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Experiments show that this method has an inaccuracy of a few degrees (about 5 in reference 36. The need of extra hardware and the need of a minimal distance among the receivers result in some disadvantages in terms of cost and size of the sensor nodes. 11.2.4 Communication Range In some cases, the only information available to estimate a distance is the communication range of the sensor nodes. If a node receives a data packet from another node, then the distance between these nodes is between zero and the maximum communication range. Usually, techniques that use this method of distance estimation do not need an accurate distance, but only an interval. To get only one distance (and not an interval), we can choose one point from the interval, like the middle point, for example. In this last case, the maximum error of this estimation will be one-half the communication range. This method of distance estimation has the advantage of being the most simple and with the lowest cost. No extra hardware is required, nor is extra computation needed to estimate a distance. On the other hand, an error of half the communication range for each distance estimation is not viable for the most localization systems. Consider, for example, a communication range of 100 m. In this case, the error of this method can be about 50 m for each distance estimation. 11.2.5 Comments About the Distance/Angle Estimation The choice of what method to use to estimate distance between nodes in a localization system is an important factor that in uences the nal performance of the system. Usually, as will be shown in the next section, to estimate a position, a node uses at least three distance estimations, each of them with an associated error. On the other hand, if only the accuracy of such methods were important, we could just use a TDoA that has lower errors. But factors such as the size and cost (in terms of hardware, processor, and energy) of the nodes must also be taken into consideration. Thus, the chosen method used to estimate distances will depend on the application requirements and also on the available resources. Table 11.2 compares each one of the methods described in this section.
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11.3 POSITION COMPUTATION When a node has enough information of distances and/or angles and positions, it can compute its own position using one of the methods that will be studied in this section. Several methods can be used to compute the position of a node. Such methods includes trilateration, multilateration, triangulation, probabilistic approaches, bounding box, and the central position. The choice of which method to use also impacts the nal performance of the localization system. Such a choice depends on the available
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LOCALIZATION SYSTEMS FOR WIRELESS SENSOR NETWORKS
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TABLE 11.2. Comparison of the Methods Used to Estimate Distances/Angles Between Two Nodesa Method RSSI Precision Meters (2 4 m) Maximum Distance Communication range Communication range few meters (2 10 m) Communication range Communication range Extra Hardware None Challenges Variation of the RSSI, interferences Nodes synchronization Maximum distance of work Work on small sensor nodes
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Centimeters (2 3 cm) TDoA Centimeters (2 3 cm) AoA A few degrees (5 ) Communication Half the Range communication range
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a The
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None Ultrasound transmitter Set of receivers None
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chosen method depends on the application, scenario, and available resources.
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information and on the processor limitations. In the subsequent sections, the cited methods will be studied. After that, some general comments will be made regarding this component and its methods. 11.3.1 Trilateration and Multilateration Trilateration is the most basic and intuitive method. This method computes a node position by the intersection of three circles, as depicted in Figure 11.6. To estimate
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Figure 11.6. Theoretical model of the trilateration: The position of the unknown node corresponds to the intersection of the three circles formed by the positions and distances to the reference nodes.
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