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.