as
ation
lonal
available
A X
lead
+o The
Ko»
imation,
e done
(56)
(57)
not
3 there
reg of
the corrections of the original plate measurements, Without doubt the answer
will provide an excellent approximation value. As a matter of fact, such an
answer may be considered as adequate in itself, if there is evidence of the
presence of systematic errors, a situation which renders an additional
treatment by a rigorous least Squares Solution superfluous. Furthermore, the
method presented with the formulas (56) and (5T) is well suited for computing
in each iteration cycle of the least squares solution as described in Chapter
IV, the coordinates of the points of the model, (Compare remark Chapter IV (B),
page no. (28). |
F. The Determination of the Mean Errors of an Observation of Unit Weight
of the Elements of the Orientation and of the Triangulation Results
The mean error of an observation of unit weight denoted by m is computed
with
mn = EY (58)
The term V'PV , may be obtained directly from the reduction of the normal
equations or by adding the squares of the individual, weighted y and V values.
The letter r, denotes the number of observational equations and d dendbes the
number of unknown parameters. Thus the mean error of a specific observation n
before adjustment is: |
m, = iy (59)
VP.
The computation of m directly from the original measurements, e.g. using the
differences of multiple observations, may lead to & yalue of greater physical
significance. The discrepancies between the different values of m, computed
with different methods provide means to investigate the presence of systematic
errors.
The mean errors of the unknown parameters in a least squares solution are
obtained by multiplying m with the corresponding weighting factors. The
inverse of the matrix of the coefficients of the final normal equation system,
is the matrix of the weighting coefficients. The diagonal elements are the
Squareg of the weighting factors associated with the corresponding unknown
parameters,
41 |
