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estimates can be obtained using this scheme. This scheme targets large-scale networks of small sensors such as those using the smart dust mote [10]. 12.6.2 Probabilistic Position Estimation Another approach to solving the uncertainties caused by errors in range or angle estimation for localization is using a probabilitistic approach [26 29]. The work in reference 27 models range measurements by a set of density functions. Nodes obtain initial range measurements using RSSI from a set of beacon nodes that are location-aware, either using on-board GPS or from manual deployment. The nodes then compute their position estimates that are represented as three-dimensional density functions. This requires prior knowledge of the density function of range that is obtained from collected sample values. Position estimates from different nodes are then combined by intersection of density functions. When nodes improve their position estimates from new information (i.e., the estimated density function becomes sharper), they broadcast this information to other nodes. A similar approach is applied in reference 28 to probabilistic localization using AOA measurements. As usual, the error for AOA measurement is modeled probabilistically from of ine experiments. The nodes utilize this information to re ne position estimates obtained from beacons. In reference [26], the authors proposed a method applied to mobile sensors that is based on Monte Carlo localization, which uses particle lter combined with probabilistic modeling. The basic idea is to rst obtain a posterior distribution of possible locations using a set of weighted samples. Nodes use a mobility model to re ne the probability distribution obtained at an initial step. In a second step, the nodes use ltering to eliminate impossible locations based on new observations. This approach has been found to work better with higher node mobility. An algorithm that applies probabilistic modeling for localization using RSSI based ranging from a mobile node is proposed in reference 29. Here, it is assumed that all sensor nodes are static while a mobile beacon node travels through the network area broadcasting beacon packets. Beacon packets carry updated location of the beacon node. As the beacon packets are received at a sensor node, it obtains new position estimates and combines them probabilistically to re ne its position estimate. 12.7 CONCLUSION Localization is a challenging problem to solve for successful implementation in small, low-cost wireless sensor nodes. Although a signi cant amount of research has been devoted to this problem, a single practical solution is hard to nd. It is likely that solutions would have to be application-speci c, because sensors are used in a large number of application scenarios and environments. Also, solutions for any application may require multiple principles for addressing the needs for all nodes. For instance, while some nodes may be able to self-localize, others may need to employ collaborative or centralized computations, depending on the situation at which it is in. Multiple methods would also improve the robustness of the localization system.
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This chapter presents the basic principles of localization, the particular challenges with respect to solving the problem in wireless sensor networks, and some existing techniques to solve the problem. This topic is likely to generate more research ideas in future because of its importance in almost all sensor network applications.
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12.8 EXERCISES 1. State some of the different techniques that can be used to measure or estimate distances from a wireless beacon generator or base station to a wireless node for localization. Give examples of systems that use each technique. For each technique, explain the technical challenges, if any, of their usage for localization in wireless sensor networks. 2. The locations of three wireless bases stations are as follows: BS1 = (0, 0), BS2 = (20, 5), and BS3 = (6, 25). The wireless system estimates that the distance from a wireless node to BS1 is 15 units, that from BS2 is 7 units, and that from BS3 is 19.4 units. Determine the location (x, y) of the wireless node using triangulation. Write all the equations and show your work. If you use a software tool such as MATLAB, attach printouts of your code. Is it really necessary to get distances from three base stations to estimate the location Explain. 3. Given that in an angle-based localization scheme as shown in Figure 12.6, the measured angle can have errors up to 5 , determine an expression for the corresponding error in the location estimate for a sensor node located at an arbitrary location (x, y). Assume that the region of operation is a 10-ft 10-ft area and the beacon generators are located at the three corners as shown in Figure 12.7a. Plot the error distribution within the square area. 4. Repeat the above problem when the beacon generators are located on a straight line along the base of the square that is, at locations (0, 0) (the left bottom corner), (5, 0), and (10, 0). 5. How is the approach for probabilistic localization different from that of estimation of location coordinates under measurement errors Explain by comparing an existing probabilistic localization scheme based on ranging with that of atomic multilateration.
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