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- A combined least-squares adjustment of all the data. In this case an S-base is
introduced, eliminating the rank-deficiency of the least-squares normal matrix.
This method is suited for free-network adjusting techniques. Known control points
are not available.
- A constrained combined least squares adjustment using all the data. Again an S-
base is introduced. In addition control points are available. The coordinates of
these control points are part of another network, normally a geodetic one, which
in most cases was measured earlier in time. These points do have some variance
which is described with respect to either a known or unknown S-base. The Delft
approach tests the quality of these control points with respect to the newly
obtained measurements. However it assumes the same S-base for both networks.
When the covariance matrix of the control points is known, an S-transformation is
needed in order to describe this matrix with respect to the introduced S-base. In
case the covariance matrix is not known one introduces an artificial matrix
describing the precision of the control points with respect to the introduced S-
base. Normally S-transformations are used for variance/covariance
transformations between different coordinate S-bases. In photogrammetry,
however, it may be possible for the S-base elements to include orientation
elements besides coordinate elements. Examples are the dependent analytical
relative orientation where attitude and position of the perspective center of the
left photograph are kept fixed as well as the x-coordinate of the right photograph
(a mixed S-base of three orientations and four coordinates) and the bundle
adjustment, where one may chose the S-base in six orientations and one distance.
The precision of control points is described with respect to a seven-coordinate S-
base.
An S-transformation between these two bases is then required.
2. S-TRANSFORMATIONS
Consider an adjustment of a geodetic/photogrammetric network using the method
of variation of the parameters (Tienstra's standard problem type ll, ref.5). The
linearized observation equations then are:
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