Using the sensor nodes to achieve target tracking is a challenging problem in resource-limited wireless sensor networks. The tracking nodes are usually required to consume much energy to improve the tracking performance. In this paper, an energy-efficient node scheduling method is proposed to minimize energy consumption while ensuring the tracking accuracy. Firstly, the Kalman-consensus filter is constructed to improve the tracking accuracy and predict the target position. Based on the predicted position, an adaptive node scheduling mechanism is utilized to adjust the sample interval and the number of active nodes dynamically. Rather than using traditional search algorithm, the scheduling problem is decomposed to decouple the sample interval and number of nodes. And the node index is mapped into real domain to get closed-form solution to decide the active nodes. Thus, the NP-complete nature is avoided in the proposed method. The proposed scheduling method can keep the tracking accuracy while minimizing energy consumption. Simulation results validate its effective performance for target tracking in wireless sensor networks.

Wireless sensor network (WSN), which consists of tiny low-cost, energy-limited, and sensing range-limited nodes, has received extensive research in recent years. The nodes in WSN, equipped with one or more sensors, can sense, measure, and gather information from vicinal area. By utilizing the wireless RF module, these nodes can transmit the gathered information from local region to remote base station through node’s multiple-hop relay. With the development of microelectronic technology, WSN has been deployed in various application scenarios to observe physical environmental change and detect events of interest [

In all kinds of practical scenarios, target tracking is one of the most important applications of WSN. Target tracking is a process of estimating or predicting the trajectories and velocities of some mobile targets by the sensor nodes in WSN collaboratively. The cooperation among sensor nodes could improve the accuracy of target’s location or velocity. The targets of tracking can be any mobile objects, such as animals, humans, and vehicles [

With the development of WSN, numerous target tracking applications have emerged in many practical projects. For instance, PinPtr [

Differing from the traditional target tracking, the target tracking using WSN brings up many challenges: keeping the tracking accuracy under the node’s resources constraints. As most existing works have mentioned, the constraints of node resources, such as sensing range, communication bandwidth, and computation ability, are critical factors to keep accuracy and to save energy for target tracking in wireless sensor networks [

Some researches focus on reducing the communication cost in target tracking. In [

Recently much attention has been focusing on sensor node scheduling to reduce energy for target tracking. The node scheduling can be classified into 2 categories: the random selection method and adaptive selection method. In random selection method, the sensing nodes are randomly selected according to a certain degree of probability; in adaptive selection method, the sensing nodes are selected according to the critical factors such as node type, detecting ability, and residual energy.

Random selection method has compared low scheduling cost and it is easy to deploy in real WSN. In [

However, sensors’ random sleep with a probability may not keep the target tracking accuracy because some sensors close to a target may be in sleep mode. Even in the target sensing region, there are not active nodes. But it is also sufficiently important to keep the performance of the target tracking. From this point of view, node selection along with the trajectory of moving target has aroused much interest. Some practical distributed sensor node selection algorithms have been proposed to improve energy efficiency with reliable tracking [

In [

Summarizing the above works, the main factors that influence position accuracy and energy efficiency of target tracking include the network communication topology, the sampling time interval, and the number of tasking sensors. The number of tasking sensors is directly related to the total energy consumption in tracking process. However, the current adaptive node selection method could not permit large candidate node set because of their high complexity.

Comprehending these factors, this paper aims to propose a novel node scheduling method with cooperative Kalman-consensus filter to reduce the energy consumption while keeping tracking accuracy. The Kalman-consensus filter is used to obtain the target state estimation and predict the next step position. The node selection problem is transformed into a convex optimization problem, which is decomposed, and a Lagrangian function is used to solve it.

The main contributions of this paper include (1) extending the classic Kalman filter to cooperative form, which can combine the local nodes’ information to improve the tracking precision; (2) proposing a joint sample interval and node selection optimization scheme, which can realize the energy consumption minimum while keeping the tracking accuracy; (3) addressing the NP-hard joint optimization problem, adopting a map method to map the selecting factor to real domain; and utilizing gradient information to get the solution rapidly.

The rest of this paper is organized as follows. The problem formulation, dynamic model, and energy model are analyzed in Section

Considering that wireless sensor network is constructed by deploying

The state matrix

The matrix

The measurement model is given by

The Kalman-consensus filter (KCF) algorithm used in this paper is mainly referred to in [

Given the initial parameters

node

(1) Obtain measurement

(2) Compute information vector and matrix of node

(3) Send message

(4) Receive messages from all active neighbors.

(5) Fuse information matrices and vectors

(6) Compute the Kalman-consensus state estimation

(7) Update the estimate state of the target

The binary detection model, described in most of the existing works [

Based on this sensing model, for a target located in

According to [

The predicted target state uncertainty is described as follows:

At each tracking step, as the energy model in [

If the current tasking node

The energy cost in receiving data by sensor node

And the total energy consumed for a tracking step is given by

Figure

Target tracking scene in WSN.

At the beginning of detecting, all sensors are in the sleep state initially, except for sensors that are on the borders of the sensor filed. The sensor nodes on borders that first found the target will broadcast the target information and start the tracking task. They will obtain the first measurement and calculate the target state estimation to select and activate the next tasking sensor nodes (including the cluster header) for the next sample interval. They will send their state prediction to the next tasking cluster.

At

obtaining measurement

computing and updating the state estimation using Kalman-consensus filter;

sending the updated state estimation

As for the cluster header, except for the above tasks, it needs to perform the following additional jobs:

fusing the state estimation

calculating the sampling interval

selecting the tasking cluster for the step

selecting a new cluster header for the new tasking cluster;

transmitting the fused target estimation

Once the sensor nodes in the tasking cluster at step

For the problem of node selection for distributed cooperative target tracking, the key issue is to form tasking sensor cluster dynamically, which directly related to energy consumption and tracking accuracy. The objective of proposed method is to minimize the energy cost of network under the condition of desired tracking error. In addition, the sampling time interval has a great influence on tracking accuracy and network energy cost. Actually, if the desired tracking performance is obtained, a bigger sampling time interval will be a better choice for energy saving.

The formation of next cluster candidate set includes two phases: the first phase is the target tracking, in which nodes that can detect the target are active; the second phase is the detection probability

In order to better express the node selecting problem, the joint detection probability (

Based on the sensor detection probability model and the energy model given previously, the node selection problem can be formulated as follows: at tracking step

Because of the complexity in computing the detection probability

As mentioned above, the fixed sampling time interval is not suitable for energy-efficient target tracking. We suppose that

According to [

By solving the following equation, we can get the suitable

At the second stage, a number of sensors are selected based on the determined sampling interval

Since

Then the resulting convex problem can be solved to find the minimum

Then, for node

Therefore, the priority ratio (which is converse to the cost ratio) for node

The cost function is the energy consumption under the target detection constraint if the nodes are selected.

The next stage is to determine the optimum

The optimal

In order to find the optimum

This iterative algorithm ends when the accuracy of

Because the solving of optimum

In order to limit the search space of optimal

Each node with the smaller cost function defined as (

While

Number of tasking node

Calculate

While (

Compute

If

Else

End;

For

Predict

If

End;

End;

End

If

Else if

End

End

The intruder detection and tracking system in military is a representative application of target tracking. To avoid the sudden attack or surreptitious scout of enemy, the wireless sensor network is deployed in the buffer region between defensive line and the enemy. When the enemy combatants or vehicles enter the buffer region, the sensor network can detect these events and report the enemy position real time so that the troops can respond immediately.

To evaluate the performance of the proposed algorithm, the software MATLAB is used to simulate the intruder detection and tracking scene. The network scene is formed by sensing range-limited sensors and the monitoring area is 100 m × 100 m with coordinates from (−50, −50) to (50, 50), as shown in Figure

It is assumed that all the sensors in the network have the same sensing parameters; that is, the sensing and communication range of each sensor are

Firstly, the proposed method is tested and verified by comparing the estimated trajectory with real target trajectory. Figure

The comparison of estimated trajectory with the real target tracking trajectory.

Tracking accuracy by using the proposed method.

To display the performance more convincingly, the proposed tracking algorithm Kalman-consensus filter (KCF) is compared with EKF, and the accuracy of target tracking is evaluated using estimated trajectory and estimated error. Figures

The comparison of the estimated value of X coordinate between KCF and EKF.

The comparison of the estimated error of X coordinate between KCF and EKF.

The comparison of the estimated value of Y coordinate between KCF and EKF.

The comparison of the estimated error of Y coordinate between KCF and EKF.

From the deviation of estimated position and actual position described in Figures

To implement the KCF, the local sensor nodes need to exchange their message packets, which include three parts: node information vector

To improve the energy efficiency, the sensor node selection algorithm is introduced into target tracking. As described in the introduction, the node selection algorithm can be classified into two categories: random selection and adaptive selection. Figures

Target trajectory using random node selection with fixed number of sensor nodes for each sensing step.

Target trajectory using the proposed adaptive node selection with various number of sensor nodes for each sensing step.

To represent this, Figure

Tracking accuracy with nonadaptive, DMTT, and ANS-KCF methods.

Figures

The number of tasking sensor nodes participating in the target tracking at different time for nonadaptive, DMTT, and ANS-KCF methods.

The sampling interval of tasking sensor nodes participating in the target tracking at different time for nonadaptive, DMTT, and ANS-KCF methods.

After that, the tracking accuracy is improved with the number of sensing nodes increasing. But the tracking process is tending towards stability with the tracking going on. Also from Figures

Finally the energy performance is evaluated. Figure

The comparison of the energy consumption for nonadaptive, DMTT, and ANS-KCF methods.

Compared to nonadaptive algorithm, the proposed adaptive algorithm has node selection procedure, which will increase the implementation complexity. From the analysis of Section

In this paper, we have proposed a novel adaptive node scheduling method for energy-efficient target tracking in wireless sensor networks. Firstly, the Kalman-consensus filter is improved to support the cooperative node tracking. Then the node scheduling problem with the energy and accuracy constraints is decomposed and analyzed by convex framework. The novelty of the proposed method lies in using index gradient rather than using brute research to decide the suitable sensor nodes. The method realizes the tradeoff between tracking accuracy and energy efficiency for resource-limited sensor networks. In our future work, we will focus on the scenario that the sensing range of a sensor will decay as energy consumption.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is partially supported by the National Natural Science Foundation of China (nos. 61003233, 61379111, and 61202342) and Specialized Research Fund for Doctoral Program of Higher Education (no. 20110162110042).