Optimal Sensor Positioning (OSP); A Probability Perspective Study

TL;DR

This paper introduces a probabilistic level set-based method for optimally positioning and directing multiple sensors with limited range, viewing angles, and failure probabilities to maximize surveillance coverage.

Contribution

It presents a novel approach combining level set methods, ODEs, and stochastic differential equations to globally optimize sensor placement and orientation.

Findings

Effective in various failure rates of sensors

Handles different importance levels of surveillance regions

Applicable to 3-D environments

Abstract

We propose a method to optimally position a sensor system, which consists of multiple sensors, each has limited range and viewing angle, and they 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 setup 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 (SDEs), to find the global maximum of the total surveillance area. The numerical examples include various failure rates of sensors, different rate of importance of surveillance region, and 3-D setups. They show the effectiveness of the proposed method.