Optimizing Sensor Nodes Placement for Fault-tolerant Trilateration-based Localization Katarina Bala´ c ALaRI, Faculty of Informatics University of Lugano, Switzerland Via G. Buffi 13, CH-6904 Lugano Telephone: +41 58 666 4709 Email: katarina.balac@usi.ch Mauro Prevostini ALaRI, Faculty of Informatics University of Lugano, Switzerland Email: mauro.prevostini@usi.ch Miroslaw Malek ALaRI, Faculty of Informatics University of Lugano, Switzerland Email: malekm@usi.ch Abstract—As computing systems become increasingly per- vasive, the number of applications that can benefit from or require localization capabilities continuously increases. In indoor environments, wireless sensor networks are a common means to perform localization, trilateration being one of the most commonly used techniques. The placement of anchor nodes influences greatly the system performance and cost. This paper addresses the placement problem for fault-tolerant trilateration based localization. The goal is to minimize the number of anchor nodes needed to localize a target anywhere in an area of arbitrary shape with obstacles, even after one anchor node fails. We propose an exact algorithm based on integer linear programming, as well as an efficient heuristic to solve this problem. The heuristic consists of greedy placement and pruning stages, and achieves the results, in terms of the number of anchors placed, within less than 0.5% of optimum on average. We validate our solutions by simulation. Keywords—Fault tolerance, Wireless sensor networks, Algo- rithms, Optimization, Linear programming I. I NTRODUCTION Localization of persons and objects is necessary for numer- ous applications, such as environment monitoring, navigation of persons and vehicles, and various safety applications. While for outdoor localization, satellite based navigation systems are a standard, for indoor localization a number of solutions of varying cost and accuracy is in use. The localization based Wireless Sensor Networks (WSNs) is frequently used for indoor environments, as well as those outdoor environments where Global Positioning System (GPS) signals are obscured. A number of wireless nodes, anchor nodes, or simply anchors are placed at the fixed and known locations within the area that needs to be covered, and the object to be located is equipped with an additional node, target node. One of the most commonly used localization techniques is trilateration, where distances from three anchors are combined to obtain the target position. The placement of anchor nodes influences greatly the quality of localization, as well as the cost of the system. With WSNs it often happens that one of the nodes ceases to function, either due to hardware or software problems, physical damage, or, if the nodes are not connected to an electric grid, battery depletion. Replacing the batteries, or the whole unit, takes time, and some applications, in particular safety applications, require high reliability and may not tolerate the downtime. For practical applications, the obstacles to wireless propa- gation are usually present, the area of interest is of limited size and often of irregular shape, and anchor nodes can be placed at a limited number of positions, due to logistic and engineering constraints, such as a need for electrical plugs and available support structures. Therefore, our approach focuses on such realistic scenarios. We address the problem of covering an area of arbitrary shape and size, while minimizing the number of anchor nodes necessary to cover the area. We request the anchors to be placed so that even after one of the anchors fails, the desired precision of localization can still be achieved in the whole area of interest. One of our main applications focuses on safety at work. In large industrial environments such as factory halls, it might be beneficial to track the position of workers, in order to ensure their safety by localizing them easily in case of an accident. These applications may require a level of fault-tolerance, to ensure that the workers can be localized even in a case when one of the units breaks down. In such environments, the rooms are large and can be of complex shapes, while the large obstacles, impermeable to wireless signals, such as pillars or machines are usually present. Placement of WSN nodes has been studied in literature for different requirements. As a rule, these problems are NP-hard. We believe our problem is NP-hard as well. Metaheuristics, such as genetic algorithms, are often used to address place- ment problems in wireless sensor networks [7]. Unfortunately, these approaches do not provide a way to show how close the solution is to the optimum. Placement algorithms with provable bounds have also been designed, and although they have a considerable theoretic significance, the approximation factors are usually too large to be of practical value. Our first focus is on designing an exact solution, by using an Integer Linear Programming (ILP) based approach. This enables the evaluation of any heuristic solution solving the same problem. The approach is also useful in itself, as it allows to get exact solutions for problems of smaller sizes, by using a tool for solving integer linear programs. We first state our assumptions and propose a simple model that will determine the quality of coverage of a single point