Application of Geometric Probability and Integral Geometry to Sensor Field Analysis

In seeking to maximize the probability of target detection by sensors randomly distributed over some region, one might consider factors such as the numbers of sensors, the detective power of the sensor, and the way in which the sensors are spatially distributed throughout the region. Many of these factors have a strong probabilistic and geometric nature. In this chapter, we use techniques from geometric probability and integral geometry to investigate coverage and detection problem for sensor ¢elds. Methods of integral geometry have been used in computing coverage probabilities in heterogeneous sensor networks by Lazos et al. [15] using many of the results in the classic work of Santaló [23]. Similarly, Rowe and Wettergren [22] used geometric probability methods to examine the reliability over time of randomly distributed heterogeneous sensor networks.