"Surveillance Coverage of Sensor Networks under a Random Mobility Strategy"

This is a paper by Kesidis, Konstantopoulus, and Phoha about the surveillance coverage of mobile sensors in a 2d or 3d space. They assume the sensors move in a Brownian motion strategy and that the sensors have a uniform spherical surveillance coverage around each device.

They give a mathematical formulation to calculate the following quantities about their strategy:

1. Contact time between sensor nodes

2. Time-until-detection of slow moving objects

3. Effects of mobility variance and sensor density

This is a good mathematical starting point to make proofs about surveillance coverage. However, you need some knowledge about set theory and probability to understand their formulation.

There are some limitations however. This strategy uses random mobility which makes things easy to formulate, but it's not clear whether this formulation will apply to deliberative surveillance strategies. In addition, the spherical sensor coverage of mobile sensors may not be a good model of our system. One would need different shapes such as cones to account for a camera surveillance network.

Further research will give us insight into what other methodologies we can use.