€ 
-43- 
in which t is the time interval between scans and T the correlation time of the Markov-Process 
aplied (it is related to x. ). The advantage of the method is, that the observation equations (12c) 
become very simple: 
ay 
A 355 
£a + 
a * dy, 
T 
While there were 18 parameters to be solved for in (12c) , there are now 6 x j parameters to be 
determined via equations of the type (121)and (12j) ; this does not appear to be a problem hbwever, 
since only. the:parameters j -1, and j * 1 will be correlated. The question is of course whether the 
flight parameters do vary under the conditions of a Markov-Process. Studies of Held /34/ and Leberl 
/59/ seem to indicate that stabilized platforms have definite (Schuler-) periodic variations of the 
various components involved. A Fourier series expansion may therefore most likely represent the 
variatious better than a stochastic or a polynomials and Fourier series expansions are much more de- 
pendent on control point configurations. It may well be that a stochastic model dois less harm to the 
data in certain cases. 
3.5. Interpolation in a Stochastic Field 
A more simplified approach is possible when the coordinate differences between (direct or processed) 
image and the transformed ground values (by use of some deterministic approximation) can be con- 
sidered as a stochastic field. 
The simplest application of this principle are the weighted arithmetic mean and the moving average 
(Baker & Mikhail /7/, Leberl /59/). The weighted arithmetic mean interpolates the discrepancies 
between measured and computed Kr an influence area of radius € from the inter- 
polationpoint j as : ax; dy; for the control points i located 
  
with the weighting function Psy expressable in terms of the distance between points p, and P;