 -7.934 -7.934 E00 4882 -500 
26 0,000  -7.934 -15.888 -7.934 DD 4840 - 400 
27 0.000 0,000 -15.8858 4.000 000 4840 O00 
28 2.0200 7.9348 -15,.,B858 7.934 0020 4842 oo 
29 7.933 0.0020  -7.934 0,000 800 $8430 O00 
si 5,575 b.975 "5,575 8.575 600 7845 400 
29 $3,151 5.575 0.000 4.575 i200 58430 500 
SS 12,1541 0,000 2.000 0,000 1200 5840 000 
S4 13,151 a. 575 0,000  -5.575 1200 5840 -500 
35 5,575  -5.575 -5.575 -6,275 600 8840 -502 
36 0.000  -5.575 -13.151  -6.575 000 3842 -500 
27 4.000 0,000 -13.151 0.000 0200 5840 020 
38 2,600 &.EIS -12.151 8.575 000 5840 600 
S9 UB.RTE 0,000 -05.575 2,000  &00 5840 000 
41 10,200 10.200 -10.2H80 10.2700 598 3750 5598 
32 19.200 10.2020 $0,000 10.200 1200 4000 5738 
3 18,071 0,000 0,002 0,000 1200 4250 O00 
44 20.800 -10,.202 3,3320 -10.200 1434 4499 -717 
45 10.200 -10.2020  -5.0020 -10.200 756 4781 -756 
$& 0.002 -10.200 -15.350 -10.200 000 5002 -797 
47 0.020 0.000 -148,529 4,000 000 5250 -837 
48 0,000 10.202 -13.985 10.2020 000 3492 875 
49 10.202  -1.0020  -3.800 -1,000 3874 2485 -086 
B-1200 mm,f-545.0mm,Format-90x635 mm, Xo-Yo-Io-0.0 
S.E.:8B-0.1 mm,B8f-0.01 mm,Bx-28yz8x '-8y'-0.005 mm 
Points 41 tc 48 are used as MCW variable points. 
Ft.49 was used as MCV only in case L of table.Z. 
3. THE MULTI-CONTROL VARIATE {MLCY) METHOD 
The idea of a single-control variable Monte 
Carlo technique for reduction of variation of 
sample observations, which thereby increases the 
precision nf the estimate, can be readily exten- 
ded to a multiple control variates technique. 
The computational procedure to be followed in 
this multiple case is explained in. íKobayashi, 
1981). Following this idea, we proceed to define 
a new random variable ZI, by 
tsYi Jobi OG IO -EDNE DD, i=1,2,.,k. ...{3.1) 
7 
   
QE2...Xhl and if D denotes the cross cova- 
e vector between Y and Xi 
? 
if 8 denotes the covariance 
x1 
r 
83 i=Covili, 143, 3,3 :=:8,2,...0, ant 
and Di= Dowl¥, 231, 4%8,2,4 0.0, «n 3e] 
then the optimal value for B-Íbi,h2,...,bk] iz 
En 
N 
m 
E 
ta 
which leads to 
157 
VarlZizVarIYi-C 8 C-VariYi(i-Rysx! sedia. mi 
Where Ryx is the multiple correlation coeffi- 
tient between Y and X.The Square of the corre- 
lation coefficient is often called the coeffi- 
rient nf determination as it represents the 
fraction of the total variation nf Y explained 
by variation nf X. Here,as EIIJ-EIYl,computed 
value of I is used as Y. The idea behind the 
multiple-control variate variance reduction is 
similar to regression apalysisicspecial case of 
analysis of covariance). However, in the regres- 
sinn analysis we usually wish to investigate the 
power of a set nf predictive variables X in 
explaining the variation nf a response variable 
Y, whereas in variance reduction by the multi- 
control variate method, we evaluate the  addi- 
tinnal reduction in the variance against the 
additional computation involved. We should bear 
in mind that it is possible to achieve any 
desired reduction of variance by using the mean 
nf a sufficiently long simulation run, Î.E., HE 
could use the arithmetic mean in place nf each 
nbservation. The MOV method has been successful- 
ly applied in studying the queueing system. 
Referring tno Graver, 196%),{Kebayashi, 1781) 
reports that multi-control  variate method 
ithree control variates) cuts the variance to 
about 8% {that is by a factor nf 12.5) nf the 
  
  
initial value. It is interesting to note that 
the mean value of I and Y would still be the 
came when the negative value before the summa- 
tion in eq.3.1 is changed to a positive sign. 
This fart has been used to modify eg.3.1 as 
follows. 
PIR)ISY4RO) Qe bi CHE ID -ETY 32 for Bich zer (38a) 
ZiRI=Yi{R3+S biCXi{R)-ELX3S for bi}? 
SIGNIFICANT RESULTS 
Some combinations / variations nf experimenta- 
tion involving HEV parameters were carried out 
through computer programs written in HE Fortran 
and implemented on Casin FP4100 micro- computer 
{IBM XT compatible) and the results obtained are