Sensor Placement for Triangulation-Based Localization

Robots operating in a workspace can localize themselves by querying nodes of a sensor-network deployed in the same workspace. This paper addresses the problem of computing the minimum number and placement of sensors so that the localization uncertainty at every point in the workspace is less than a given threshold. We focus on triangulation-based state estimation, where measurements from two sensors must be combined for an estimate. This problem is NP-hard in its most general from. For the general version, we present a solution framework based on integer linear programming and demonstrate its application in a fire-tower placement task. Next, we study the special case of bearing-only localization and present an approximation algorithm with a constant factor performance guarantee. Note to Practitioners-Sensor networks can provide robust and scalable solutions to the localization problem which arises in numerous automation tasks. A common method for localization is triangulation in which measurements from two sensors are combined to obtain the location of a target. In this work, we study the problem of finding the minimum number, and placement of sensors in such a way that the uncertainty in localization is bounded at every point in the workspace when triangulation is used for estimating the location of a target. We present an efficient geometric algorithm for bearing-only localization which can be used for the deployment of camera-networks. We also present a generic framework for arbitrary uncertainty metrics, and demonstrate its utility in an application, where watchtowers are deployed to detect forest fires.