h.2.2. Interpolation and Filtering of Exterior Orientation. 
4 4 
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re 
  
In the case where the exterior orientation is measured, a preliminary 
step in reducing the data should be undertaken. This step entails the 
elimination of the error of measurement, which is possible to a certain 
extent, using the methods developped in the theory of random functions. 
In the following, reference is made to section 2.2.2 on the stochastic 
model of exterior orientation. 
The measurements of f(t) (the vector of the elements of exterior orien- 
tation)-are-erroneous. S80, to use—the proper values for tne exterior 
orientation, the measured quantities have to be reduced for the error 
of measurement which has to be estimated; i.e. the measurements have 
to be "filtered". 
The registration of the measurements f'(t) of the 6 components of ft) 
can be discrete or continuous and analogue or digital. For numerical data 
handling, however, a digital, discrete form is required. For the digiti- 
zation a certain interval At for the discrete measurements is to be chosen. 
  
One has to realize, that, in the frequency domain, all frequencies > E 
are certainly lost. This critical frequency is also called "Nyquist-frequency" 
[66 ]. One has to choose it in a trade-off between numerical effort and 
accuracy. In this way, the components of the vector process f'(wt) become 
stochastic sequences: 
p i=l (+) i = 0, 15 2 6.909999 
: jm 2. 
The problem now is to estimate f(t), or better g(t), from the measured 
£0). 
To this end, the mean m(t) has first to be subtracted from the measurements. 
4 
Not going into the theory of aerodynamics to find a reasonabl theoreticall 
8 3 
justified model, a flexible and general way is to eliminat m(t) with.the 
Q 
B 
mo. o 
— 
NO. Q 
Dal 1 > reer x 
help of a "moving average" (see Kendall | 66], Yaglo 
procedure which is very successful in its application to digital terrain 
models. In this, m.(t.) is estimated as the weighted mean of a pregiven 
à 4 
© 
M 
d 
1 p & AN 
number of measurements L(t; -1), GUT RB, 62e) fU. -n 
t — t + 
ft + 01); f.(55, 112), ean. ul lt, +n). The weights are to be chogen 
i J 1 J 
in such a way, that the estimated m.(t.) can be interpreted as the 
ordinate of & polynomial of order p: