3.2.3.2 Uniformity analysis
To measure the uniformity of the distribution, the pdf of the final position of robots
is estimated non-parametrically using the Parzen window estimator [Par67]. The
estimated pdf of the distribution is shown in figure 3.5. The side view of the same is
shown in figure 3.6 to display the variation in the pdf in better light. From these two
figures, we can clearly see that the distribution is almost uniform over the circular region.
In the simulation, the variance of the Gaussian distribution used in the estimation was
fixed as 0.1. The variance of the estimated pdf over the circular region was calculated and
found to be 3.0196e-004, which is very small justifying the uniformity of the final
distribution of robots.
0.4 -
0.3
0.2
01
Y Coordinate -1 -1 X Coordinate
Figure 3.5 Estimated pdf of the final position of robots using Parzen window estimator