filtering, 8.5.0. 
The more efficient methods rectificate the image data by 
using the exact relations between image and terrain coordi- 
nates (collinearity equations) and describe the time de- 
pendent variation of the exterior orientation parameters of 
the sensor in a more or less rigorous way. Up to now mainly 
polynomials or Fourier functions were used for that purpose. 
The unknown polynomial or Fourier coefficients are estimated 
by a least squares adjustment using a sufficient number of 
control. points. 
A TIME DEPENDENT MATHEMATICAL MODEL FOR LINE WISE GENERATION 
OF REMOTE SENSING DATA 
In 1976 a general model was suggested by H. Ebner /1/ which 
starts from the collinearity equations as well, but des- 
cribes the variation of the exterior orientation parameters 
in a new way. It considers that this variation is caused by 
the dynamic reaction of the airplane on air turbulences and 
by the piloting system. Both together cause, that the de- 
viations Aw, A$, AK, aX o» AY 4» AZ, of the airplane from the 
nominal values don't increase with time, but remain within 
certain (time independent) boundaries. 
In 1976 stationary stochastic processes , for instance first order 
Gauss Markov processes (GMP) have been considered as a suitable 
model for describing the mentioned variations by time, par- 
ticularly because of their assymptotically time independent 
variance. In the meantime the model has been extended to a 
mixed order GMP. Empirical investigations however have 
shown, that the second order GMP, a special case of the 
general mixed order GMP, is the most suitable one to de- 
scribe the variation of the exterior orientation parameters 
(for further information see /27). 
The second order GMP is a stationary stochastic process. In 
discrete formulation it can be desribed by the following 
equation.