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For the stochastic model of the observations, the 
following assumptions were made: the observations 
are not correlated, while the weights of the GPS 
observations and the observations of the ground 
control points are evaluated with respect to the 
weight unit of the photogrammetric observations. 
The observation equations listed above, together 
vith those derived from the seven-parameter 
solution, are adjusted simultaneously. 
TESTING THE STATISTICAL SIGNIFICANCE OF GPS 
PARAMETERS 
The test of significance of the GPS parameters was 
to determine if the parameter values were 
significantly different from zero and/or if 
parameter groups were significantly different from 
each other. In this way insignificant parameters 
are either eliminated from the adjustments or 
grouped with other parameters: thus  over- 
parametrization of the system is avoided. 
The tests of significance were formulated as 
statistical hypotheses and are tested using the 
test quantities developed in [3]. 
A null hypothesis which indicates that the 
parameter values are not significantly different 
from zero can be written as 
Hoc: BYGLY 30 
When testing the significance between groups of 
parameters (e.g., different GPS parameters 
introduced per strip), a null hypothesis, which 
assumes that the parameters in group 1 are not 
significantly different from the parameters of 
group 2, can be formulated as 
Ho Foil gi] s isl. 4m 
where 
m 
Gi 
E(.) 
number of parameters in the groups 
the parameter values 
indicates mathematical expectation 
superscripts 1 and 2 show the 
parameter groups 
To assess the test statistics, the weight 
coefficient matrix of the GPS parameters should be 
evaluated, by applying Gaussian reduction in the 
reduced normal equations. In this way the GPS 
parameters are orthogonalized with respect to 
model orientation parameters and their weight 
coefficient matrix can be isolated. 
TEST DATA 
Using both simulated and real data photogrammetric 
independent model blocks could be generated at 
different scales, with different measuring errors 
and randomly generated model orientation 
parameters, while the GPS data could be produced 
with different observation errors and with 
different kinds of systematic errors modelled with 
constant, linear and quadratic terms and their 
combinations. 
The real data were taken from the "Flevoland" test 
field in The Netherlands (the flight took place on. 
June 1987). The block consisted of 16 parallel 
strips, each with a length of approximately 4 km. 
A Wild RC 10 aerial camera with a focal length of 
213.67 mm was used (photo scale 1:3800). 
The photogrammetric measurements were carried out 
on a Kern DSR1 analytical plotter and the 
independent models were analytically formed. 
The GPS instrumentation consisted of two Sercel 
receivers, one stationary NR52 receiver at a known 
reference point (see fig. 1) and one TR5SB 
receiver onboard the aircraft. 
The coordinates of the ground control points were 
determined using both conventional geodetic 
methods and GPS. Further information and detailed 
analysis of the block data can be found in 
[6,10,11].. 
À part of the block consisting of four strips with 
15 to 18 models per strip (66 models in total) was 
used for the experiments. The part of the block 
and the available control points are shown in 
figure 1 by the dashed lines. 
    
  
   
LARSERPAD 
VOGELWEG 
   
  
  
      
A A A à 
  
RE 
  
  
  
  
  
  
  
  
    
  
  
| GOOISE WEG 
  
DE 
  
a Ground control point 
Q Stationary GPS receiver 
Figure 1. The test field "Flevoland" 
EXPERIMENTS AND THEIR ANALYSIS 
A number of experiments were carried out with 
simulated data to test the mathematical and 
stochastic models and the computer programs, and 
to verify and enhance the conclusions drawn from 
the experiments with the real data. 
The findings of these experiments were 
incorporated in the analysis of the experiments 
with the real data. Here the results of two 
experiments related to the testing of the 
significance of the GPS modelling parameters are 
presented. 
In the first experiment, a block of two strips 
with 10 models per strip was generated. It was 
controlled with four XYZ points at the block 
corners and a chain of height control points at 
both the beginning and end of the block. The 
generated GPS data contain constant and linear 
terms, The adjustments were performed using 
constant (CT), linear (LT) and quadratic (QT) 
stripwise modelling, i.e., a total of 18 
parameters were used. 
The three groups of parameters were tested per 
strip for their significance according to the 
statistical tests developed in [3]: the results 
are given in table 1. 
505