Target Assignment by Physical Modelling

Now we want to investigate the influence of the connection range. We simulated the probability that a connection exists between two arbitrary sensors by a Fermi function, i.e., a function which is 100 % for small distances between two sensors and vanishes for large distances. It drops to 50 % at a distance CR which is roughly the mean connection range.

The mean distance between neighboring sensors on a square lattice is 10. In all previous movies, we used a CR of 14, i.e., each sensor is connected with its neighboring sensors with a very high probability, then to its next nearest neighbors with a probability of roughly 50 %; this probability decreases further with increasing distance.

The movies below show simulations for a target tracking range R=30 and the 10x10 sensors placed on a square lattice. The simulations were done rather fast with v=100. At the beginning of the movies, the connections between the single sensors are shown. At the end of these movies, two special frames are shown: the first of these shows the coverage of each target as a time line. We kept the number of moving targets constant during the whole simulation, i.e., if a target vanishes, a new target appears at the left. A thin black line indicates the appearance of a new target. The specific color at a certain point in time represents the number of TCs tracking simultaneously the proposed target. (For the color code have again a look at the table.)
The red circles in the second of these two final frames shows for each moving target the number of time steps in which a target is tracked plotted versus the number of time steps in which it is alive, i.e., in which it could be tracked. The blue crosses denote the number of time steps of longest continuous coverage. The green line is simply an y=x-line, on which both the red circle and the blue cross are if the target is tracked in its whole life time. As these three special frames are rather important for this investigation, we additionally show them separately as GIF-files.

• Connection Range CR=20
  • 5 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 10 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 15 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 20 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 25 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 28 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 30 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 35 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 40 moving targets
    (tracking of targets, time steps tracked), connections between sensors)

• Connection Range CR=14
  • 5 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 10 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 15 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 20 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 25 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 27 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 30 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 35 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 40 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

• Connection Range CR=10
  • 5 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 10 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 15 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 20 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 22 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 25 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 30 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

• Connection Range CR=7
  • 5 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 10 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 15 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 20 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 22 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 25 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 30 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

• Connection Range CR=6
  • 5 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 10 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 15 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 18 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 20 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 25 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 30 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

• Connection Range CR=5
  • 5 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 10 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 15 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 17 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 20 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 25 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 30 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

• Connection Range CR=4
  • 5 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 10 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 13 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 15 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 20 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 25 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 30 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

• Connection Range CR=3
  • 5 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 10 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 12 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 15 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 20 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 25 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 30 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

• Connection Range CR=2
  • 5 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 8 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 10 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 15 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 20 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 25 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 30 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

• Connection Range CR=1
  • 5 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 7 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 10 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 15 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 20 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 25 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

  • 30 moving targets
    (tracking of targets, time steps tracked, connections between sensors)

For an investigation, whether it is really necessary to use Simulated Annealing and whether the Greedy algorithm would already be sufficient, click here.