# Classification between Failed Nodes and Left Nodes in Mobile Asset Tracking Systems +
## 4 Node Classification  
In this section, a node classification method is introduced. The classification is between nodes that _failed_, therefore not being able to transmit RSSI-included messages, and nodes that _leave_ the target detection region. These nodes are defined as _failed nodes_ and _left nodes_, respectively, and comprehensively termed _disconnected nodes_. A straightforward solution is to use the last reported location of a disconnected node. If the final location of a disconnected node is within a monitoring area, then the node is considered to be a failed node. Otherwise, the node is considered to be a left node, which naturally left the target monitoring area. However, this method is not suitable for this system, since all anchor nodes are deployed within the monitoring area or on the boundary of the region. As a result, the developed system and many monitoring systems are incapable of \"detecting\" packets that are external to this area.  
To overcome this shortcoming, the method proposed in this work uses two trends associated with the neighbor counts and the ratios of the boundary nodes included in the neighbors. Let \(m\) be a mobile node, \(B\) be the boundary of a monitoring area, \(d\) be the Euclidean distance between \(m\) and \(B\), \(N(m)\) be the number of \(m\)'s neighbors and \(N(B_{m})\) be the number of \(m\)'s neighbors on \(B\), \(N(B_{m})\leq N(m)\). Then, while \(m\) moves far away from the monitoring area, as \(d\) increases, \(N(m)\) decreases and \(N(B_{m})/N(m)\) increases. Finally, both \(N(B_{m})\) and \(N(m)\) become zero when \(m\) loses all communication links with its neighbors. Figure 4 shows these concepts.  
In Figure 4, the thresholds, \(T_{nc}\) and \(T_{r}\), are used to determine whether a disconnected mobile node sends its last value from either inside or outside of the monitoring region. To calculate \(T_{nc}\) and \(T_{r}\), a mobile node disconnected from a WSN is mapped onto the nearest location on the boundary of the monitoring area from its last location. Then, the two values, \(T_{nc}\) and \(T_{r}\), are estimated. Based on the trends and the thresholds, the proposed method classifies a disconnected mobile node as either a left node or a failed node. The two trends are complementary to each other in various environments. For example, the trend of the neighbor counts reported by a mobile node within the monitoring area may decrease due to barriers, such as walls, other medical assets and people.  
Figure 3: Map of the emergency room.  
In this case, an incorrect decision caused by the trend of the neighbor counts can be corrected by observing the ratios of boundary nodes. However, the proposed method does not incur an additional communication cost, because the neighbors' data are essential to calculate the position of a mobile node in a radio-frequency-based positioning system.  
From the above concepts, the proposed method can possess the following properties. Let \(A_{I}\) and \(A_{O}\) be the area within (_i.e._, inside) and outside the region of a monitoring area, in which the radio signals of the boundary nodes can propagate, respectively. If the ratio of the boundary nodes of a mobile node is greater than zero, the node is considered to be outside the monitoring area with probability \(A_{O}/(A_{I}+A_{O})\), where \(A_{O}\cap A_{I}=\phi\). In addition, let \(m\) be a mobile node that has left a sensor network without failures and stayed outside a monitoring area, \(l\) be the line segment crossing \(v\) and \(w\), which are \(m\)'s two nearest nodes on the boundary of the area, \(d_{1}\) be the length of \(l\) and \(d_{2}\) be the shortest distance between \(l\) and \(m\). If \(0<d_{1}\leq r\), the communication range of a node, and \(m\) is located in the line segment, \(l\), with the distance \(d_{2}>0\), then \(d_{2}\) is greater than \(\sqrt{r^{2}-(d_{1}/2)^{2}}\).