Mobile Target Tracking with Multiple Objectives in Wireless Sensor Networks

Abstract

Tracking mobile targets in wireless sensor networks (WSNs) is of utmost importance in surveillance applications. As it is often the case in prior work that the accuracy of tracking heavily depends on high accuracy in localization or distance estimation, which is never perfect in practice. These bring a cumulative effect on tracking (e.g., target missing). Recovering from the effect and also frequent interactions between nodes and a central server make tracking operation slow and energy-inefficient. Inspired by these, we design a tracking scheme, called t-Tracking, to address the target tracking problem in WSNs considering multiple objectives: low capturing time (e.g., the tracking time required to get around a target in a defined distance), high energy efficiency, and high quality of tracking (QoT). We propose a set of fully distributed tracking algorithms, which answer the query whether a target remains in a “specific area” (called a “face” in localized geographic routing, defined in terms of radio connectivity or local interactions of nodes). When a target moves across a face, the nodes of the face that are close to its estimated movements compute the sequence of the target’s movements and predict when the target moves to another face. The nodes answer queries from a mobile sink called the “tracker,” which follows the target along with the sequence. t-Tracking has advantages over prior work as it reduces the dependency on requiring high accuracy in localization and the frequency of interactions. It also timely solves the target missing problem caused by node failures, obstacles, etc., making the tracking robust in a highly dynamic environment. We validate its effectiveness considering the multiple objectives in extensive simulations and in a system implementation.

Appendices

Appendix A

Mitigating the Difficulties in Face Generation and Regeneration

In Sects. 3.1, 3.3.1, and 4.2.1, we have described the face generation at the system initialization and node organization into faces (or face regeneration) during tracking operation, respectively. In this appendix, we discuss some difficulties in face generation during target tracking.

According to the geographic routing algorithms, a node carries out routing through the boundaries of faces intersected by virtual edges, transmitting a packet from a source node u to a destination node v by employing a local right-hand rule technique. This is the technique by which a packet is forwarded along the next edge clockwise, or counterclockwise, from the edge where it arrived. Such a technique requires all faces to traverse completely on the way to a destination (more specifically, there exists no path from node u to node v) or to terminate when node v is eventually reached. This algorithm has limitations—they involve a number of faces, and require exchanging information between them. Thus, a large number of nodes of those faces are actively involved in carrying out an application task that may not be efficient for an envisaged WSN application. For example, if we considered all of the faces and the nodes that correspond to a particular node (e.g., the monitor), the frequency of interactions in the WSN during each tracking of target tracking would be high, resulting in a high energy consumption in the WSN.

Also in the planarized network model, the greedy forwarding technique work well in dense WSNs. But It experiences routing failures in more realistic, non-uniform node placements, where it suffers from so-called local minima, i.e., nodes with no direct neighbor closer to the destination than themselves [64, 66].

To make the techniques practicable in this application, we make some modifications on it. We determine the boundary of a face region rather than to generating only planar subgraphs. That can reduce the chance of having local minima [66].

We determine the boundary of a face region rather than to only generating a planar subgraph. In more clearly, we can determine a boundary/perimeter of a subset of nodes, that encloses all nodes of a connected component and contains all local minimum nodes on its border. This has to be achieved by a fully reactive and localized algorithm, which cannot rely on knowledge of the 1-hop neighborhood in advance. Locations of 1-hop neighbors have to be requested explicitly by message exchange. That can reduce the chance of having local minima.

We consider that a node u communicates to the nodes in the face to which it belongs and also maintains connectivity through its adjacent neighbors along the boundaries of the faces using the right-hand rule technique. Only the face, to which a node u belongs, is traversed completely and one of its immediately neighboring nodes, v, of the face is the destination node. More explicitly, a node u needs to know only its own, and its adjacent neighboring node v’s locations. u grows its radio range $R_c$

$$\begin{aligned} \forall u \in V\quad {r_c}(u) = \max \{ d(u,v)|v \in V \wedge (u,v) \in {E_{RNG}}\} \end{aligned}$$

(22)

as in (22) until all its neighboring nodes are found in the not-yet-covered face. Thus, the number of faces which a node belongs to reduces to a few faces.

There is a class of protocols and algorithms in the literature focusing on network planarization that helps us to make the improvement on the correctness on face generation at the system initialization. These include disconnection between the nodes, incorrect edge removal, insufficient edge removals, cross-links, link or node failure, establishing direct link, hole/obstacle problem, non-ideal radio ranges, network instability, and so on [6, 51, 52, 64, 65, 74,75,76,77, 82,83,84,85,86,87,88,89,90,91,92]. Furthermore, we think that there may still remain some of the difficulties when using faces in a practical environment. This is why, we ensure to the preservation of faces by regenerating them at a certain moment; e.g., when the nodes in a face can detect t or receive a request to detect t before t’s moving to the face. The face prediction helps to achieve this. We consider to maintain a linear link list between nodes of faces, which can help mitigate irregularities found in faces and can provide online fault tolerance.

In the following, we discuss some concerns/questions that are essential to make more clear the tracking through faces.

Concern 3

Given the initial radio broadcasts on the generation of a planar graph, what if $v_1$ can also hear $v_{12}$ and $v_{20}$ in Fig. 2 during a tracking operation?

Our response to this concern goes to the sensor node organization rules described in Sect. 4.1. Referring to Fig. 2, $v_1$ may hear both $v_{12}$ and $v_{20}$. However, neither $v_{12}$ nor $v_{20}$ can be an adjacent neighboring node of $v_1$. To generate faces effectively, we put some preferences on nodes’ interactions, by which both $v_2$ and $v_5$ cannot be the witness between $v_1$ and $v_{12}$, and between $v_1$ and $v_{20}$, respectively. If there are several neighbors reachable under the same radio range (e.g., $v_1$ may hear $v_{12}$, $v_{20}$, or may also hear $v_{11})$, a decision is made on this situation, which node should be the adjacent neighboring nodes of $v_1$; in other words, whether a node like $v_{12}$ should be included in a face or not. There are two preferences to decide on the situation: (i) the minimal Euclidean distance from u to v; (ii) whether or not v is the first node by using the right-hand rule technique (having no witness). If these two conditions are not met, $v_{12}$ is excluded from $v_1$’s adjacent neighboring node list (i.e., connected to another face). Similarly, $v_{20}$ is excluded from $v_1$’s adjacent neighboring node list. We can emphatically say that they are neither the immediate neighbors nor the distant neighbors of $v_1$.

Concern 4

According to the rules of node organization techniques described in Sect. 4.1, do all the nodes of all the neighboring faces of a specific face (where t is currently moving) involve in tracking?

According to the rules of node organization into faces, we only consider a t’s current moving face ($F_i$) and the predicted face $F_j$, and the edges and nodes of these faces associated with the monitor and backup nodes. We need to mention an underlying issue of the localized face: When t travels across $F_i$, not only is the closed face covered, but an additional area is also covered by each node’s working area, since each node of $F_i$ contributes a part of its working area inside $F_i$. The rest of the working area of the node is on the outside of $F_i$, which is included with a neighboring face and is not mainly our concern, except that there is the event of t’s missing. The outside/additional area of $F_i$ can be calculated by the rest of the working areas of all of the nodes of $F_i$. In this example, the number of nodes of $F_i$ is still the same. Such an area can be effectively used in the event of t’s missing. If any node corresponding to $F_i$ can detect t outside of $F_i$ in its working area, the adjacent face of $F_i$ immediately becomes the new $F_i$, and one of the node become monitor based on the detection probability ($P_d$) on t and another node becomes the backup, just like the target detection and tracking operation start at the beginning. They send a message to the monitoring and neighboring nodes in the previous $F_i$ to change their active state $s_i$ to inactive state $s_2$ (excluding the node if any node belongs to the new $F_i$). The calculation of additional area coverage can be found in existing localization approaches, e.g., [93].

Concern 5

What is the main purpose to treat two nodes as “monitor” and “backup” for the tracking?

In many localization techniques, such as TOA, TDOA, AOA, or MPS, a large number of nodes (3 to many) requires to participate in tracking. In many cases, most of the nodes of the network should be awake during a tracking. Tracking schemes with target localization-free require more nodes, such as Forms needs a lot of nodes (12 to many) in each period of tracking. In t-Tracking, one of the main purposes or advantages of treating the monitor and backup as the common nodes between the faces, $F_{i}$ and $F_{j}$, is to minimize the number of participating nodes in target tracking. For example, $v_{5}$ has 5 adjacent faces with 12 neighboring nodes in Fig. 2, and node $v_{1}$ has 3 adjacent faces with 8 neighboring nodes. However, nodes $(v_{1}$ and $v_{5})$ together directly correspond only 2 faces with 7 neighbors. Thus, in a normal case of tracking, the number of nodes involved in tracking can be minimized from 20 to 7. This also implies that a number of nodes that hear about t’s approaching become active. Among them, the number of nodes that do not participate in tracking (they may be basically idle and unnecessarily consume energy) can be minimized. Another purpose is to provide robustness in tracking. In the case that the monitor has any problem due to any reason, the backup takes the role of the monitor. Target detection and localization is mainly performed by using their previous “cooperation information”.

Appendix B

More Concerns with the Proposed Tracking Algorithms

Concern 6

Does $P_d^c$ (the combined detection probability) estimation really result in a successful tracking operation?

As t moves toward the monitor and backup, the distance $d(l_i^s-l_i)$ between t and each of the nodes decreases and the $P_d^c$ between the monitor and backup increases. In most cases, $P_d^c$ between the pairs of neighboring nodes should decrease. The steady decrease in the distance increases in the probability, meaning that t is moving from the monitor and backup to new monitor and backup (from $F_i$ to $F_j$, as shown in Fig. 3(b)). When $P_d^c$ by any two nodes (the monitor and backup) is the highest, compared to its probabilities in the previous instants and to probabilities of the neighboring pairs of nodes, the chance that t crosses the edge between them is high, resulting normally in a successful tracking step (STS). We think that there may not happen such a case that $P_d^c$ of two pairs of nodes is the same. However, because of the node organization into faces, there has a possibility that $P_d^c$ of two pairs of nodes can be close.

Recall that in Sect. 4.2, we have mentioned that the angle between two or three adjacent neighboring nodes can be estimated to decide in which face t is in. This can also be used to reduce the above possibilities. However, such estimation may bring additional complexity in computation. Regarding the relevant information of the node organization into faces, we set three conditions for any pair of nodes to be the monitor and backup: (i) $P_d^c$ should be higher than other pairs of nodes; (ii) they should be the adjacent and also be the immediate neighbors; (iii) they should be in the same face $F_i$ (e.g., $F_2$).

These conditions reduce the wrong selection of the monitor and backup as well as the wrong detection of t, resulting in a successful tracking operation.

Concern 7

Is there any big deal of detection error in the estimation of $P_d^c$ between two nodes? More precisely, according to the scenario presented in Fig. 4, how does the system detect that t is going to cross between $v_1$ and $v_5$, not between $v_1$ and $v_3$, or between $v_5$ and $v_4$.

This is quite similar to Concern 6. But we want to discuss it in another point of view, which may help understanding the target tracking through faces.

If t moves, it must move toward another face $F_j$, but initially the system does not know which face t is moving toward. In fact, tracking t is not only based on t’s movement direction, also based on the direction of the nodes (or which face) t is moving toward. As shown in the scenario presented in Fig. 4a–c, it may move toward any face, i.e., toward $F_3$ by crossing the edge between $v_6$ and $v_7$, toward $F_{12}$ by crossing the edge between $v_5$ and $v_6$, toward $F_{10}$ by crossing the edge between $v_7$ and $v_2$, and $F_{18}$ by crossing the edge between $v_2$ and $v_1$. It may also turn back to $F_{1}$ by crossing the edge between $v_1$ and $v_5$. In an extreme case, if t turns back, it should be easily detected as it is still under detection (within $R_s$ of the same nodes). When such a case happens, $d(l_i^s-l_i)$ continues to decrease as time goes on, which was increasing in the previous some time instants. $P_d^c$ between any pair of nodes should be increased or decreased (see Concern 6). This indicates that t is still moving inside $F_i$ and may move across from $F_i$ to $F_j$. There is no chance that t is crossing another edge between another pairs of nodes (e.g., between $v_1$ and $v_3$, between $v_3$ and $v_4$, between $v_5$ and $v_{24}$, or others) without going through the edge between the monitor and backup or the edge between any pair of nodes of $F_i$ (which are also common nodes between $F_i$ and $F_j$). Thus, there should be no big deal of detection error.

Concern 8

Suppose that t is moving toward face $F_7$, how does it work? More precisely, how does the system knows that t is moving toward $F_7$, not $F_3$, or $F_9$ in Fig. 2? Actually, in the beginning, how does the system detect t is in $F_1$?

To reduce the confusion about the target tracking, we raise Concern 7. In fact, this is similar to Concern 6 in the sense that we discuss Concern 6 considering t’s moving through an edge between any two nodes (the monitor and backup), while we can discuss Concern 7 considering t’s moving through an edge between two faces. The two nodes (a pair) are the common nodes between the two faces. In other words, the edge between the two nodes (a pair) is also the common edge between the two faces. The underlying techniques are the same. We emphatically say that, in t-Tracking, it is non-trivial to determine exactly at which face t is currently located and moving, and then which face t may move. We have elaborated how the above conditions can be obtained in Sect. 4.2 and Algorithm 2.

Concern 9

Why is the “face prediction” preferred to the target movement prediction?

Depending on finding accurate movement prediction, providing quality of tracking (QoT) is difficult in a practical, unpredictable environment. Because of faults in the WSN, noise in the environments, or any other reasons, if there are prediction errors, it becomes tough to relocate t further. Particularly, it is tough when considering the fast tracking operation and radio and energy constraints in the WSN. This is why, we first roughly find the movement information of t inside a face and the prediction information. Then, we convert these into a “face prediction”. We do not find any second-order error adjustment on the localization or on the estimation of the $P_d$. Up to this point, we have assumed that t can be detected by the monitor and backup, which are the end nodes of a “direct edge” (the “common nodes” between two faces), that t is about to cross to. Thus, to avoid an unexpected loss of tracking, the tracking is based on the face prediction.

Concern 10

What if t is no longer in the detection range of a $F_i$? We handle this extreme case that may appear during tracking operation. Assuming that t has disappeared or is missed during tracking, t may be out of $R_s$ of any of monitor and backup. This may be due to several reasons: irregular signal patterns, especially when (i) a face size is too small in the situation that network density $\rho$ too high or low in the local areas and (ii) t is much faster than normal. In such a case, the WSN in t-Tracking still has the ability to track/capture t. This case is mitigated by extending the face area coverage (see Concern 2).

Suppose that there is the event of t’s missing reported by the monitor for whatever reason. When the monitor broadcasts a message about the event, the distant nodes start sensing (or which are already in sensing function), since they are in $s_0$. If t is sensed by a distant node in its $R_s$, but is outside of $F_i$, the corresponding face in which t is sensed becomes a new $F_i$. The distant node becomes the monitor, and it issues a message to the nodes in the previous $F_i$ and finds a backup. All of the nodes, including previous monitor and backup in the previous $F_i$, revert to $S_2$, and the nodes in the current $F_i$ start target detection and face detection algorithm.