|
|
navigation parameters belong to "m" orbits. The object
coordinates of control points belong to another group. The a
priori variances of all observation groups are calculated during
the bundle block adjustment. The estimated values of the a
prirori variances are used in the last step of the adjustment.
4. 3 Method for elimination of systematic errors
in the navigation observations
Planetary image data are obtained normally from many orbits.
The corresponding time difference can be very large. From this,
the navigation parameters between different orbits, and every
navigation parameter within a orbit, can contain variable offsets
and drifts. We define one offset and one drift for every
navigation parameter within an orbit.
Because the initial navigation data are not well known, and
difficult to estimate, we will adjust only those parameters which
have the most influence on the results of the adjustment. The
least influential navigation data remain fixed.
For the elimination of the systematic errors, we perform the
bundle block adjustment in several stages:
In the first adjustment, we assume that there is no offset and
drift. After this adjustment we have improved the navigation
observations. Using the method of least squares reference to the
following equations, we can calculate the offsets (eq. (5)), or the
offsets and drifts (eq. (6) ):
"jQ 7 nC) o
or
"j() 7 *n() 7 5j*n() (e
where ""= x0, y0,z0, P, @, K .
The meaning of the other symbols was explained earlier.
The adjusted offsets and drifts for all groups of the navigation
data and the standard deviations are stored in an output file.
With the output information, we can determine which
navigation data contain the systematic errors. If the adjusted
offset and drift in (6) are larger than their standard deviations,
this implies that the navigation data contains systematic errors.
If this requirement is satisfied only for an offset (eq. (5) ), there
exists only an offset parameter. Because the adjusted parameters
are correlated, the estimated values are probably not correct. We
can only detect whether there exist offsets and drifts in the
navigation data, by this approximate method.
In the second adjustment, the offsets and drifts found are used
as unknowns in the bundle block adjustment (eq. (3) and (4) ).
The offsets and drifts, to which the estimated values are much
larger than their standard deviations in this adjustment, are used
as unknowns in the last adjustment.
5. SIMULATED CALCULATION
In our bundle block adjustment of planetary image data,
simulated and practical tests were carried out. The simulated
data are useful for checking the correctness of our methods. The
simulated data are produced as follows: First, we carry out the
bundle block adjustment for the example image data (a part of
Test 1 in the section 6) resulting in adjusted object coordinates.
In the second step, we use the backward method for the
calculation of the image coordinates for these object points.
Finally, we add known random errors, known gross errors, and
known systematic errors (offset and drift) into the observations.
The simulated data come from two cameras, and two orbits
(Table 1).
Control Number ofConjugate {Image Size of
points images points points pixel
10 32 40 344 150 (m)
Table 1: Simulated data
5.1 Elimination of gross errors
Thous, our simulated data contain twenty gross errors in the
image observations, one gross error in the position, in the
orientation and in the control point observations. Ten of the
gross errors in the image coordinates are "large errors". Their
values lie between 500 and 3000 (pixels) (group 1), that is, the
actual values are very much larger than their true values. There
are ten gross errors in the image coordinates (group 2).
The three methods, Sequent, Robust and Baarda, are applied
separately here for searching for gross errors. All ten "large
errors" in the image coordinates are eliminated by the Sequent
method, in the first step of the adjustment. The Robust method
finds only seven "large errors" in the image coordinates. The
remaining errors, particularly the three "large errors", greatly
corrupt the adjusted results. In comparison, the Baarda method
finds all gross errors, in all observations (Table 2).
Error Size of Sequent Robust Baarda
types errors
group 1 of 500 (pix.)
image to 10/10 10/7 10/10
points 3000
group 2 of |10 (pix.) :
image to 10/0 10/0 10/10
points 40
positions 2 (km) - - 1/1
orientations [0.2 (deg) |- - 14/4
control
points 2 (km) - - 171
limit value = 10 (km) for the Sequent method
limit value = 4 for the Baarda method
Table 2: Elimination of gross errors I
Error Sequent |Sequent
types Robust Baarda
group 1 10/10 10/10
group 2 10/9 10/10
positions - 174
orientations |- 1/1
points - 1/1
Table 3: Elimination of gross errors II
In practice we always use the Sequent method during the first
step of the adjustment. After that, the Robust, or the Baarda
method are used in the bundle block adjustment. In this
example, the Sequent method has eliminated the ten "large
errors" in the image measurements; the Robust method finds
nine errors in these observations. The Baarda method has found
ten errors in the image measurements and all three gross errors
in the other observations (Table 3). These results show, we
should either use, in combination, the Sequent and the Baarda
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
method, or the
block adjustme
5,2 Variance
The simulate
groups of im:
position orier
coordinates ©
estimate five :
adjustment. O
are estimated,
the position c
modules, with
examples are |
ID). Three diff
initial 2, and
priori varianc:
not dependent
estimated 1
initial 2
estimated 2
initial 3
estimated 3
Table 4: A pi
[Values
true
initial 1
estimated 1
initial 2
estimated 2
initial 3
estimated 3
Table 5: A |
5.3 Elimir
The simula
(example 1
2). Using
determined
