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A Prototype Optical Tracking System Investigation and Development - page 130 / 170

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Results and Discussion

Good algorithm convergence

Poor algorithm convergence

0.1

0.1

Actual position error Point cloud std. dev.

Actual position error Point cloud std. dev.

0.08

0.08

Error (m)

0.06

0.04

Error (m)

0.06

0.04

0.02

0.02

00

10

20

30

40

50

00

10

20

30

40

50

Iteration

Iteration

(a)

(b)

Figure 8.13 The minimisation algorithm’s performance varies considerably depending on the initial quaternion used. (a) shows a good example of convergence and (b) shows a bad example. The only difference between these two tests was the initial quaternion used.

research is required to determine the relationship between the initial conditions and the algorithm convergence.

lthough the algorithm did not converge in Figure 8.13b, this does not mean that F (q) or the algorithm implementation is incorrect. By setting the initial value of q to the correct

value, the variance was determined to be of the order of 10

15

m2. This indicates that there

is value of q that will reduce the variance to near zero. Therefore, this value of q could be located if a better performing minimisation routine were implemented.

graphical representation of the algorithm converging is shown in Figure 8.14. Initially

the variance shown by green triangles is large.

fter each iteration the variance decreases

as shown by the decrease in size of the point cloud.

8.4

Summary

These results provide an insight into the stationary performance of the Black Spot mod- ules. Three variables were investigated; namely intensity, distance, and angle. Each of these variables is found to affect the variation in centroid positions. The intensity trend is

hyperbolic.

n increase in observed marker intensity above approximately 80 at 300 µs has

little effect on the variation in centroids, however, below this threshold the standard devi- ation climbs dramatically. The standard deviation increases approximately linearly with distance but this is a much weaker trend than that of intensity. The angle (position within

the FOV) has also been shown to influence the standard deviation.

quadratic curve with

a minimum near the centre X coordinate was fitted for the standard deviation versus X coordinate. Data suggests that there is a region between approximately 100 < X < 500

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