A Protocol for Tracking Mobile Targets using Sensor ... - CiteSeerX

A Protocol for Tracking Mobile Targets using Sensor Networks H. Yang and B. Sikdar Department of Electrical, Computer and Systems Engineering Rensselaer Polytechnic Institute Troy, NY 12180 Email: {yangh2,sikdab}@rpi.edu

Abstract— With recent advances in device fabrication technology, economical deployment of large scale sensor networks, capable of pervasive monitoring and control of physical systems have become possible. Scalability, low overhead and distributed functionality are some of the key requirements for any protocol designed for such large scale sensor networks. In this paper, we present a protocol, Distributed Predictive Tracking, for one of the most likely applications for sensor networks: tracking moving targets. The protocol uses a clustering based approach for scalability and a prediction based tracking mechanism to provide a distributed and energy efficient solution. The protocol is robust against node or prediction failures which may result in temporary loss of the target and recovers from such scenarios quickly and with very little additional energy use. Using simulations we show that the proposed architecture is able to accurately track targets with random movement patterns with accuracy over a wide range of target speeds.

I. I NTRODUCTION Advances in the fabrication and integration of sensing and communication technologies have facilitated the deployment of large scale sensor networks. With their capability for pervasive surveillance, control of physical systems and economical large scale deployment, sensor networks and their applications have tremendous potential in both commercial and military environments. However, the need to coordinate such large networks as well as their inherent limitations like power constraints, distributed coordination and ad hoc deployability lead to a number of challenges in the design and deployment of sensor networks. In addition, the application specific communication and system requirements may put additional constraints on the design and coordination of such networks. In this paper, we address the issue of scalable coordination and operation of a large scale sensor network specifically designed to track mobile targets. One of the most important areas where the advantages of sensor networks can be exploited is for tracking mobile targets. Scenarios where such network may be deployed can be both military (tracking enemy vehicles, detecting illegal border crossings) and civilian (tracking the movement of wild animals in wildlife preserves). Typically, for accuracy, two or more sensors are simultaneously required for tracking a single target, leading to coordination issues. Additionally, given the requirements to minimize the power consumption due to communication or other factors, we would like to select the bare essential number of sensors dedicated for the task while

all other sensors should preferably be in the hibernation or off state. In order to simultaneously satisfy the requirements like power saving and improving overall efficiency, we need large scale coordination and other management operations. These tasks become even more challenging when one considers the random mobility of the targets and the resulting need to coordinate the assignment of the sensors best suited for tracking the target as a function of time. In this paper we propose a architecture for managing and coordinating a sensor network for tracking moving targets. However, the proposed architecture is quite general and can be easily adapted for use in other applications. The problem of tracking targets with sensor networks has received attention from various angles. In [6], the authors consider the case where a set of k targets need to be tracked with 3 sensors per target from the resource requirement viewpoint. They show that the probability that all targets can be assigned 3 unique sensors shows phase transition properties as the level of communication between the sensors increases. In [12] an information driven sensor collaboration mechanism is proposed. In this mechanism, measures of information utility are utilized to decide future sensing actions. Collaborative signal processing aspects for target classification in sensor networks is addressed in [7]. Tracking based on relations in the targets is discussed in [13]. Techniques for locating targets using a variety of mechanisms have been proposed in [5], [11], [10]. However, current literature does not address the issue of a scalable architecture for coordinating a sensor network for the purpose of target tracking. Nor is there any existing work which deals with the feasibility, minimization of computation and communication overheads and understanding the tradeoffs in such systems. In this paper we address these issues. In this paper, we propose a distributed and scalable prediction based algorithm (the Distributed Predictive Tracking algorithm) to accurately track mobile targets using sensor networks. The algorithm uses a cluster based architecture for scalability and robustness. Power conservation is one of the key design guidelines of this protocol and we assume that most of the sensor nodes are in the hibernation mode at any given point in time. Given a target to track, the protocol provides a distributed mechanism for locally determining the optimal set of sensors suitable for the task. Only these nodes are then activated, minimizing the energy spent on tracking.

Additionally, the protocol uses a predictive mechanism to intimate cluster heads about approaching targets. Based on this prediction, the cluster head activates the most appropriate sensors for the task immediately before the arrival of the target. This reduces the likelihood that the target is lost while allowing most sensors to stay inactive most of the time. Our simulation results show that the protocol is successful at accurately tracking randomly moving targets over a wide range of speeds. We also show that the proposed architecture has a robust failure recovery mechanism which can recover lost targets (caused by both prediction and node failures) quickly and with very low power usage. The rest of the paper is organized as follows: In the following section we present an overview of some of the challenges in developing a protocols for large scale sensor networks. Section III presents our distributed tracking algorithm and Section IV presents simulation results validating its effectiveness and accuracy. Finally, Section V presents the concluding remarks and possible future work. II. C HALLENGES A large scale tracking system with sensors gives rise to a number of design challenges with constraints specific to scenarios with sensor networks. In this section, we discuss them in detail and lay the groundwork for our proposed protocol for target tracking. We describe the various issues associated with sensor networks that need to be addressed by any protocol being developed for application in sensor networks. We comment on general requirements of such protocols and also on issues specific to the scenario of target detection using sensor networks. The power limitation due to the small size of the sensors, the large numbers of sensors which need to be deployed and coordinated, and the ability to deploy sensors in an adhoc manner give rise to a number of challenges in sensor networks. Each of these needs to be addressed by any proposed architecture in order for it to be realistic and practical. 1) Scalable Coordination: A typical deployment scenario for a sensor network comprises of a large number of nodes reaching in the thousands to tens of thousands. At such large scales, it is not possible to attend to each node individually due to a number of factors. Sensors nodes may not be physically accessible, nodes may fail and new nodes may join the network. In such dynamic and unpredictable scenarios, scalable coordination and management functions are necessary which can ensure a robust operation of the network. In the light of target tracking, the coordination function should scale with the size of the network, the number of targets to be tracked, number of active queries etc. 2) Tracking Accuracy: To be effective, the tracking system should be accurate and the likelihood of missing a target should be low. Additionally, the dynamic range of the system should be high while keeping the response latency, sensitivity to external noise and false alarms low.

The overall architecture should also be robust against node failures. 3) Ad Hoc Deployability: A powerful paradigm associated with sensor networks is their ability to be deployed in an ad hoc manner [3]. Sensors may be thrown in an area affected by a natural or man made disaster or air dropped to cover a geographical region [4]. Thus sensor nodes should be capable of organizing themselves into a network and achieving the desired objective in the absence of any human intervention or fixed patterns in the deployment. 4) Computation and Communication Costs: Any protocol being developed for sensor networks should keep in mind the costs associated with computations and communication. With current technology, the cost of computation locally is lower than that of communication in a power constrained scenario [2]. As a consequence, emphasis should be put on minimizing the communication requirements. 5) Power Constraints: The available power in each sensor is limited by the battery lifetime due to the difficulty or impossibility of recharging the nodes. As a consequence, protocols which tend to minimize the energy consumption or power aware protocols which adapt to the existing power levels are highly desirable. Additionally, efforts should be made to turn off the nodes themselves if possible in the absence of sensing or coordination operations. In the next section, we present our proposed architecture for scalable and accurate tracking of mobile targets. The protocol specifically aims at minimizing the communication and control overheads while using a cluster based approach to achieve scalability. III. A D ISTRIBUTED A LGORITHM FOR P REDICTIVE T RACKING In this section we describe our proposed protocol for efficiently tracking mobile targets with sensor networks. The Distributed Prediction Tracking (DPT) algorithm is specifically aimed at addressing the various challenges outlined in the Section II while accurately tracking moving targets. As the name suggests, this algorithm does not require any central control point, eliminating the possibility of a single point of failure and making it robust against random node failures. The tracking task is carried out distributively by sequentially involving the sensors located along the track of the moving target. Our algorithm assumes a cluster based architecture for the sensor network and the choice was motivated by the need to ensure the sensor network’s scalability and energy efficiency. A number of clustering algorithms have been proposed in literature ([1], [8] and the references therein) and in this paper, we are not concerned with the details of the clustering mechanisms. Any suitable clustering mechanism from those proposed in literature may be used and we note that our protocol does not impose any specific requirements or restrictions on the choice of the clustering algorithm.

A. Assumptions of the DPT Algorithm We now describe the assumptions made by the DPT algorithm. While no assumption is made on the choice of the clustering algorithm, we assume that the Cluster Head (CH) has the following information about all sensors belonging to its cluster: (1) Sensor identity, (2) Location and (3) Energy level. When tracking a moving target and deciding which sensors to use for tracking, the cluster head’s decision-making procedure will be based on this information. The assumptions about the sensors are enumerated below. These assumptions are realistic and targeted at reducing the energy cost and prolonging the whole network’s lifetime as well. 1) All sensors have the same characteristics 2) Sensors are randomly distributed across the whole sensing area with uniform density. 3) Each sensor has two sensing radii, normal beam r and high beam R. The default operation uses the low beam and the high beam is turned on only when necessary. The following relationship holds between the energy consumed by the low and high beams: Elowbeam r2 = 2 Ehighbeam R

(1)

4) A sensor’s communication and sensing channel stay in the hibernation mode most of the time where they consume minimal energy. The communication channel will wake up routinely to receive possible messages from its cluster head. The sensor will perform sensing according to its cluster head’s requirements. In order to produce accurate enough information to locate the moving target, our algorithm requires that at any given time there should be at least 3 sensors to sense the target jointly. We choose 3 sensors as the compromise between increasing accuracy and minimizing the consumed energy (note that this is not a hard assumption and depending on the sensor node specifications the number may vary). The choice for the number of required sensors per target intrinsically decides the sensor density λ nodes/m2 of the sensing network. To minimize the likelihood of missing a target, the probability p that an arbitrary point inside the sensor network can be sensed simultaneously by at least 3 sensors with their normal beams should be close to 1. Since the sensors are assumed to be uniformly distributed over the sensing region and the number of sensors is large, the distribution of the number of nodes in any given area A is Poisson with rate λA. The probability that there are 3 or more sensors within the low beam sensing range of any arbitrary point is then given by: p=

2 ∞ X e−λπr (λπr2 )i

i=3

i!

(2)

From the above expression, substituting a desirable value for p, say 0.99, the required node density λ can be easily obtained. No specific assumptions are made about the movement pattern of the targets. However, we assume that the targets

originate outside the sensing region and then move inside. Also, it is assumed that the movement of each tracked target needs to be forwarded to a central location which we term the sink. In reality, the sink could be either a special node or a terminal associated with a human. B. The Distributed Prediction Tracking Algorithm The fundamental guideline followed throughout the the design of the DPT algorithm was to keep the algorithm as simple as possible. With a simpler algorithm both the calculations and the communications between sensors or clusters become less, thereby reducing the energy consumption rate of the nodes and increasing the whole network’s lifetime while simplifying the hardware and software requirements at the nodes. The DPT algorithm comes into play after sensors are deployed and clusters are formed. DPT distinguishes between the border sensors, sensors located within a given distance of the border, and non border nodes in terms of their operation. While border sensors are required to keep sensing all times in order to detect all targets that enter the sensing region, the non-border sensor’s sensing channel hibernates unless it is specifically asked to sense by its cluster head. Since the target is assumed to move from outside into the sensing area, it will be detected by the border sensors when trespassing the border. As soon as a target is detected, a sequence of tasks in the order of “sense-predict-communicate-sense” are carried out distributively by a series of sensors that located along the target’s track. This forms the essential idea behind the DPT algorithm. We now introduce and explain the main components of the algorithm. 1) Target Descriptor Formulation Algorithm: In order to identify the target and provide the target’s location information, cluster heads use a Target Descriptor (TD). The following items are incorporated in the TD: 1) Target identity 2) Target’s present location 3) Target’s next predicted location 4) Time stamp A cluster head uses the Target Descriptor formulation algorithm to obtain the TD for each target it is tracking. We now describe this process in greater detail. In order to describe the TD formulation algorithm we will first introduce the notation of “upstream cluster head” and “downstream cluster head”, which are defined according to the cluster heads’ relative location along the target’s moving track. Let CH1 , CH2 , CH3 , · · · , CHi , · · · , CHN denote the sequence of cluster heads that become involved with tracking the target’s as it proceeds from its very first location to the last. CHi formulates T Di as the sensing result. Each descriptor is sent all the way back to the sink (either sent intact or after being aggregated) for further processing as well as to the downstream cluster head CHi+1 . We now describe how T Di is formulated at CHi . The “Target Identity” is created when the target is first detected. This identity is unique and all cluster heads that co-track this target use it to identify the Target Descriptor that they

generate. As described in detail subsequently in this section, in order to facilitate the smooth tracking of the target, CHi predicts the future location of the moving target, and informs the downstream cluster head CHi+1 ahead of time about this target. All inter cluster head communication uses this unique identifier to unambiguously identify the target as it passes through the sensing region. The next element in T Di is the target’s present location. As described before, for each sensing point a sensor-triplet is necessary to accurately locate the target and formulate the target descriptor. Each of the three sensors in the triplet individually obtain the relative position of target and then send this location information to the cluster head. The cluster head then aggregates this information (for example through triangulation) to obtain the target’s present location. Details of how the sensor-triplet is selected is given in Section IIIB.2. The third item in T Di is the target’s “next predicted location” and indicates the predicted location where the target will be after a given period of time. This predicted location is used by the cluster head to determine the most likely downstream cluster heads that the target is approaching and inform them in advance about the oncoming target. The downstream cluster heads can then use this information to direct its appropriate sensors for the sensing task. To keep the calculations and communication overhead low, this predication is only based on an estimation of the target’s present moving speed and direction. Suppose the target’s present location in T Di−1 is (xi−1 , yi−1 ), and (xi , yi ) in T Di . Then we can estimate the target’s speed as p (xi − xi−1 )2 + (yi − yi−1 )2 v= (3) ti − ti−1 while the direction is given by xi − xi−1

θ = cos−1 p

(xi − xi−1 )2 + (yi − yi−1 )2

(4)

Based on this information, the predicted location for the target (xi+1 , yi+1 ) after a given time t is given by xi+1 yi+1

= =

xi + vt cos(θ) yi + vt sin(θ)

(5) (6)

To be more precise, it can be shown that the target’s next location obeys a two dimensional Gaussian distribution with (xi+1 , yi+1 ) as the mean. By directly using (xi+1 , yi+1 ) as the “predicted next location” we aim to simplify the cluster head’s calculation and minimize the volume of messages exchanged between cluster heads and sensors. The accuracy of the “prediction” is very important if downstream cluster heads are to be identified accurately and the overall tracking mechanism is to be effective . While many prediction mechanisms are possible, what we have chosen is a linear predictor, which only uses the previous two locations to linearly predict the third location. We can also adopt higher order prediction, which predicts the nth location information based on previous n − 1 actual locations. Higher

Fig. 1.

Search for the sensor-triplet with normal beam.

order prediction results in more accurate results, though, at the cost of greater energy consumption. In Section IV we analyze the performance of our prediction mechanism. We note here that even with higher order prediction, the target miss probability (the likelihood that the target falls out of the sensor-triplet’s sensing range) can be fairly large under certain circumstances, specially in the presence of highly random target movement. To handle such cases, the tracking algorithm should to have a failure recovery mechanism to re-capture the lost target and we discuss this in detail in Section III-B.3. The last element in T Di is the “Time Stamp”, which indicates the time this T Di was created. 2) Sensor Selection Algorithm: After cluster head CHi predicts the location of the target, the downstream cluster head CHi+1 towards which the target is headed receives a message from CHi indicating this predicted location. With information of all sensors belonging to CHi+1 available in its database, the search algorithm running at CHi+1 is able to locally decide the sensor-triplet to sense the target. The selection rule chooses 3 sensors (if possible) such that their distances to the predicted location are not only less than the sensor’s normal beam r, but also the smallest. After the sensortriplet is chosen, CHi+1 sends them a wake-up message so that they are ready to sense the target. If the prediction and selections process succeeds, after sensing, each sensor will send a location message to CHi+1 , who then formulates T Di+1 based on this information. This process is shown in Figure 1. If CHi+1 in unable to find enough sensors eligible for this sensing task with the normal sensing beam, it will try to search for eligible sensors within a distance R, the higher sensing beam, from the predicted location. The selected sensors, whose distance from the predicted location is greater than r and lower than R, will now be contacted and instructed to sense with their high beam, while the rest of the sensors in the triplet use their normal beam. The sensor search process with high beam

Fig. 2.

Search for the sensor-triplet with highbeam

Fig. 3.

Coordination between multi-cluster

is illustrated in Figure 2. If CHi+1 is unable to find enough sensors even with high sensing beams, it asks its neighboring cluster heads for help. This is shown in Figure 3. 3) Failure Recovery: In this section we discuss the recovery scheme in the presence of link/node failures or prediction errors. We first identify the possible failure scenarios. As described in the previous subsections, each upstream cluster head formulates a target descriptor and sends it to the expected downstream cluster head. If the upstream cluster head does not get any confirmation from the downstream cluster head after a given period of time, then it assumes that the downstream cluster head is no longer available and the target has been lost. Another failure scenario occurs when the target changes it direction or speed so abruptly that it moves significantly away from the predicted location and falls out of the detectable region of the sensor-triplet selected for the sensing task. This

Fig. 4.

Failure scenario where the target is out of range.

scenario is depicted in Figure 4. In both of these failure scenarios a straight forward solution is to wake up all sensors within a given area, which is calculated based on the target’s previous actual location. The “re-capture” radius σ is an important parameter in this process and is decided by the target’s moving speed and time elapsed since it was last sensed. The appropriate choice of σ is basically an optimization problem: how to find the minimal number of sensors so that this whole area is covered? However, solving this problem is not cost effective when one considers the sensor’s computation capability and cost. Our recovery scheme is based on similar principles, but is kept simple in order to be suitable for sensor networks. The recovery process is broken into various levels: 1) First level of recovery: Let the currently selected sensortriplet switch to high beam if they were using the normal beam previously. If this succeeds, then follow the normal “sense-predict-communicate-sense” cycle. 2) Second Level of recovery: Figure 5 shows the basic operation of the second level of recovery. If the first level of recovery fails, a group of sensors which are around r meters away from Li are activated. These sensors will actually be able to monitor a circular area of radius 2r. 3) N th level of recovery: If the second level of recovery does not succeed, then another group of sensors that are (2N − 3)r meters away from Li are activated to locate the target. It is apparent that the second or higher level of recovery costs much more energy than the first level. Using simulations, we have verified that the failure probability of the first level recovery is quite low. Thus the energy consumed in the case of missed targets is not significant. 4) Energy Considerations: One of the major objectives of the DPT algorithm is to improve the energy efficiency of the network. To achieve this, firstly, the DPT algorithm accommodates the sensor-hibernation mechanism to save energy and

of this message, CHi+1 , which is a one hop neighbor of CHi , is also able to receive T Di . Thus T Di is effectively transmitted to CHi+1 at no additional communication cost. While some energy is consumed at CHi+1 to receive this message, the benefit brought by the predication far outweighs this communication cost. From these energy saving strategies, we can see that the DPT algorithm is designed such that energy is consumed on demand. Now suppose that we have to sense N points on the target’s moving track, and the prediction for each point has a miss probability of pmiss . We assume that a sensor will consume µ units of energy every time it obtains the target’s location using the normal beam. Then, the energy consumed to sense one location with high beam is given by µR2 /r2 . The energy required for obtaining the Target Descriptor for one location can be expressed as Fig. 5.

2nd level of failure recovery

prolong the sensor network’s lifetime. Most of the sensors stay in the hibernation mode until they receive an activation message from its cluster head. At any time, only those sensors that are chosen to sense the target need to be active, while all others can still hibernate. This is made possible by predicting the target’s “next location”. If there is no prediction at all, a large amount of sensors have to stay active in order to sense the target, which will result in fast energy depletion. While the “putting-sensor-into-hibernation” mechanism does save energy, it also induces a larger information collecting delay, which is the biggest obstacle to real time tracking. Fortunately, this drawback is also overcome by the “predication” mechanism, which requires the upstream cluster head to predict the target’s location with respect to the information transmission time of the downstream cluster head. Thus the downstream cluster head can be ready ahead of time, and the delay introduced by hibernation is suppressed. Secondly, sensors use the normal beam whenever possible. Only when a cluster head is unable to find suitable 3 sensors for the sensing with the normal beam, it will check whether switching to high beam will satisfy the sensing requirements. We prefer to let the sensor switch to high beam instead of asking neighboring cluster heads for help in the very first iteration because in sensor networks, the communication cost is the most significant energy killer [9]. The cooperation between different cluster heads will involve more communication cost than that with the sensing done under the control of a single cluster head. Although to achieve this the cluster head has to conduct a little bit more calculations, the energy consumed for these computations is much less than required for coordinating with neighbor cluster heads. Thirdly, while the transmission of T Di by CHi to the downstream cluster head seems to incur an additional communication cost, in most cases, this cost is minimized. This is because of the the fact that, no matter what, T Di has to be sent to the sink. Due to the omnidirectional transmission

Etotal = (1 − pmiss )Esuccess + pmiss Ef ailure

(7)

In the case of a success, the target is detected by three sensors using their normal beam. The energy consumed is thus 3µ since there are 3 sensors involved Esuccess = 3µ

(8)

According to our failure recovery strategy, the energy consumed in the case of a failure is: Ef ailure = 3µ + 3EHB PHB + (1 − PHB )(3EHB + µ min{n : πσ 2 }) n

R2 = 3µ(1 + 2 ) + (1 − PHB )µ min{n : πσ 2 }(9) n r As indicated in the Section III-B.3, if failure occurs we first let the active sensor-triplet switch to high beam and sense again. The second term in the equation above accounts for the energy consumed in this stage. The third term represents the energy consumed by the final solution: activate the “minimum number” of sensors, n, required to monitor the area of πσ 2 and re-capture the lost target. σ is dynamically adjusted according to the the target’s speed and re-capture result. In Section IVB.2 we obtain an expression for PHB using the Chebyshev inequality. From the equations above we can see that it critical to keep pmiss small enough so that the energy consumed for recovery will be minimized (since failures cause extra communication between clusters and sensors which dramatically increase the energy consumption). In Section IV we comment on this probability for our proposed algorithm. 5) Algorithm Pseudo-code: The whole DPT algorithm consists of two parts, one running at the sensor and the other running at the cluster head. Both of these are messagedriven algorithms, which means all operations are triggered by messages received from outside. Algorithms 1 and 2 present the pseudo code for the DPT algorithm running at the sensors and the cluster heads respectively. The protocol uses a number of message types which are exchanged between the sensors and the cluster heads and we enumerate them below:

Algorithm 1 Algorithm running at each sensor while (1) do switch(event) { event 1: object detected send an ”Object detected” message #01 to CH; stay awake; set Timer awake; break event 2: sensing requested by CH start sensing; finish sensing and send message #21; shutdown communication and sensing channel; break event 3: high beam sensing requested by CH start sensing; finish sensing and send message #21; shutdown communication and sensing channel; break event 4: timeout send message #12 to CH and initiate hibernation; shutdown communication and sensing channel; break } end while

Message #01: [Message #, sensor ID, target location] This message is sent from a sensor to the cluster head when an object is detected. Message #02: [Message #, TD] A cluster head sends this message to wake up suitable sensors in its own cluster to sense the designated target. Message #03: [Message #, TD] On receiving this message from the cluster head, the sensor switches to high beam sensing. Message #12: [Message #, next wake-up time] This message is sent from the sensor to its cluster head to indicate that the sensor is going into hibernation mode and its next wake-up time. Message #21: [Message #, target location, next wake-up time] This message is sent from the sensor to its cluster head to report the tracking result. After sending out this message, by default the sensor will shut down its communication channel and start hibernation. Message #31: [Message #, CH ID, Unique Cooperation number, TD, Number of sensor needed] This message is sent from one cluster head to its neighbor cluster heads when it is unable to find enough sensors to track the object. Message #32: [Message #, CH ID, Unique Cooperation number, Number of sensor available] On receiving message #31, eligible cluster heads will respond with this message to initiate the co-sensing procedure. Finally all sensing information will be sent to the cluster head who requires cooperation who will also formulate the final TD. Message #33: [Message #, CH ID, TD] When upstream CH finishes sensing, it will send this message to the downstream

CH. IV. S IMULATION R ESULTS In this section we present simulation results to evaluate the performance and effectiveness of the DPT algorithm. The simulation study mainly concentrates on the following aspects of the algorithm: 1) The miss probability, pmiss , which quantifies the likelihood that the active sensor-triplet fails to detect the target. This parameter can be used to evaluate the quality of the prediction under different situations (for example different tracking resolutions, t). 2) The adaptability of the algorithm to target’s different speeds. 3) Average energy consumed for tracking. A. Simulation Setup We simulated a scenario where a target moves randomly within a 2-dimensional sensing area. The simulator was developed to track this moving target, statistically observe the miss probability and the energy consumed. The simulation program is a discrete-event simulator developed using ANSI C. We first distribute the sensors uniformly over a field of size 600m×600m. As described before, the node density λ should be large enough so that for any arbitrary location within the sensing region there are at least 3 sensors which can monitor it with their normal beam. After doing the calculations with r = 35, we obtain the node density as 0.01, with the probability of successfully finding the sensor-triplet larger than 0.99. The movement pattern of the target follows the random waypoint model wherein the direction of the target is randomly updated at fixed intervals. The speed of the target is a variable parameter which we use to evaluate its impact to the tracking quality. B. Simulation Results 1) Miss Probability vs. Tracking Resolution: The DPT algorithm allows some difference between the target’s actual location and the predicted location without missing the target. The target’s next location obeys a two dimensional Gaussian distribution with the predicted location as the mean. Although the probability that it actually falls exactly at the predicted point is 0, the DPT algorithm is feasible in the sense that the active sensor-triplet will be able to monitor an area, in which the predicted location is covered and not just one point. However, in the presence of highly random movement the target may indeed move outside this covered region. Using simulations, we characterized this miss probability statistically under different “Tracking Resolutions”. We define the Tracking Resolution as the time length between two consecutive sensing points with the intuition that as the resolution becomes finer, the miss probabilities will decrease. For each resolution we measure the number of times the target is missed in 100 sensing points. At each of these points the target changes its direction arbitrarily between 0-360 degrees.

Comparison of Actual Track and predicted Track 600 actual moving track predicted moving track 500

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Miss Probability vs. Resolution 1 speed = 1m/s speed = 5m/s speed = 10m/s 0.8

miss probablity

Algorithm 2 Algorithm running at each cluster head while (1) do switch(event) { event 1: message #01 received: new target search for 3 sensors with normal beam if (3 sensors found) then send message #02 to the 3 sensors set timer information=1 else search for 3 sensors with high beam if (3 sensors found) then send message #03 to the 3 sensors else send message #31 asking other CH’s for help set timer help=1 end if end if break event 2: message #31 received: CH asking for help if (eligible & no other CH responded so far) then send message #32 to neighboring CH send message #02 to the 3 pre-found sensors set coord flag = help asking CH’s ID end if break event 3: message #12 received: sensor hibernation calculate the sensor’s next wakeup time break event 4: message #21 received: target information if (3 messages received) then timer information = 0 if coord flag=0 then formulate the TD send TD to downstream CH and the sink else send location nformation to CH=coord flag end if calculate the sensor’s next wakeup time end if break event 5: timer information timeout if coord flag=0 then formulate the TD using available information send TD to downstream CH and the sink else send location nformation to CH=coord flag end if break event 6: timer help timeout formulate the TD using available information send TD to downstream CH and the sink break } end while

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Fig. 7. Relationship between the miss probability and tracking resolution for various target speeds.

In figure 6 we show how the target predicted location compares with the target’s actual location. We note that the predicted track follows the actual movement of the target very closely. For the results in Figure 6, the target’s speed is 15m/s and the normal/high sensing beam is 35/55m. Figure 7 shows the relationship between the miss probability and the tracking resolution. As expected, the miss probability keeps increasing as the tracking resolution becomes coarser. With a finer resolution, the magnitude of the error caused by the target’s speed and direction changes are smaller, which helps the linear prediction used in the DPT algorithm achieve a better accuracy. It is also apparent that the miss probability is inversely proportional to the target’s speed. This implies that for a faster moving target we need to increase the tracking resolution to counter the rise in the miss probability. This is also intuitively true since with the same resolution the faster moving target is more difficult to trace. Figure 7 provides a quantitative description of the relationship. 2) Miss Probability vs. sensing radius/moving speed: Figure 8 shows the relationship between the miss rate and

Miss Probability vs sensing radius/moving speed

Miss points distribution

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Largest distance between sensor-triplet and target for missed points mean 55

largest distance to the 3 sensors

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Fig. 8. Relationship between the miss probability, target’s moving speed and the sensor’s sensing radius

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Statistical characteristics of the missing points

8000 Energy consumed

ratio of the target moving speed to the sensing radius. We note that when the target’s magnitude of displacement in unit time becomes more and more comparable with the sensor’s sensing radius, the miss probability increases exponentially. This can be intuitively explained by the fact that when the sensing radius is comparable to the target’s displacement in unit time, it becomes more and more likely that the sensors will be unable to sense the target with their normal beams. Thus, the cluster head will increasingly have to resort to high beams or cooperation from neighboring cluster heads in order to locate the target. This is an important factor that needs to be considered while designing the sensing network. We now present a more rigorous study of the statistical characteristics of the missed points and use it to find the power consumed by the network. For the case under consideration, in addition to the default parameters mentioned earlier, the normal/high sensing radius is kept at 35/55m, the target’s speed is 15m/s and the tracking resolution is 1 sec. Among the 2000 sensing points, the tracking system missed 59. For each missed point, we calculate the largest distance to the 3 active sensors as Di = max{d1i , d2i , d3i }

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1000

0 0

V AR(Di ) = 35.4416

400

Fig. 10.

600

800

1000

1200

1400

1600

1800

2000

Energy consumed for tracking 2000 points

probability that the maximum distance to the sensor-triplet is greater than 55m is bounded by 1 − PHB

= =

(10)

where d1i , d2i and d3i represent the distances between the target’s actual location and the 3 active sensors respectively. For the 2000 tracking points, the mean and variance of Di is obtained as E(Di ) = 43.9359

200

≤

P (Di ≥ 55) 1 P [|Di − E(Di )| ≥ (55 − 43.9359)] 2 1 V AR(Di ) = 0.1448 (12) 2 (11.0641)2

From Eqn. (7) and (9) the expression the energy consumed for sensing one point is given by Etotal = (1 − pmiss )Esuccess + pmiss Ef ailure with Esuccess = 3µ

In Figure 9 we plot Di for each of these 59 missing points. According to the Chebyshev inequality:

Ef ailure = 10.41µ + 0.1448µ min{n : πσ 2 }

V AR(Di ) (11) x2 For example, if we choose the sensor’s high sensing beam as 55m, then the probability that the target is missed, i.e., the

In the equation above, minn {n : πσ 2 } is much larger than the other terms because it includes the cost of many communications between sensors and their cluster head or among cluster heads.

P [|Di − E(Di )| ≥ x] ≤

n

In Figure 10 we plot the energy consumed by the network for sensing these 2000 points. We can see from the figure that the energy consumed is around 6900 units, while the minimum amount of energy required for the sensing is 6000 units. According to our theoretical calculation, the overall energy consumed should be 552 ) ≈ 6437µ 352 The difference in the two values represents the amount of energy spent in error recover using the second or higher levels of recovery (the term corresponding to minn {n : πσ 2 }). We can see that the amount of energy spent in failure recovery forms a small percentage of the minimum energy required for tracking. During the simulation we also noticed that the expectation and variance of D became larger when the target moves faster. However, the expectation and variance of D reduce when we select a smaller Tracking Resolution. These results imply that with the sensors normal/high sensing beam fixed, we can adjust the Tracking Resolution according to the target’s speed to achieve acceptable performance. It should be pointed out that in this figure we did not include the energy consumed by the border sensors, which are awake all the time. The border sensors consume significant amounts of energy and it is an open problem to devise an efficient policy for coordinating them in order to minimize the energy consumption. An alternative approach could be to keep the node density higher near the borders so that once some of the border nodes fail, others in the area can be activated without reducing the effective sensing area. Etotal = 2000(3µ) + 59(3µ

V. C ONCLUSIONS AND F UTURE WORK In this paper we proposed a feasible solution for distributed tracking of mobile targets using sensor networks: the Distributed Predictive Tracking algorithm. DPT’s essential idea is to predict the target’s future location based on known previous locations. Since it is totally distributed, it scales well without having any central point of failure and can be easily extended to tracking in 3-dimension. While a simple first order linear predictor is used for the prediction, our simulation result show that the tracking performance is satisfactory overall, with particularly good performance at higher tracking resolutions. In addition, this algorithm is specifically aimed at minimizing the energy consumption of the network, a very important consideration for sensor networks. We are currently working on more complicated prediction algorithms in order to achieve lower miss rates for a given tracking resolution. Additional work can also be conducted on interpolation mechanisms at cluster heads when a sensor reports multiple targets simultaneously. The relationship between energy consumed and prediction accuracy also remains an open issue. Another possible direction of work is to accommodate mobile sensors. With mobile sensors the scenario complicates considerably and significantly different approaches to the solution may be necessary.

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