go
The difference is
D0 StdP PsDt dPDi
and further for nearly perfect inputsexpressed in terms of models
Dom Sim XdPm.
The establishment of an error model dPm is based on physical
understanding of the operations concerned and on the related
analysis of disturbances.
Frequently the model dP m is established in stepsstarting with
a coarse model and refining it gradually with the knowledge
gained, and stepwise refined, experimentally.
The unknown parameters of dP m can be estimated from a given
input structure Si and the measurable distortions D0 in the output.
This estimation can be based on the method of least squares,
which is convenient also for the judgment of the accuracy.
Another problem, deserving some attention, is the separation of
random and regular errors, dr -}- dm, and the detection of individual
sources within each group. The separation and detection may be
seriously hampared by the cumulative sum- and mutual compen
sation of the partial errors in the output. This may be true even
in the case of simple operations described by accurate mathe
matical models. If the partial errors are not sufficiently distinctive
in the output, the separation of corresponding error sources is
unsharp or even impossible. In such cases, it is expedient to classify
the sources of errors into groups with similar effects in the output.
Thus instead of individual sources, groups of them are represented
in the mathematical model. The separation of such groups is con
siderably easier.
The comparative tests are generally restricted to the judgment of
distortions D0 in the output. This judgment applies to the represen
tative values (e.g. mean and extreme values) of the system para
meters, to representative input structures, and to representative
(e.g. mean and extreme) environments. The structure of the process
for a given application is irrelevant; the system may be regarded
as a black box.
4.6. Power of a testing method
The power of a testing method is determined by its adequacy
and consistencyThe power may be measured by the amount of
knowledge on the performance gained in a test (when applied to an
imperfect system). It can be estimated analyticallywith error
synthesis and error propagationor experimentally.
Since the analytical approach is assumed to be known to photo-
grammetrists, we shall restrict some further considerations to the
experimental approach.
