Several recent works have discussed the design of country border surveillance systems based on WSNs. A majority of the proposed solutions have displayed the WSN nodes as a linear network, so that every movement going over the barrier (or line) of the sensors is detected [7] - [9] . Compared to full coverage, the barrier coverage provided by a perfect linear deployment requires only a few sensor nodes, but experiences more radio disconnections, due to sensor failure and energy depletion. In addition, this kind of linear architecture presents two drawbacks: first, it does not permit the tracking of intruders, since the intruders are only detected when they cross the line of sensors and their future movements cannot be tracked. Second, the sensor nodes are not able to locally determine whether the barrier full coverage is ensured.

On the other hand, solutions using k-barrier coverage require that all crossing paths in the monitored region around a spatial line are covered by at least k distinct sensor nodes. Such solutions include the 3-layered hybrid network architecture for border patrol, called Bordersense that has been proposed in [10] . Bordersense deploys advanced sensor networking technologies utilizing multimedia sensor nodes, mobile sensor nodes, and scalar sensors, which could be installed underground or above the ground. The high cost of the deployment of multimedia sensors (including cameras) makes Bordersense hard to deploy for larger borders and the uniformity of sensor distribution difficult to achieve, except when an appropriate deployment scheme is designed taking into consideration the environment complexity.

The case of border surveillance when sensors are randomly and uniformly deployed has been also investigated in a few works. Even though uniform sensor deployment is useful in theoretical scenarios, it remains unrealistic in the real cases, where a non-uniform placement is experienced due to several environmental features such as dense vegetation and rough terrain. In addition, most of the published works do not provide a mathematical control of the sensing coverage, so that coverage hole can be detected and repaired.

On the hand, the authors in [11] presented the design of border surveillance solutions using wireless sensor networks while providing the following contributions: first, a global network architecture for border surveillance based on three types of components operating in a thick line architecture was set up along the border. Second, a deployment strategy that copes with many constraints on the WSN operation, coverage maintenance, connectivity preservation, and routing quality of service was designed. Finally, a mechanism of routing management to ensure efficient data relaying and reporting between the different node layers. Even though target tracking and target moves prediction were not addressed in [11] , the solution presents interesting aspects such the mathematical control of the sensing and communication coverage quality.

On the other hand, one can see that some other proposed frameworks for border surveillance assumed that a line- (or a thick-line) based WSN offering barrier or k-barrier coverage is provided. Under this assumption, the solutions attempted to reduce the number of needed sensors to monitor the crossing of a given border; but, the improvement is obtained at the expense of efficiency reduction and tracking limitation. In other words, line- based deployment at best ensures the detection of all intrusion attempts, but will not allow to take an internal decision about tracking the intruders. Furthermore, the coverage provided by these solutions is not realistic due to environmental factors and sensors dropping techniques (air-dropping or manned dropping, for example). Another limitation of the proposed models is the silence they observe about the connectivity and prompt reactivity issues.

In addition, one can see that target tracking under surveillance systems presents very special constraints with respect to the common WSN-based monitoring of two dimensional areas. Indeed, tracking in border surveillance should be done in real-time mode, should be available all the time, should be continuous, and should be able to help predicting the exit time and zone for the monitored area. The objectives of the next subsection are to survey the works performed in WSN-based target tracking approaches and to discuss their limits with regards to the aforementioned differences.

We can classify the target tracking techniques into several categories, based on the sensor activation modes, the network topologies and the sensor partition techniques they use. Node activation can be naïve, randomized, selective, based on trajectory prediction, or duty cycled [12] . Naïve activation based tracking techniques, where all nodes are in active (or tracking) mode all the time, are among the simplest and general tracking techniques. In such context, the sensing nodes report their local measurements to the sink node. The latter follows the target motion in relation with the reported measurement and attempts to predict the target positions in the future. Naive activation ensures high tracking quality; but, it offers the worst energy consumption and provides heavy communication to the sink node, since sensors are all the time sensing, estimating, reporting, or data relaying.

Tracking methods using naïve activation are not robust because the WSN they use is more prone to energy depletion, traffic congestion, sensor failure, and even security attacks. In the following, we consider the other solutions and mainly discuss two major overlapping categories; namely, the hierarchical and prediction-based classes of tracking [13] [14] . We also analyze their drawbacks with respect to border surveillance requirements.

WSN-based surveillance applications features are characterized by the nature of the environment where the applications take place and the degree of the tracking efficiency required for the applications. In the following, we discuss the most important WSN characteristics needed to achieve efficient mobile target tracking in a hazardous environment. Some of these characteristics have been discussed in [10] and [6] .

Communication infrastructure: as mentioned before, two common types of WSN communication models are currently used to achieve surveillance: the hierarchical and the flat networks. While the first structure allows the existence of nodes, called cluster heads, capable of performing sophisticated operations and having more energy than simple sensor nodes, the nodes in the flat structure have the same capabilities and should collaborate to relay any report from the generating node to the sink node. In both models, surveillance should be able to optimize the energy consumption and keep connectivity. While hierarchical infrastructures should reduce the relaying activity within clusters, the flat architecture should reduce the number of sensors involved in event collection and target tracking.

Deployments cheme: The deployment of sensor nodes in a surveillance application in an irregular environment cannot be accomplished according to a deterministic choice. Due to the hostility of the physical environment, direct human control of the sensor nodes serving the surveillance application may be hard to achieve, and might be impossible in certain situations. Typically, sensor nodes are dropped from manned/unmanned aircrafts in a given area and should provide total sensing coverage, in some sense. Therefore, a control mechanism should be attached to the deployment scheme to allow measuring the required level of coverage any time. The control may use a large set of parameters that can be effectively monitored, including node density, sensor range, and k-coverage capability.

Energy management: The energy resources of a sensor node are limited because of the sensor size and cost constraints. In fact, localization, sensing functions, and communication techniques could not be performed without taking into consideration energy constraints. In addition, high-resolution information about the monitored area is often needed, requiring the use of energy-aware techniques. Energy is the most important factor occurring in the determination of the WSN lifetime. The required lifetime in the surveillance context should last as long as possible. Therefore, the sensors should be able to be automatically recharged after their amount of energy is consumed, or they should be replaced upon energy depletion or failure. Moreover, to provide surveillance continuity, the system should be able to estimate energy consumption for every sensor and determine in advance the energy failure moment to provide sensor replacement.

Mobile target tracking: Three major requirements have to be fulfilled by sensors in a surveillance system: First, the sensors should be unnoticeable, meaning that their positions should be hard to determine by non-autho- rized parties and their size should be limited. Second, the sensor nodes should be able to locate targets moving under a reasonable speed v in the monitored area (generally,). Third, the sensor nodes should be able to collaborate with each other to construct the path followed by a target and predict its exit zone from the monitored area.

Monitored area coverage: The sensor nodes in a surveillance application should collaborate to achieve sensing coverage of the whole area in order to collect useful events when they occur and to build continuously the path followed by any target trying to cross the area. In addition, the WSN needs to be connected so that any collected event or target related information is forwarded to the sink node, via the other nodes if needed. Since the communication coverage of a single sensor node is basically dependent on the sensing range of the sensors attached to it, the communication requirements of the surveillance system should depend heavily on the sensor sensitivity to track targets. The WSN must be able to minimize the errors related to mobile target detection and feature measurements.

The deployment of sensors for border surveillance may be made in a strip along the borderline of a country with a width sufficiently large. The system should be able to track mobile targets (including individuals, animals, and vehicles), help following their paths, and estimate their exit points from the strip. To this end, the deployment schemes and scheduling activity of the WSN may need comply with two categories of rules: the density controlling rules and the scheduling rules. In the following, we discuss some of these rules.

Density related requirements. It is obvious that the quality of target detection and tracking depends on the number of deployed sensors and the surface of the given strip. An efficient deployment scheme should guarantee that every point in the strip, where a target can be, is sensed by at least one active sensor. However, knowing that the target enters the strip from one edge of the strip and exits it from the other edge, this condition can be achieved by the following rules:

Monitoring line rule: At least one sensing line should be active to detect the beginning of a crossing action. The sensing line is nothing but a sequence of sensors separated by at most twice the sensing range of the sensors. This line should be parallel (in some sense) to the borderline so that an object crossing the strip should traverse it. Furthermore, to provide premature detection, the sensing line should be close to the borderline. The number

of sensors that form the sensing line should be higher than, where is the sensing range of the sensors and L is the length of the borderline. Most of the time the sensing line is physically a broken line requiring many more sensors than.

Density rule: More generally, if the coverage of every point in the strip is required, the number should be higher than

where W is the width of the strip. The formula assumes that the strip is bounded with a surface equal and that any sensor, except those on the border of the strip, has at least 6 sensor neighbors (i.e., the traditional pavement in cellular networks). This rule guarantees he high probability that every point in the strip is covered by a sensor, provided that the deployment is uniform.

Scheduling constraints. It can be easily seen that the scheduling scheme within surveillance systems should be able to comply with two contradictory objectives. They are the sensor lifetime and the sensing continuity. Three rules can be distinguished.

Lifetime rule: The lifetime of the sensors should be as long as possible, assuming that the energy consumption should be reduced for all sensors and that any target crossing should be detected. This means that the scheduling operation should handle sensor sleeping, target detection, and target tracking tasks with different strategies. The first sensors in charge of target detection should belong to at least one established line of surveillance, for instance; and in that case, the line should be maintained to provide energy reduction and modified from time to time. On the other hand, sensors in charge of tracking must be awakened only when needed.

Prediction Awake rule: Sensors in charge of tracking are awakened when the detected target occurs in their vicinity. Awake sensors in charge of tracking an active target should collaborate to predict the next positions (in the next time slot) of the detected target and reduce the number of the sensors to wake up upon target detection. The prediction of the next positions should be able to help determining which sensor(s) to wake up in the next time slot. Position prediction must take into consideration the geographic nature of the monitored area and the history of target motion.

Tracking continuity rule. Only a few sensors should be awakened to provide continuous target tracking so that targets can be monitored properly (at any time slot) until exit time. Since the time is slotted, we assume here that continuous tracking means that the surveillance system is able to locate the target at any time slot after its/his first detection. Let us notice, however, that this definition can be reduced by changing the expression “any time slot” by the expression “every n time slots”, for small values of n.

To be detected, the target should move at a speed (counted in meters per time slot) higher than a given minimum speed and lower than a given maximum speed, depending on the characteristics of the detecting sensors. The following rules, called target mobility rules and target path rules, define how the target moves towards the exit edge of the border strip under uncontrolled or controlled time mode.

Target mobility rules. Assuming that the target is at position p at time slot t, a mobility rule supposes that the new position of the target at the following time slot is randomly located in a sector zone centered in p, at a distance d from p and an angle with respect to the borderline randomly selected in interval and, respectively, assuming that and. Figure 3 depicts the mo-

bility rule of the target. The angle characterizes the maximal deviation with respect to the shortest exit direction. Indeed, ensures that the target is moving towards of the exit edge of the strip.

The distances and correspond to the minimal speed and the maximal speed of the target during one time slot. It is obvious that should be strictly positive and that should be commensurate

with sensing range, the sensor sensitivity, and the slot duration. In particular, when is very large, the border surveillance system may not be able to detect the target. Moreover, if, the target can keep moving parallel to the borderline without getting out from the strip. Finally, if, the target may spend a quasi-infinite time to exit the strip.

Target path rules: Several rules can be reasonably used to model the target path. A first rule assumes that the target approaches the exit edge of the strip with at least meters at every time slot (or a given number of slots). The minimum value of displacement may be determined in function of the maximal deviation

and the minimal target velocity using the following formula

This rule states again that and that the maximum time that the target may spend to reach the exit edge of the strip is given by

where is the distance of the initial place to the exit edge and is the floor function. Since the target motion towards the exit edge depends on the nature of the strip (e.g., including vegetation, obstacles, and geographic diversity), our target model allows the distance d made by the target in one time slot to be randomly selected to help representing the strip nature effects on the target path. Modeling the path followed by a target during n time slots starting from time slot can be done by a sequence defined by

where n is the number of time slots used to observe the target, is the identity of the sensor observing the target at the k^th slot, is the position of sensor, and is the (angular) position of the target observed at the k^th slot with respect to.

Let be the distance between and, one can easily deduce that, if measures the distance between and the exit edge, the following relations hold

and

since for all. Therefore, we can deduce that the series is decreasing. It stops when becomes lower than.

Thus, we have the following result.

Proposition 2. Assume that the aim of a target is to reach the exit edge of the border strip and that the monitoring line active has detected him/it at time slot and that the density rule, the mobility rule and target path rule are satisfied. Then, the following statements stand:

1) The path modeling process converges in a finite time, meaning that the target will reach the exit edge in a time shorter than a maximum time given by

2) The maximum length l of the path followed by the target between its detection point and time termination is given by

Proof.

The process has been shown to terminate by providing the computation of the maximum time to reach the exit edge, provided that the motion of the target is governed by the mobility rule. One can easily see that at every time slot after (i.e., after a first detection is performed), the next position of the target is closer to the exit edge of the strip, provided that the mobility rule is satisfied. The process terminates when the sensing disk of the detecting sensor overlaps the exit edge of the strip and that expected next position is out of strip. This means that the process stops at the slot when

Computing the length of the target path travelled until time slot k is given by. This length is bounded as follows

The inequalities can be easily stated using the mobility and target path rules, knowing that, for all j.

Let us now study the sequence defined by, as obtained by the mobility model after a target is detected, and let us update it at any slot where a new observation of the target is made by a sensor. The objectives here are to maintain the modeled path of crossing target and to estimate his/its exit time and exit place efficiently. Let us first summarize the technique we use to achieve this. The technique is iterative and maintains three variables as time slots go; namely, the current position, the next positions, of the target, the expected zone of exit (i.e. a segment on the exit edge), and the expected time of exit.

During step n, the predicted position of the target is replaced by the observed position. This process helps selecting the next sensor that will insure the tracking continuity in the time slot and delimiting the exit segment. Once selected, this sensor updates the predicted position of the target according to its observation. Then, the next positions, in the time slot, , of the target knowing its position are approximated using the mobility model presented in the above subsection,

Let us now show how the sink node predicts the exit time of a target along with its exit segment, as it is kept informed by the target motion. To this end, we consider the following notations: Let be the sensing disc of a sensor s tracking the target at the time slot. Let be the diameter of this disc parallel to the exit edge of the strip, and be the projection of on the exit edge. We refer to the resulting segment as the potential exit segment of the target at time n. Finally, let be the segment on the exit edge delimited by the intersections between the edge and the two possible lines drawn from the expected position and forming an angle with the exit edge. We refer to the segment as the exit segment of target at the time slot. Figure 4 depicts these segments to clarify the notations.

Let us compute the different segment using and the distance. If and, we have:

・

・

・

・

・

・

where half of the length of segment. It is simply given by:

The following result studies the evolution of the potential exit time and exit segment of the target, assuming that the distance separating the target from the exit edge decreases of at least meters every time slots, as a result of the mobility model. A similar result can be obtained if the assumption is replaced by the following weaker one: the distance separating the target from the exit edge decreases of at least meters every timeslots ().

Proposition 3. a target crossing the border strip and and be the series of potential exit segments and exit segments, respectively. Then, the following statements hold, provided that the target follows the target mobility rule:

1) The length of segment satisfies the inequality for all k:

2) The two sequences and are finite and converge to the same segment limit, which is length.

3) If position is attained by the target at time slot n, then the target will reach the exit edge at a time, where

Proof.

First, let us notice that using the mobility rule we can show that the inclusion holds and the sequence is strictly decreasing. Let us now prove the equality

Figure 5 depicts the segments and. One can see that the function:

This function is continuous. Let an angular representation of. For a given, the function reaches its minimum for or (points a et in Figure 5). It reaches its maximum at (points b in Figure 5). This shows that:

where:

and

Second, one can deduce from the first statement that is strictly decreasing and that

The two series are finite since at every step the target approaches the edge by at least meters (and by at most meters) each time slot and that the tracking process stops when a sensor close to the exit edge wakes up to track the target. The distance of this sensor to the exit edge is therefore smaller than.

The number of elements in these series is thus lower than as stated by Proposition 2.

Third, it has been shown in Subsection 5.1 that if the target is detected at a position p then it reaches the edge before a maximum time given by:

One can also easily show that the target will arrive after a time

Applying these inequalities, when, gives the following: if the target it position at the time slot, then the target will reach the edge at a time, where:

Various methods can be utilized to estimate the time of exist. One could estimate, set at time slot k, by

Another method computes the average distance per slot travelled by the target and set, at time slot k, an estimation of the exit time by:

The simulation model is built by considering that the area to be monitored is of size meters and that it is partitioned into of squares of 25 meters side. A set of sensors of size is deployed uniformly in that strip (one in each square). The sensors are assumed to have the same sensing range varying in the set and that is wider than π/12. The communication range on the sensors equal to. In the following numerical experiments we will discuss the impact of the sensing range, the targets’ arrival law, the angle, and the size of (or target speed) on the performance of the surveillance coverage and its ener-

gy consumption. For this, we will conduct simulations by varying in the above set, in, and in {5,10,15}. Targets will be assumed to arrive uniformly in time and space.

Three major objectives will be studied in the sequel. First, the quality of coverage (including the barrier) will be discussed. Second, the discontinuity ratio will be analyzed as a function of important factors including, and. Third, the efficiency of our method will be discussed in terms of communication overhead and exit estimation quality. Such studies will help dimensioning the deployment process and the value of to reduce the number of active deployed sensor and guarantee tracking continuity.