The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part Bl. Beijing 2008 
In Equation 11, the weight matrix W is equal to W = ct^V,” 1 
where \ ( includes the a’ posteriori partial covariance matrices 
of each best estimation, of each solution. 
It should be mentioned that due to the fact that partial solutions 
are non-correlated, the best estimation of Equation 11 is 
equivalent to the corresponding estimation. This can be 
calculated from the simultaneous solution of buildings and 
LiDAR points, which have taken place in the initial solutions of 
the system 10 through Equations 6 and 7. The a’ posteriori 
standard deviation of unit weight a 2 0 with the corresponding 
covariance matrices of the parameters and the observations are 
calculated based on Equations 8, 9 and 13. 
(12) 
contain 4 LiDAR strips (point cloud) and a block of 4 aerial 
images strips over the same area, each containing 4 images 
(Figure 2). For both sensors, an integrated GPS/IMU system 
provided the georeferencing. Traditional aerotriangulation was 
performed on aerial images using GCPs measured by geodetic 
means (0.1m stdv) producing the EO (Exterior Orientation). 
The bundle adjustment resulted in positioning accuracies (EO 
parameters) averaging 0.08, 0.08, and 0.10 meters in X, Y, and 
Z, respectively. The orientation accuracies average 10, 10, and 
9 arcsecs in co, cp, k, respectively. 
In the central part of the survey (also called “test field”) 24 
buildings, mainly medium sized, have been selected and 
photogrammetrically restituted (point dataset). These buildings 
(called ‘buildings-positions’) are located in the overlapping area. 
In Figure 2, an image mosaic, the selected buildings and 
LiDAR strips are illustrated. These buildings are assumed as the 
reference dataset. The area which is occupied by the selected 
group of buildings is about 300,000 m 2 with a perimeter of 
2250 m. 
=OoA(a t Wa)~ 1 A T (13) 
The statistical valuation of the adjustment’s results concerns not 
only the assumptions, which have been made (initial hypothesis 
H 0 ) related to mathematical and statistical model of adjustment, 
but also the reliability of the observations. 
As it has been mentioned, that proposed method assumes that 
the reference dataset is derived by photogrammetric means 
(surface P) and the target dataset consists of the corresponding 
LiDAR points (surface Q) captured over the same overlapped 
area. It should be mentioned that the reference dataset can be 
derived by any other source such as by terrestrial laserscanning. 
But in this research, they were aerial photos of interest. 
The general check of this hypothesis H 0 is achieved by using 
the ratio K/ a l in combination with the % 2 distribution, with r 
degree of freedom. 
The hypothesis H 0 , according to the reliability of the 
observations, is checked based on the ratio v iy /o.. of each 
observation i by using the normal distribution z for a level 
meaningfulness a=0.001. 
The data snooping procedure led to the conclusion that 
approximately 4%-5% of the observations include outliers. The 
above results are in agreement with what have been proven in 
Pothou et al., 2007. 
4. DATA DESCRIPTION 
After implementing the proposed method, it was first tested on 
the simulated data for boresight misalignment estimation 
(Pothou et al., 2007). Next a new dataset, provided by ODOT 
(Ohio Department of Transportation) and CFM (The Center for 
Mapping, OSU) was used for intensive testing. In London, 
Madison County, Ohio, LiDAR point clouds and direct digital 
aerial images were collected in several missions over an urban 
test area. The city includes mainly residential houses and a few 
bigger buildings (such as warehouses and factories). 
The 55 mm focal length, DSS digital camera, with 9pm pixel 
size, was laboratory calibrated prior to the test flights. The test 
area was simultaneously surveyed by an Optech ALTM 30/70 
LiDAR system of the Ohio Department of Transportation. At 
FOV of 40°, 50 Hz scanner frequency and 70 kHz pulse rate, 
the point density was about 5-8 points/m 2 . A set of 16 images 
with adequate coverage of the region, which contained survey 
control points, was identified. The flight plan consisted of two 
parallel strips and two perpendicular strips. Therefore, the data 
Figure 2: Highlighted buildings distributed in the area and 
LiDAR strips’ orientation 
5. EXPERIMENTS AND RESULTS 
The first part of the algorithm is an enhanced version of Pothou 
et al., 2007 method which calculates the boresight 
misalignment parameters and their standard deviation for each 
strip over each individual building. In this individual solution a 
data snooping procedure eliminates outliers before estimating 
the boresight parameters (Equation 7). The second part of the 
algorithm calculates the total solution (Equation 11) where 
combinations of buildings and strips are involved (with their 
individual weights).