nal 
U 
a- 
en a 
re 
Molenaar /15/ has proved that in the case of only random influences the estimators 
p, 3%, WT 8532, TS | are indeed unbiased, but not sufficient estimators for 
the corresponding parts of the trace of the variance-covariance matrix of the 
estimated check point coordinates. 
The r.m.s. errors (estimators) are often accepted to be unbiased without any sta- 
tistical investigation or from the plots of the residuals a systematic deformation 
is stated or not. Molenaar /15/ has shown, that a sophisticated statistical treat- 
ment is possible to get a better decision basis. He interprets the photogrammetric 
adjustment as an adjustment in steps and is thus deriving the test criterions. 
In the following the corresponding test criterions are derived with help of the 
concept of the general linear hypothesis (29), which seems to be a Tittie bit 
clearer and which makes evident at the same time a suitable computational strategy. 
We suppose the statistical model (28) and start from the null-hypothesis that the 
"n (at, «6T 
is the weight coefficient matrix of the esti- 
common residual vector dX 
; ^ 2 
buted with dX~ N(dX, 04 x)" Gex 
mated check point coordinates. 
A 
, 427) is multi-dimensional normally distri- 
Thus mo becomes 
  
ETT S ySez gti, p = 2p, * p; = total (47) 
PPpl pl pl number of check point coordinates 
with 
dX = sub-quantity for the check points of dx (see (13) 
S S ; ST SI uS. al 
X” = "true" check point coordinates vector X" 2 (C, Y ,Z ) 
"à - vector of the approximate values for the check point 
coordinates in (1) 
Mostly * - xN = 0 can be introduced. 
Hence we get the test criterion 
R : 
T = A , (48) 
p'oo 
with 
-1 
Rs (di- M d af oS) n 
SPh vS in^ b SP h. xs 
» (SP 5-xS) q^ CEP ex) 
If in model (1) the check point coordinates are arranged at the end of the com- 
plete solution vector, then Qi is obtained without additional effort during the 
triangular factorization of (ATPA) - see Section D1. Under H, 1 is distri- 
buted as the central F (p,r). The power of the test depends on the alternative 
hypothesis and may be computed as mentioned before. Mostly it is advisable to 
base the alternative hypothesis on. the assumption of a polynomial deformation. 
In any case the rejectionof the null-hypothesis should give rise to examine both 
the additional parameter model (or even to introduce such a model) and the con- 
trol and check point accuracy. 
It is easy to see how the test criterions for special coordinate vectors, e.g. 
X, Y independent on Z, can be derived.