## 3 General Concept and Passive Detection
### Practical Issues in Passive Detection
#### 3.2.2 Node Localisation  
GPS is a most popular means to determine the location of nodes. In order to minimize overhead, most localization systems only utilize one or multiple anchor nodes equipped with GPS chips, rather than mounting GPS chips on every node [40]. These anchor nodes periodically broadcast their current position to other sensor nodes and help them to estimate their locations.  
For monitoring applications that intend to operate as long as possible, battery life is the major restriction since nodes in the network are usually unreachable after being deployed. Therefore an unnecessarily high updating frequency, such as one sample per second, is pointless as monitoring lasts weeks or even months. A push-to-fix mode has been proposed for long-term operating applications [41]. It puts the GPS to sleep most of the time, and location is only updated at relatively long time intervals (such as every two hours or even more). This mode can be helpful to GPS embedded nodes. In this paper, nodes have a very low frequency in position change; therefore, a longer update time interval, such as one sample per day, is more than enough. Since each location updating process can last for up to 30 s, the energy cost of a GPS embedded node could be limited to as low as 31.08 Joule per day [41]. If normal 18650-size cylindrical lithium-ion battery cells [42] (3.3v, 1.6-Ah) are adopted, the GPS embedded nodes can operate for more than one and a half years, at a meager cost since this type of battery is mature and cheap.  
As illustrated in Figure 2, the trilateration approach [43] based on the received signal strength is the most suitable for node localization in WSNs thanks to its implementation simplicity and low hardware requirement. The fundamental idea is as follows: the locations of anchor nodes are broadcasted periodically and the nodes that need to be located can exploit this information to estimate the distance from anchor nodes by measuring the received signal strength (RSS). Suppose the coordinates of anchor nodes 1, 2 and 3 are \((x_{1},y_{1})\), \((x_{2},y_{2})\) and \((x_{3},y_{3})\), the coordinates of the node location to be determined is \((x_{0},y_{0})\), and the distances between three anchor nodes to this node are \(d_{1}\), \(d_{2}\), \(d_{3}\). \((x_{1},y_{1})\), \((x_{2},y_{2})\) and \((x_{3},y_{3})\) and are set as centres. Three circles are drawn with radius \(d_{1}\), \(d_{2}\) and \(d_{3}\), respectively. These three circles are supposed to intersect at \((x_{0},y_{0})\), which can be determined by solving the equation set as follows.  
\[\begin{cases}(x_{1}-x_{0})^{2}+(y_{1}-y_{0})^{2}=d_{1}^{2}\\ (x_{2}-x_{0})^{2}+(y_{2}-y_{0})^{2}=d_{2}^{2}\\ (x_{3}-x_{0})^{2}+(y_{3}-y_{0})^{2}=d_{3}^{2}\end{cases} \tag{9}\]  
Similarly to any localization method, the trilateration approach cannot be 100% accurate. Its accuracy may suffer from distance estimations errors. To mitigate the effect of these errors, a very straightforward solution is to extend the trilateration method to the multilateration technique, which is to determine the intersection of circles centered at more than three reference positions (anchor nodes). Other efforts have been made as well, such as the authors in [44] who proposed three cluster methods to deal with the problem of no intersection point. Moreover, least-squares (LS) optimization [45] can be used to minimize the gap between actual distances and estimated distances.