International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
  
intersection is carried out at the same epoch À . As a 
consequence, instead of using the C4, to build up 
C, - the variance-covariance matrix output of KF is 
used. This analysis will be looked at in the next 
section. 
4. INTEGRATING PHOTOGRAMMETRY 
AND INS IN A KALMAN FILTER 
The previously described initialisation remains the 
same. The items that differ are: the employment of 
the lever-arm and angles transformation, and the 
Kalman Filter. 
Before talking about these items, we consider the 
flowchart of Figure 4. The algorithm can be depicted 
as follows: 
  
Known initial 
position 
  
  
  
Initialisation 
Capture photos 
  
  
in image (x, y) and compute 
their X, Y, Z by intersection 
  
  
  
; 
: 
Measure features’ coordinates 1 
: 
' 
  
  
  
Move ^s" seconds 
and capture photos 
| 
Measure features” coordinates in image 
(x, y) of known X, Y, Z. Compute Xq. 
Yo. Zo. 0. ©, K of the two images by 
resection 
Apply lever arm and 
boresight corrections 
Prediction, = 100 Hz t 
[RR IMU output 
  
  
  
  
  
  
  
  
  
  
  
  
Update. | Hz 
  
Kalman Filter 
  
  
Output position and 
  
  
  
  
attitude 
Lr Apply lever arm and 
peer boresight corrections 
  
  
  
  
Perform intersection to 
map (mare) features 
  
  
  
  
  
Figure 4: Flowchart of the Photogrammetric and INS 
integration 
Initialisation: 
l. Position and attitude of the two cameras 
considered as known 
2. Intersection is employed to map objects 
After mapping enough objects: 
1. Vehicle moves 
2. Resection computes the cameras’ EOP 
using the features mapped from the 
previous location 
o 
Lever-arm and angles transformation (and 
boresight) are applied to the EOPs to 
determine the IMU's position and attitude 
4. IMU and resection outputs are integrated in 
Kalman Filter to compute filtered position 
and attitude of the current location 
Lever-arm and angles transformation (and 
boresight) are applied to the filtered 
position and attitude to determine the EOP 
of the cameras 
6. Intersection is used to map more objects 
from the current location 
7. Vehicle moves and algorithm repeats 
Un 
"The lever-arm and angles transformation are different 
in steps 3 and 5. In the following, only the angles 
transformation is discussed; the lever-arm is dealt 
with similarly. 
4.1 Angles Transformation 
The angles transformation applied in Step 5 is used to 
transform the output of the KF to the camera's 
reference frame to perform the mapping. This is well 
documented in the relevant literature (Skaloud and 
Schaer, 2003). The complete transformation is: 
"n 
Ra = RS Rg) RS, (15) 
where Rz, = transformation matrix between 
mapping and camera frames 
Rf = transformation matrix between IMU 
and camera frames (depends on the 
definition of the axes) 
Rj = transformation matrix between IMU 
and carth-fixed frames, i.e., KF output 
R$, = transformation matrix between 
Earth-fixed and mapping frames 
The boresight correction applied in Step 3, is exactly 
the inverse of Equation (15). In the step, the user is 
going from R$, to Rj, and this takes place as 
follows: 
1°, XL Ar 
R£-RS [Ri] n$ (16) 
In this stage, we showed the relations among the 
coordinate systems for the transfer of position and 
attitude. In the second section, the KF is described. 
4.2 Data Integration Via Kalman Filter 
The navigation KF can link either the INS 
measurements (orientation rates and accelerations) or 
the integrated values (coordinates, velocity, 
orientation) with external measurements. 
In open spaces, GPS measurements play the role of 
external measurements. In areas with limited GPS