Optimal Sensor Positioning; A Probability Perspective Study

We propose a computational method to optimally position a sensor system. Each sensor has limited range and viewing angle, and it may fail with a certain failure rate. The goal is to find the optimal locations as well as the viewing directions of all the sensors and achieve the maximal surveillance of the known environment. We set up the problem using the level set framework. Both the environment and the viewing range of the sensors are represented by level set functions. Then we solve a system of ordinary differential equations (ODEs) to find the optimal viewing directions and locations of all sensors together. Furthermore, we use the intermittent diffusion, which converts the ODEs into stochastic differential equations, to find the global maximum of the total surveillance area. The numerical examples include various failure rates of sensors, different rates of importance of the surveillance region, and 3-dimensional setups. They show the effectiveness of the proposed method.