altitude and speed have exact the normal values h 0 and v 0 . . If the 
real values v and h differ from the normal values, than formula*2> 
changes to 
m 
AT 
Vo • AT 0 
V ■» h - -S 
But there is one problem. The formula 2 for exemple assumes the 
knowledge of the angular speed over the sampling period. To make 
the formula practicable, one need a prediction of h(t). If we 
knew the future, we could compute the right moment to get 
equidistant image lines. This is possible by using the well 
known Kalman-FiIter, a linear filter algorithm. It bases on a 
model of the airplane motion and contains determinist and 
stochastic contributions. /2/ The so called Euler-Equations 
describe the rotation of a rigid body. They are nonlinear coupled 
determinist equations. 
à-x \ 
- 
M y 
Im* I 
The Jj 
are the moments of 
speeds 
around 
the 
three 
the angular 
airplane axes. The Mj are external 
torques. They contain all kinds of external disturbances, 
produced for exemple by wind and turbulences. With respect to 
these sources, M; have to be described with stochastic terras. 
First experimental test data (see also /1/) show an 
autocorrelation function with time constants of about 10 times of 
the normal sampling period. This allows the construction of a 
simple bandlimited model: 
+ s*; h; * (**) I'eX.Y.* 
<(m>= o <ç. (t) s n -su-t') 
Here is ^ (t) a white noise source. The solution 
stochastic low pass equation is bandlimited and 
distributed. The spectral power density function is : 
of this 
normaly 
The stochastic model contains 6 Parameters and ^t which can be 
found by experimental data analysis. They are related with three 
cut-off frequencies and the three standard deviations of the 
torques. But there are some problems beacause of the nonlinearity 
of the Euler-Equations and the nonlinear relations between the