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control point coordinates are introduced as free of errors (diag (Pp) + 9), like 
it is often required in practice, and if the additional parameters^are treated as 
free unknowns (P = 0), the ordinary GauB-Markov Model, i.e. the usual case of 
Adjustment of Observations is obtained. 
The matrix Pp allows to introduce a-priori known accuracy standards of the control 
point coordinates; the same applies to the matrix P7 and the additional parameters. 
Using Pp = 0 the system becomes singular. 
Under certain circumstances and with certain parameter sets the treatment of sys- 
tematic errors as free unknowns (P, - 0) may lead to remarkable deteriorations of 
the condition of the system of normal equations. Therefore it is expedient to in- 
troduce P7 # 0, thus protecting to some extent against overparametrization. 
With Pp? Owe obtain a weighted minimal fitting (with respect to a 3-dimensional 
similarity transformation) of the photogrammetric points onto the control points. 
With the set of additional parameters from (1) we are fully flexible, there is no 
restriction concerning their number and type. This enables us to introduce block- 
invariant parameters, just as parameters which belong to a single strip, to a 
certain group of images or even to a single image. 
In close-range applications this concept has to be extended by observation equa- 
tions for additional measurement elements as angles, distances and exterior ori- 
entation parameters and by some special conditions as straight line conditions, 
surface conditions, angle conditions and so forth. For the purpose of the follow- 
ing studies these equations can be omitted without loss of generality. 
The same applies to other image geometries which may replace the perspective re- 
lations. 
For the determinability of systematic errors and the related eigenvector problem 
see Grün /11/. 
The problem of a suitable choice of an additional parameter set was recently dis- 
cussed in Grün /10/. Thereby the functional, numerical and statistical advantages 
of bivariate orthogonal parameters, introduced by Ebner /6/, have been emphasized. 
A strategy in additional parameter construction, i.e. the choice of the design 
matrix A, (see (1)) must consider two basic requirements: 
- The estimation of x and 06 in _.(3) has to:be unbiased, i.e. the systematic 
deformations have to be modeled as well as possible 
- The variances of the additional parameters (and of the other parameters of 
system (1))should be as small as possible. 
To the first point experiences, gained over many years, have shown that polynomi- 
als are a proper device in modelling systematic image errors. Thereby the favour- 
able property of bivariate polynomials consists in its capability to compensate 
the total systematic effect at all points of a presumed regular image point screen 
(Ebner /6/). 
The second requirement, which includes equally the demand for minimal covariances, 
leads to the condition 
0. = (A pA) | mes Min , (4) 
or if only the additional parameters are regarded