# Tracking Mobile Sinks via Analysis of Movement Angle Changes in WSNs
## 1 Introduction  
Wireless Sensor Networks (WSNs) consist of a large number of distributed sensor nodes, which are widely applied for data collection. To make WSNs practical, many problems need to be properly handled, including limited network life due to limited energy storage, low connectivity under a low node density, and especially the hotspot problem causing early death of nodes and network partition. To address these problems, WSNs with mobile sinks have been explored for their potential positive effects on prolonging network lifetime and even collecting data in a sparse network. However, in WSNs with mobile sinks, the traditional routing protocols for static sinks are no longer applicable and new challenges emerge because the location information of mobile sinks changes dynamically. It has been shown that the mobility of sinks can provide advantages for data collection, therefore, some studies concentrate more on how to control the trajectories of mobile sinks [1; 2; 3]. The limitation of these studies is that mobile sinks are assumed to move along predetermined routes in most of the cases, which is not practical in real WSNs. To achieve a more flexible application, some data collection protocols have been proposed to allow mobile sinks to move randomly [4; 5], which however requires a large amount of energy and data overhead for announcing the location information of themobile sinks. SinkTrail [6] is a typical mobile sink tracking method allowing random mobility of mobile sinks. In SinkTrail, trail messages need to be broadcast to each network node and the trail reference information of each node needs to be updated after each movement of the mobile sink. The frequent broadcasting of trail message and the updating of trail references results in a large amount of overhead, network congestion and could reduce the network lifetime due to high energy consumption [7]. In this paper, Detour-Aware Mobile Sink Tracking (DAMST), an energy efficient mobile sink tracking method with movement angle changes analysis, is developed for lowering energy consumption and data overhead. Figure 1 shows a typical scenario for DAMST. In Figure 1, while a mobile sink passes through a region (the circular shadow region in Figure 1), and in case that it considers the information of this region should be transferred at some future time (the scale of the region could be decided by the mobile sink), it will firstly appoint a node in this region as a Region Agent (RA). The RA is responsible for collecting the data of the whole region. Then, the mobile sink chooses nodes on or near its trajectory as footprints and records their location information. When the mobile sink needs information from the RA at some time, it will send a data query to the RA and get a reply from the RA along the movement trajectory marked by the footprints. However, we notice that sometimes the moving trajectory of the mobile sink (the black curve in Figure 1) may take too many detours and not be suitable for data collection over a long time range. Therefore, to obtain an energy efficient data transition path from the RA to the mobile sink and reduce data overhead spent on storing the location information of useless footprints, DAMST is designed to help mobile sinks delete footprints on the detours of the moving trajectory by analyzing movement angle changes from one footprint to another. In Figure 1, after the mobile sink moves from a RA (Node 1) to a current node (Node 2) along a trajectory (the black curve), by analyzing the movement angle changes on the trajectory, the mobile sink can effectively cancel most of the location information of the footprints on detours, only reserve location information of three useful footprints L1, L2, and L3, and further establish an energy efficient data transition path consisting of the rest footprints L1, L2, and L3 from the RA to the current node. The main contributions of this work may be summarized as follows:  
Figure 1: A typical scenario for DAMST. 1.