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| with Givens,
duced normal
x object points
The lighter shaded portions of the structure correspond to
U and d of Eq. 4. This structure is expanded by six rows
and columns (dark shaded portions) to provide storage
for the submatrices associated with a particular image.
Assuming a consistent system at any particular stage of
the process, U and d are fully occupied. The introduction
of a new image into the system begins by setting all
matrix elements of the image submatrices to zero. All
observation coefficient vectors for a given image are
rotated through the entire structure via Givens
Transformations. All subsequent images are treated in
the same manner. lf observation deletions or re-
measurements are required in a previously introduced
image, its existing associated submatrices must be re-
positioned in the dark shaded areas. The necessary
observation vectors are then rotated through the system
with weighting appropriate for either insertion or deletion.
Back substitution into the U,d system at any time yields
the current solution vector for the object point
parameters.
3.2 Approximate Values
Providing optimum initial parameter values for OLT is a
major concern associated with sequential processing in a
non-linear model such as the collinearity equations. The
costly re-linearization of the system is avoided by using
the same set of initial values throughout the sequential
process. Coarse values may eventually cause drift in the
solution vector sufficient enough to produce a detrimental
effect upon efficient blunder detection and precision
evaluation. The solution is two-fold. The most obvious
answer is to provide good approximate values. This is
not always possible. However, for the assumptions
presented here, namely highly convergent imagery with
measurement restricted to signalised targets, this is
reasonable. Secondly, the performance of a periodic
simultaneous solution provides a "clean" version of the
parameter vector which may be used as the basis for
continuing sequential updating. The procedure is
straightforward. A minimum of four convergent images
is needed to obtain a consistent, reliable system. Four
well-distributed rays per object point are necessary for
blunder detection with data snooping. All object points
with four rays which meet a pre-established geometric
criteria are included in a simultaneous adjustment. From
LU
ZU
a
Figure 2: Reduced normal equation matrix structure
for sequential estimation
137
this consistent system the sequential procedure begins.
The parameters of newly introduced images are
determined by space resection and the coordinates of
new object points with sufficient observations are
determined by spatial intersection.
3.3 Compensation for Systematic Errors
Extending the mathematical derivation above to
accommodate = additional parameters for the
compensation of systematic errors is a simple matter.
For a full bundle adjustment with self-calibration these
may include interior orientation parameters of focal
length and principal point coordinates, plus those of
radial and decentring distortion. Among researchers
reporting experiences in OLT there is a general
agreement as to the importance of additional parameters
in the sequential process. However, to the authors’
knowledge, there are no published findings in which the
effects of additional parameters in OLT are examined.
The capability of recovering these additional parameters
is enhanced in a convergent network and their presence
has a direct influence on object point precision. With the
primary objective of monitoring object point accuracy, the
inclusion of these additional parameters must be
addressed. During OLT, changes in interior orientation
will likely occur which will in turn influence overall
precision. Two approaches should be studied with
respect to their effect on the variance of object
coordinates. The first involves the utilisation of additional
parameters from a prior calibration throughout the
procedure and the second is based on updating the
additional parameters periodically with a simultaneous
adjustment and proceeding with a fixed interior
orientation.
3.4 Blunder Detection
Baarda's strict data snooping technique, based upon the
examination of standardised image coordinate residuals,
is one method which has been utilised for blunder
detection in the bundle adjustment procedure. There
have been more efficient modifications to data snooping
such as the "unit observation vector" method (Gruen,
1982), but the technique remains computationally
intensive and has proven to be the most time consuming
aspect of previous implementations. Investigations into
less rigorous, approximate techniques are needed.
Graphical procedures which are simpler and less
expensive to implement, hold great potential for the
detection of gross errors in OLT. Ongoing research will
compare the efficiency and accuracy of both the "unit
observation vector" method and graphical techniques.
3.5 Appropriate Datum
It is necessary to establish an optimal, consistent system
prior to the start of the sequential procedure. In industrial
photogrammetry the preferred means of accomplishing
this is through the implementation of a free-net
adjustment with inner constraints (Fraser, 1982). An
important problem to be considered is that of countering
the datum defect throughout the sequential procedure.
Two basic options are outlined below.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
