and the same for Gy ei = 3,4). In matrix notation 
r X 
36, OG. 4 3C, A Xl 
OE qc A YI 
-- - » 
[58] jb ^ d E) yi dy, 
epi Tf | 
Buses s. $6. - 
: mn STE A y4 
dx; y dvi | 
or 
G = E(G) + M . e 
By definition 
| - T 
V(G) = E {(G-E(G)).(G-E(G))} = 
= E{M.e). M.e)T } = 
= M.E {e.eT} MT 
T ; 
where E {e.e } = V(X), and in acordance with (1) s 
V(G) » c? M.MI- 10 
13 
: : T 16 
after compütation. M M'.- 4. I, and then 19 
VG) mur (2) 25 
2x2 28 
31 
Standardized deviations m 
>4 
For each model we can compute two deviations: d;=1, 1) and - 2 
dpz7lp-l5,, whose common variance is 402 (in accordancé with(2)), pa 
where .C* is the variance .difined in (1), or as usual, the. - a 
variance of unit weight for the measurements of photo-coordina He 
tes of fiducial marks. a > 
The standardized deviations are (d,-4a)/402 and (d,-dp)/40°. - de 
We can assume that the two sets of deviations are normally - 25 
distributed and also that d4-d,-0. So, the two sets of standar 51 
dized residuals, d4/4c2 and dp/4c7? are the observed values of ce 
the same random variable, d, normally distributed N(O,l). 7 
The numerical values obtained in the next section confirm the 70 
assumption. 75 
‘| 76 
Numerical example 79 
First at all we compute the deviations da and dp for the whole AG 
block. Second we compute the mean, mg, and the variance og, for 25 
the whole da and dy. 91 
If the measurements are free of gross errors the mean mao and 5 
C4 220, that is the standard deviation of unit weight for the - 97 
measurements of photocoordinates of fiducial marks is cg/2.