The "Sequent" 
paration of the 
> also identifies 
ion parameters 
pplied to lunar 
proved from a 
have different 
are very few 
vorse than the 
. Even for the 
Davies et al, 
TA 
njugate image 
screen. These 
ues of object 
ed. These are 
for each point. 
easurements, a 
the "Sequent" 
pecified. This 
ments, a long 
ts, and a small 
dard deviation 
the given limit 
point and is 
it is found, we 
jint. In every 
duced. If the 
" than the limit 
| "bad" image 
3 errors. From 
; for the future 
NT 
bundle block 
ters and object 
nates are from 
one camera, or many cameras, the navigation parameters are 
from different orbits, and the object coordinates of control 
points are included as uncorrelated measurements in the 
adjustment. The navigation observations can be transformed 
through the spacecraft trajectory and the nominal camera 
orientation. 
The offset and drift parameters of the navigation data can be 
used as observations in the adjustment, if their values are 
known. If we only know that offset and drift exist for the 
navigation, but we do not know their values, these parameters 
are used also as unknowns in the adjustment. We will discuss 
this problem further in section 4. 3. 
The collinearity condition is the basis for the bundle block 
adjustment (Kraus, 1994). It consists of non-linear equations. 
After linearization of the collinearity equations, we obtain the 
following error equations: 
Vi(x) ^ 8; (x)X05 * ai (y)y0, * 21(7)70 
*41(9)9j * 31(9)95 * CK) 
")X*k T3;y)Yk-8jzyk-l(x: Da 
Vi(y) 7 bigyX0j * bigyyY0, * biz 
*bi( o9; + Pico) ®; + Pipe)” 
Dunphy TO 
These unknowns represent the six elements of the navigation 
0., y0,, z0;, ¢., @;, x.) for image j, and the object 
(10,70 205, 9 j [j^ K,) forimage] j 
coordinates for the conjugate point k (xp Yio Zp )- Vix) and 
Vi(y) are the improvements for the image point i. 
The error equations of the other observations are summarized as 
follows: 
For the control point observations of point k: 
"Gr Gn Qu 
"ko) 7k Ik) m 
(2)c 
Vio P eI * 
are the observations. 
where f(xy Ge) and Iz) 
For the spacecraft position observations of image j: 
(20) "305 50) uiro) 7, 0) GR 
*jyo) 729 lj) "*ntyo) *; noo): OP 
(3)c 
Vi(z0) 7 0j -!j(z0) ^ *n(z0) ^ 5j^n(z0) ' 
where Lixo) Ij (y0) and Li(z0) are the observations. 
For the spacecraft orientation observations of image j: 
"o7 *j-lj(oy-9n(p) ^ Sj]nqg): (D 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
(4)b 
(4)c 
Vj(e) ^j ^l j(v) - 9n(v) - 5j *n(o) ' 
Vite) = Lice) Tne) 7 3j an) * 
where / 
io» !jto) 
and /. are the observations. 
JO) 
In (3) and (4), c nC) and d nC) are the offset and drift of the 
navigation parameters for orbit (group) n. s j is the distance 
difference of the orbit for image j. 
The unknowns, their standard deviations, and the corrections of 
the observations are calculated using the method of least 
squares with reference to these error equations. 
4.1 The Robust and Baarda method 
We can use the Robust method (Klein et al. 1984) and the 
Baarda method (Baarda, 1968) for the elimination of gross 
errors of the observations in the bundle block adjustment. The 
Robust (Danish method) can identify quickly a large number of 
blunders in a single run, but the method is less effective if the 
redundancy numbers show great variation. The Robust method 
eliminates only gross errors in image observations, but does not 
search for gross errors in other observations (position, 
orientation, and control points). The results (Table 2) show that 
if very large errors exist in the observations this method will not 
find all of them. 
The Baarda method is much better at finding gross errors in all 
observations. We can search for gross errors not only in image 
observations, but also in position, orientation, and control point 
observations using this method. There are generally no, or very 
few control points available for the adjustment of planetary 
image data. Therefore the navigation parameters for every 
image, should also be used as observations in the adjustment. 
An observation, which contains a gross error, is not always 
eliminated, but instead a smaller weight is applied to the 
measurement. For example, Pnew = Pold / 5, where Pojg is the 
correct weight. The new weight Pnew is then used for this "bad" 
navigation observation, in further iterative adjustments. 
The Baarda method is allowed to eliminate only the largest 
error in every iterative adjustment. Unfortunately this method 
requires more computing time if there are a large numbers of 
gross errors. 
4.2 Variance estimation 
There are a lot of different kinds of observations in the 
adjustment of planetary image data. Every kind of observation 
has a specific precision, but these are unfortunately unknown. 
A priori variance of the observations need not be known, if 
there is only one kind of observation for the adjustment. But a 
priori variances must be used for determining the weights in the 
adjustment with more than one kind of observation. We can use 
the mathematical method of variances estimation (Roa 1971). 
Zhang (1990, 1994) has successfully used this method in the 
adjustment of a network with angle and distance measurements, 
and in the adjustment of gravity measurements. 
This method is used in the paper for the bundle block 
adjustment of planetary image data. The observations apply to 
single groups. The image observations divide into "n" groups, if 
the images are taken from "n" cameras, The position and 
orientation observations are created in "m" groups, if the 
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