**1. Introduction**

In the past years, the development in micro electromechanical systems (MEMS), radio frequency (RF), integrated circuit (IC), etc., greatly enhanced the advancement of wireless sensor networks (WSNs). As an ubiquitous sensing technology, WSNs find more and more applications, such as structural monitoring [34], precision agriculture [3], gas-leak localization [14], volcano monitoring [33], robot navigation [4, 15], health monitoring [20], to name a few. For most existing applications of WSNs, the location information is crucial. For example, in the structural monitoring application, we can conclude that the structure is out of condition if fault is detected by one or more sensors in the network of sensors mounted everywhere on the structure. However, we are unable to accurately report the faulty position without localization capability of the WSN. In contrast to other type of networks, e.g., Internet, a prominent difference is that WSNs are location-based networks. Therefore, the design of localization hardware and localization algorithms is an important procedure in the development of a WSN system.

There are mainly two classes of localization approaches for WSNs: one is pre-localization and the other one is self-localization. The pre-localization method measures the position of sensors in the deployment stage. After the deployment and position measurement, the position is stored in the memory of the sensor. For this method, any movement of the sensors will result in errors in the location information. Differently, the self-localization method computes the locations of each sensor based on real-time measurements and therefore is robust to the variance of the environment. With GPS devices embedded, sensors are enabled with self-localization capability. However, the relatively high cost of GPS devices often makes it not practical to apply GPS to all sensors in a network. Instead, the strategy with a portion of sensors equipped with GPS as beacons and using triangulation or trilateration to iteratively determine the positions of blind sensors based on the distance or angle measurements between neighboring sensors provides a less expensive way for self-localization [13, 16, 26]. Although many GPS devices are saved, as a tradeoff, the sensors are required to have the ability to measure the distance or the relative angle to its neighbor, which may result in

©2012 Li and Li, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0),which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ©2012 Li and Li, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### 2 Will-be-set-by-IN-TECH 290 Wireless Sensor Networks – Technology and Protocols

costs for extra hardware. Without introducing extra hardware, received signal strength (RSS) based distance measurement method [17, 30], relying on the estimated distance according to the signal strength received from the neighboring sensor, provides a promising direction for self-localization. Another promising self-localization method is range-free localization, which even does not require the information on the signal strength received from the neighbor but the connectivity information, i.e., a sensor only need to know who is its neighbor. This technology implies that localization can be a by-product of communication since connectivity information can be obtained in communication. For example, if Sensor *A* can communicate with Sensor *B*, then we conclude they are connected. Due to this promising property, range-free localization is becoming more and more popular in both practice and research. In this chapter, we investigate the range-free localization of WSNs.

Dynamic models gained great success in realtime signal processing [28], robotics [12, 22], online optimization [29], etc.. In this chapter, we overview our previous work on dynamic model based range-free localization [10, 11, 25]. Particularly, we will examine two dynamic models for the real time localization of WSNs. The models are described by nonlinear ordinary differential equations (ODEs). The state value of the ODEs converges to the expected position estimation of sensors. Both of the two models find feasible solutions to the formulated optimization problem. Particularly, the second model, by exploiting heuristic information, has a tendency to converge to better solutions in the sense of localization error. The real time processing ability of the models allows possible movement of the sensor nodes, which often happens in mobile sensor networks [23]. Besides the real time localization capability, another prominent feature of the proposed models is that both of them are completely distributed, i.e., each sensor in the network only need to exchange information with its neighbor and thus no message passing is needed in the network. This advantage makes the proposed algorithms scalable to large scale networks involving thousands of sensors or more.

The remainder of this paper is organized as follows. In Section 2, some preliminaries on range-free localization of WSNs are presented. In Section 3, we formulate the localization problem from an optimization perspective. Two dynamic models are presented in Section 4 to solve the formulated optimization problems. In Section 5, simulations are performed to demonstrate the effectiveness of our method. Section 6 concludes this paper.
