POINT Xum Yum REMARKS 
A -71. 24. Static 
B 45. -34-. Static 
C -167. -60. Static 
D 14. -112. Static 
B1 0. 4. Dynamic 
B2 9. 8. Dynamic 
B3 21: 12: Dynamic 
B4 21. 15. Dynamic 
B5 18. 10. Dynamic 
Table 1 : Simulated Image Residuals with a 15 Millisecond 
Exposure Offset (with No Analytical Offset Determination) 
On the basis of the expected motion of the helicopter during the 
offset period, ie 15 milliseconds of transit at uniform attitude, 
an analytical approach was developed. This approach is 
dependent on the motion being stable and in a uniform direction 
during the offset period. For this trial, on the basis that the 
helicopter would be flying in on "steady" approach, this 
assumption was valid. 
Consider the standard collinearity equations of the least 
squares bundle adjustment. If motion is assumed to be constant 
then the object space offset between camera exposures can be 
solved as an unknown in the adjustment process. In addition to 
the standard parameter set, three additional unknowns 
representing the object space offset between the two exposures 
in each coordinate direction, can also be determined. If 
considering only two cameras the equations take the following 
form, however the equations can readily be extended to 
multiple cameras configurations with multiple camera offsets, 
ie one set for each camera pair. 
M (XX AX) +m(Y-Y + AY) + M(Z-Zi+AZ) 
+ + += 
J 
m(X[-Xj+aAX)+m(Y-Y +AY)+m(Z-Z+AZ) 
XX + DYNAMIC ..(2) 
m (XX) +m(Y iY) +m(Z-Z;) 
Xi-Xg+ STATIC — ..(3) 
f is the principal distance 
X; is the x image coordinate 
where 
Xo is the x image principal point offset 
X., Y, Z, are the coordinates of point j 
xi Yi Zi are the coordinates of camera i 
AX, AY, AZ are the exposure offsets 
These equations can similarly be developed for the y image 
coordinate. Note that in the case of static targets, ie where no 
object space movement due to the camera exposure offset is 
expected, the coefficient components AX, AY and AZ are set to 
zero and do not contribute to the estimation of the camera 
exposure offset, however do provide a datum reference for the 
determination. The equations shown include the three 
additional parameters for camera exposure offset in three 
dimensional space. For the added assumption that motion is 
restricted to the horizontal plane, then only two additional 
parameters need be solved, with AZ being explicitly 
constrained to zero. 
Table 2 shows a sample of the resulting image residuals after 
inclusion of parameters in the least squares solution for 
determination of the object space camera exposure offset. For 
this simulated data set a 15 millisecond exposure offset was 
introduced. The recovered camera offset estimates were 
0.546, 0.543 and 0.005 metres in X, Y and Z respectively. 
   
This corresponds to a recovered heading of 45.1 degrees 
(simulated 45 degrees) and a velocity of 99.7 knots 
(simulated velocity 100 knots). Of interest is the 
distribution of part of the offset into the Z component, due 
primarily to the relatively weak network configuration which 
was proposed. 
POINT Xum Yum REMARKS 
A -11 5. Static 
B 4 -6. Static 
C -6 0. Static 
D 2 -6. Static 
B1 0. 2 Dynamic 
B2 -2. -1. Dynamic 
B3 0. 8. Dynamic 
B4 3. 1 Dynamic 
B5 0. -6 Dynamic 
Table 2 : Simulated Image Residuals with a 15 Millisecond 
Exposure Offset (with Analytical Offset Determination) 
With further simulations and solution for only the planimetric 
shift component, ie assumption of horizontal flight over the 15 
millisecond period, the recovered offsets were 0.547 and 
0.546 in X and Y respectively. This corresponds to a 
recovered heading of 45.05 degrees and a velocity of 100.09 
knots. In the case of a weak network, the use of these 
additional parameters needs to be carefully selected in order 
not to degrade the solution or introduce biases. In the case of 
the AHRS trial the assumption of horizontal flight during the 
period of exposure was adopted and the resulting least squares 
solution was restricted to a planimetric camera exposure 
offset solution. 
Timing 
During design for the trial, timing specifications were set at 1 
second. This timing was for correlation of photogrammetric 
derived attitude data and the AHRS derived data. The timing 
reference was to be the GPS time standard which was encoded 
onto all attitude outputs on the AHRS data bus. In principle 
this was a simple task with correlation of the CRC-2 clock, 
determined as the photogrammetric time reference, to the GPS 
standard with clock drifts being determined at regular 
intervals. The CRC-2 time was printed on all exposures, 
ensuring easy reference. During trial testing, however, it was 
determined that timing was significant at the 0.1 second level, 
and as the least count of the CRC-2 clock was 1 second an 
ind dent timing mechanism needed to be established. 
        
   
Figure 6 : Apple Macintosh Timing Reference