## 3 Localization Algorithms in WSNs
### Range Free Localization Algorithm
#### 3.1.3 Mobile Anchor Based  
In this technique, a mobile anchor with GPS capability moves into a sensing area and periodically broadcast its current geometric coordinates. The other sensor nodes collect the location coordinates of the mobile anchor node. Later, the sensor nodes choose three non-collinear coordinate points of the mobile anchor node and apply different mechanisms to estimate position. Based on this principle, several localization algorithms are devised [30; 73; 74; 75; 76].  
The author in [73] proposed a geometric conjecture (perpendicular bisector of the chord of a virtual circle) based range free localization algorithm, where a mobile anchor traverses a sensing area and periodically broadcasts its current location coordinates. The neighboring sensor nodes keep track of entering and departing anchor coordinate points to construct a chord on its communication range. The sensor node repeats this process until it gets at least three coordinate points from the moving anchor node on its communication range. The line segments between these three selected coordinate points create two chords on its communication range. Later, the perpendicular bisector of the two cords gives the position estimates of the sensor nodes. To further improve the localization accuracy, the author in [74] proposed a geometric constraint based localization scheme. In this scheme, the selection process of the three anchor coordinate points on the communication range of the sensor node remains the same as in [73]. Initially, the intersection of the selected two anchor coordinate points determine the constraint area of the sensor node. This process is repeated with another two intersected points to further narrow down the constraint area of the sensor node. Finally, the average of all the intersection points give the position estimates of the sensor node.  
Another approach [75] proposed a constraint area based localization using mobile anchor. In this approach, the specific type of moving anchor's trajectories create a specific type of constraint areas for the sensor node. To identify the potential location of the sensor node within different constraint areas, a number of intersections are created within different constraint areas until the final arrival of the coordinate points before the final departure of the anchor node. Each intersection further narrow downs the potential location of the sensor node within the overlapping constraint areas. However, the scheme shows high localization error when random waypoint mobility model is used for the moving anchor node. Also the scheme is computationally expensive due to multiple intersection computation. Another approach [76] proposed a curve fitting method along with a mobile anchor node to calculate the location of the sensor node. In this approach, the arrival and departed coordinate points of the moving anchor nodes are recorded and this is repeated as many times as the moving anchor re-enters the communication region of the sensor node. The localization begins through fitting a curve on the few selected coordinate points on communication range and iteratively refined through Gauss-Newton method. The center coordinates of the fitted curve define the position of the sensor node. Another mobile anchor based localization is proposed in [30], where the localization begins with approximation of the geometric arc parameters. The approximated arc parameters are used to generate the chord on the virtual circle. Later, the perpendicular bisector of the chords along with the approximated radius are used to estimate the position of the sensor node. The accuracy is improved for boundary nodes too.  
Although several techniques are devised so far, a common pitfall to all mobile anchor based localization schemes arise when considering the longer periodic interval of the message send by the anchor node and the irregular radio propagation pattern.