_2 
P G = —j^-E is the weight matrix for GPS- 
°"gps 
determined camera stations whose coordinate 
accuracy is cr GPS . 
According to the principle of the least squares method, 
the normal equations of combined bundle adjustment is 
as follows: 
B T B + P C 
B T A 
B T C 
• 
• 
X 
' B T L X +P C L C ' 
A T B 
a t a+a t p g a 
A T C 
AP g R 
A T P 0 D 
t 
a t l x +a t p g l g 
C T B 
C T A 
C T C + P S 
• 
• 
c 
= 
C T L X + P S L S 
• 
R T P C A 
• 
R t P g R 
R T P 0 D 
r 
rT Pg L o 
• 
d t p g a 
• 
d t p g r 
d t p g d 
d 
_ DT Pg L G 
considered as a measure for the root-mean- 
square error of the image coordinates; and <j c 
is the accuracy for the ground coordinates of 
observed control points. 
P s is the weight matrix for the fictitious 
observations of additional parameters, which can 
be specified at the signal-to-noise ratio in 
images. 
Compared with the normal equation structure of 
conventional bundle adjustment with self-calibration 
parameters, equation 5 can be viewed as the extension 
with two sets of additional unknowns r and d. But 
only five of the additional submatrices (A T P G R , R T P G R, 
A T P G D, R t P g D, and D T P G D) contain non-zero 
coefficients. The major common parts of the normal 
equations have still maintained the well known matrix 
structure of the conventional bundle adjustment. Then, 
the reduced normal equations can be obtained by the 
standard numerical procedures, leading to the well known 
banded-bordered matrix structure for unknowns t, c, r 
and d. Hence, any of the established numerical solution 
techniques can be applied to solve such a system. 
However, taking into account the correction terms of the 
linear drift error in combined bundle adjustment, the 
adjustment may be faced with singularity. In this case, the 
planning of the block must prepare enough ground 
control points and/or specific flight pattern [Ackermarm, 
1991]. 
Fig. 2 Functional Model of WuCAPSgps