Prediction-based Dynamic Energy Management in Wireless Sensor Networks

Energy consumption is a critical constraint in wireless sensor networks. Focusing on the energy efficiency problem of wireless sensor networks, this paper proposes a method of prediction-based dynamic energy management. A particle filter was introduced to predict a target state, which was adopted to awaken wireless sensor nodes so that their sleep time was prolonged. With the distributed computing capability of nodes, an optimization approach of distributed genetic algorithm and simulated annealing was proposed to minimize the energy consumption of measurement. Considering the application of target tracking, we implemented target position prediction, node sleep scheduling and optimal sensing node selection. Moreover, a routing scheme of forwarding nodes was presented to achieve extra energy conservation. Experimental results of target tracking verified that energy-efficiency is enhanced by prediction-based dynamic energy management.


Introduction
Wireless sensor networks (WSNs) utilize a large number of intelligent micro-sensor nodes with sensing, processing and wireless communicating capabilities to implement complicated tasks in the specific sensing area. With the strict energy constraints of wireless sensor nodes, dynamic energy management has become a challenging issue that must be addressed in WSNs. To treat the problem of energy efficiency, it is easy to envision that certain energy optimization mechanisms may be applicable. In particular, the dynamic energy management architecture has been proposed in [1]. The awaken scheme has been carefully discussed at the protocol level [2]. As energy consumption of WSNs is application-oriented, energy management of specified applications, such as target tracking, should be studied. However, very little has been done for specified applications and therefore none of these methods make use of the information about the target state, which contains rich hints for a more reasonable sleeping and sensing scheduling of nodes. Also, optimization performance may be enhanced by making use of distributed computing capability.
Considering the energy efficiency of measurement in WSNs, we present a prediction-based dynamic energy management method, which takes node idle time and communication energy consumption into account. First, particle filters (PF), which can estimate non-linear and non-Gaussian dynamic processes, could be directly applied to the non-linear system model, while other traditional methods, such as extended Kalman filter (EKF), may bring serious model errors [3,4]. To solve the nolinear problem of target state prediction, PF is employed here. Then, idle time is estimated and a sleep schedule is designed for each node so that any node can become a sensing candidate on time. Moreover, we perform in advance reasonable optimization of the sensing process. Since communication energy is a critical aspect of energy consumption, distributed genetic algorithm and simulated annealing (DGASA) are presented to optimize communication energy consumption in WSNs, which assigns computation task to a number of nodes to boost up the optimization ability. In the application to target tracking, target position is predicted by PF and node selection optimization is achieved by DGASA. A routing scheme with forwarding nodes is studied as well. Energy consumption is analyzed during target tracking and efficiency of prediction-based dynamic energy management is demonstrated.
The remainder of this paper is organized as follows: Section 2 discusses collaborative sensing model and energy consumption model in WSNs. In Section 3, our prediction-based dynamic energy management mechanism is presented, where we describe several potential awakening mechanisms, target prediction with PF and energy optimization with DGASA. We have studied the target tracking application with prediction-based dynamic energy management in Section 4. Section 5 provides prediction and optimization results during the procedure of target tracking, and analyzes the network energy consumption with optimized node selection employing dynamic energy management. Finally, our conclusions are presented in Section 6. region to collect the data through the network and maintain the information of node positions and communication paths [5,6]. Wireless sensor nodes are densely placed, so that a number of nodes can potentially make simultaneous observations. This will allow a collaborative sensing model and energy consumption model to be introduced.

Collaborative Sensing Model
Let us assume that each wireless sensor node can produce bearing angle estimates of the target in the sensing range [7]. For the time instant t, the target is located at (x target ,y target ) and detected by n nodes, where n > 2. Each node i, placed at (x i ,y i ), can acquire the angle: Where v i is direction finding (DF) error, which is zero-mean, Gaussian distributed with constant variance σ Θ 2 .
DF lines of these nodes can't intersect at a common point due to DF error. Therefore, the non-linear least square estimation is adopted for target location, with the nodes sensing collaboratively [8]. Matrix representation for measurement equation of n nodes is: Since n > 2, the least square solution of X exist. According to least-square criteria, choose X as an estimation of X to minimize ( ) ) J X : We can acquire The estimation error covariance matrix is defined as: We can find Collaborative sensing accuracy is defined by the error ellipse.

Energy Consumption Model
Let us assume that each wireless sensor node consists of sensing, processing, memory and communication components. With multiple power modes, these modules can support different levels of power consumption and functionality. Accordingly, each node can have a set of sleep states based on various combinations of module power states [1]. Each state s k has power consumption P k , and the transition time from active state and back is given by τ d,k and τ u,k , respectively, where τ k = τ d,k = τ u,k . As shown in Table 1, we define five states; "Tx" and "Rx" denotes "Transmit" and "Receive" respectively. And the extra power consumption of radio module for data transmission between wireless sensor node i and j is calculated as [10]: where r denotes the data rate, n 0 denotes the path loss index, α 1 denotes the electronics energy expended in transmitting one bit of data, α 2 > 0 is a constant related to the radio energy, and d ij denotes the distance between the two nodes. If we define t p,q = │τ pτ q │ as the transition time between state s p and s q , then energy consumption due to state transition can be calculated as: where p and q are indices of node state referred in transition.

Potential Awakening Mechanisms
According to the mentioned energy consumption model, several potential awakening mechanisms can be implemented on each wireless sensor node: (1) Event-driven on s 3 : As shown in Figure 1(a), when there is no target in the sensing range, the node keeps its state on s 3 . Once any target moves into the range, the sensing module will generate an interrupt to awaken the node to state s 1 . Node will go back to state s 3 after sensing and transmitting.
(2) Awakening periodically to s 1 : The node can go to the deepest sleep state s 4 and is periodically awakened to state s 1 by the timer, as shown in Figure 1(b). If there is any target inside the sensing range, the node will complete measurement and communication, then go back to state s 4 . Otherwise, the node will directly go back to state s 4 .
(3) Awakening periodically to s 2 : This works similarly to the approach of awakening periodically to state s 1 , but the state to which node is awakened periodically is s 2 . Figure 1(c) shows that the node can respond to incoming messages, and expect the ones which have tasks in that period. All the nodes are set back to state s 4 by the announcement of the sink node.
(4) Prediction-based dynamic awakening: As shown in Figure 1(d), we present a dynamic awakening mechanism which adopts the approach of awakening to state s 2 and take node idle time into account as well. The PF algorithm to be introduced will perform the prediction of target state. Each node use predicted target state to estimate idle time so that it can keep state s 4 in as many (n idle ) periods as possible and minimize energy consumption. (c) (d)

Target prediction by Particle Filter
PF is a sequential importance sampling method which is based on Monte Carlo simulation and Bayesian sampling estimation theories and evolved from the Bootstrap nonlinear filtering algorithm [11]. Here, we use PF to draw prior information about the target state, which means the property of target for measurement. For example, we usually take position information as the target state in target tracking applications. With the time index k, we define variable x k to describe the target state and accordingly the variable y k can be obtained after observation.
In Bayesian sampling estimation theory, the posterior density p(x k │y 1-k ) can be inferred from the prior density p(x k │y 1: PF then uses the Monte Carlo simulation method to approximate the posterior density by N particles with the associated weight ( ) ( ) For solving the difficulty of sample from the posterior density function, the sequential importance sampling method is used, which samples from a known, easy-to-sample, proposal distribution q(x 0:k │y 1:k ) , where x 0:k is the historical state variables and y 1:k is the corresponding observation. The recursive estimate for the importance weights of particle i can then be derived as follows: And then the estimated target state can be approximated by

Energy optimization by Distributed Genetic Algorithm and Simulated Annealing
With a predicted target state and awakening mechanism, we can assume that there are N sen candidate nodes for sensing in certain sensing period. As wireless sensor node transfer data to achieve collaborative sensing, we can design a highly efficient and low complexity algorithm to optimize communication energy consumption.
To make use of the distributed computing capability of WSNs, we present a distributed hybrid algorithm. This algorithm is implemented on a number of nodes which work together to enhance optimization of performance. Meanwhile, the advantages of two kinds of optimization method, GA and SA, are combined to get a global optimal solution.
Given an optimization problem, GA encodes the parameters concerned into finite bit strings, each of which presents a possible solution to the problem, and then works with a set of strings, called the population, using reproduction, crossover and mutation operators in a random way but based on the iterative evolution of the fitness function. On the other hand, SA start at an initial random solution state, and a sequence of iterations is generated. A perturbation mechanism is applied, which transforms the current state into a next state selected from the neighborhood of the current state. If this neighboring state has a lower cost, the neighboring state is accepted as the current state. If this neighboring state has a higher cost, the neighboring state is accepted with a certain probability determined by the acceptance criterion.
GA can retain useful redundant information about what it has learned from previous searches by its representation in individual solutions in the population. Critical components of past good solutions can be captured, and can be combined together via crossover to form high quality solutions. SA retains only one solution in the space and exploration is limited to the immediate neighborhood. However, SA possesses a formal proof of convergence to the global optimal, which GA does not [12]. Therefore, to combine the two methods offers good potential for obtaining an optimum solution. Figure 2 presents the framework of DGASA. Assigned with the population of solutions from GA, each available node in current period runs SA for a specified time. Then solutions of SA will perform crossover and modulation to generate a new population of GA. An optimal solution for energy consumption is obtained by iteration.

Target Model
In target tracking applications, we discuss a vehicle target which moves randomly in a twodimensional sensing field with a maximum speed v max and a maximum acceleration a max [13]. For surveillance purposes, reliable detection should be provided and the position information of target should be reported according to a specified sensing period.
To improve the tracking performance of the maneuvering target, the acceleration inputs must be considered in the system model, so we use the motion of target model which was constructed by Duh [14]. It can compensate the maneuver bias directly and it does not have to assume any a priori knowledge of the maneuver target. This process model is given by: The observation model is: is the input vector consisting of the acceleration components in the x and y directions and V(k) and W(k) are the process noise and measurement noise; both sequences are assumed to be uncorrelated white Gaussian noise sequence with zero means and the variance matrices Q(k) and R(k), respectively.
In Equations (13) and (14), F is the model state transition matrix, G 1 (k) is the coupling matrix for maneuver inputs, G 2 (k) is the process noise input matrix and H is the model output matrix. The related matrices are given by: where T is the sampling time interval. With this target model, the prediction result of PF is the target position at the next sensing instant.

Sleep Scheduling
When there is no target in the region of WSN, the system is on standby in case of any target gets into it. Any wireless sensor node could be sent to the deepest sleep state. However, it should be awakened on time when target comes around. Then we schedule the sleep time as the following two phases: (1) Setup phase: Initializing the network, we assume that no target is in the region. The minimum time for a target getting into the sensing range of each node can be estimated according to the shortest distance to the WSN boundary d min and the maximum velocity of target v max : For the possible target position at the next sensing instant, the neighboring nodes should be sent to state s 2 so they became sensing candidates and get ready to be awakened. Accordingly, the idle time is calculated as: Then the number of idle periods is: where floor is rounding function.
Thus, wireless sensor nodes that are close to the WSN boundary will be awakened periodically. We define these nodes as boundary nodes, and the others are defined as inner nodes.
(2) Tracking phase: Once a target enters the region, sink node announces the prediction of target current position (x target ,y target ) over the network. All the nodes in state s 2 will receive the message and estimate the idle time according to its coordinates (x i ,y i ): For any new target that may possibly enter the region, each node should still be ready for sensing after t idle , so in this case the number of idle periods is calculated as: Respectively, n idle and n′ idle are used to schedule the state transition of nodes in these two phases. The sleep time of nodes is prolonged as much as possible without missing any events.

Communication Scheduling
Let us assume that a group of wireless sensor nodes in the neighborhood of the target are supposed to gather the acquired data and transmit it to a sink node during each sensing period. Each node in the sensing group signals with the same transmission power, then the sink node can obtain the sequence of the distance to each node according to the received signal power. As shown in Figure 3(a), the packet is forwarded from far to near. Each node combines its data into the packet, and finally the nearest node sends the packet to the sink node.
Let the sink node be denoted by Node 0 . The set of nodes from near to far is denoted by , so the energy consumption metric can be calculated according to Equation (8): where d ij is the distance between Node i and Nodej, and P is the packet size.
However, the neighborhood of the target may be far away from the sink node, so it would require a large amount of energy, even for the nearest node transmitting the packet. Thus, we select a number of nodes randomly from the inner nodes for packet forwarding. These nodes are defined as forwarding nodes. And the selection criterion is: each inner node selects a random number in [0,1]; if it exceeds a threshold T, then it is selected to be forwarding node. The threshold T is defined as in [15]: where p is the percentage of forwarding nodes, r is the current period number, and mod is the complementation operator. Each inner node should decide whether it is forwarding node in every period during its sleep time and it should wake up to state s 2 on schedule as a forwarding node.
As shown in Figure 3(b), if the nearest node in the sensing group chooses a shortest path adopting one of the forwarding nodes, then the energy consumption metric can be calculated as: where ∆E denotes the extra energy consumption of the forwarding node.

Node selection optimization
In this case, the optimization problem is selecting a group of nodes from the candidate sensing nodes in order to minimize communication energy consumption. Let us assume that there are N candidate nodes for selection. The coding scheme for each possible solution of DGASA is described in Figure 4. The i-th code of the solution indicates whether the i-th candidate node is selected for sensing, where "1" denotes node is selected while "0" denotes node is not selected. For example, Figure 4 shows that node i and j are selected for sensing.
Taking the semimajor axis of the error ellipse as the metric of collaborative sensing error, we assume that sensing error should be less than A 0 in a target tracking application. Then the fitness function of each possible solution is: where A=σ l , defined as the collaborative sensing error with the possible solution, and E 0 is a constant which is larger than the upper bound of energy consumption metric E(E′). Minimizing the fitness function, the sensing accuracy is optimized first. Once accuracy of application is satisfied, the energy consumption metric is optimized for energy efficiency.

Simulation environment
Assume that the sensing field of WSN is 400 m x 400 m, in which there are 256 wireless sensor nodes equipped by peroelectric infra-red (PIR) sensors with sensing range r sensing = 60 m and root mean square (RMS) of DF error variance σ Θ = 2 0 . We set 1  and 0 3 n = in the energy consumption model. The sensing period is set as 0.5 s, and then the sample period of PF is 0.5 s accordingly. The performing time for node selection optimization is set as 0.15s for all the following simulations. According to Section 4.1, we generate a trajectory of 120 points as shown in Figure 5, in some part of which the target moves on its maximum acceleration a max and maximum velocity v max for generalization. Here, a max = 10m/s 2 , v max = 40m/s, and sensing error threashold A 0 = 0.6 m. Simulations are performed using Opnet Modeler, which is a simulation platform for communication networks and distribution systems. The network models are established according to the proposed energy management mechanism. We employed CSMA/CA as the MAC protocol. The wireless channel model was bpsk, data rate was 1 Mbps and simulation duration was 60 seconds.

Network simulations of dynamic energy management mechanism
First, we run simulation of WSN to analyze the energy conserved by prediction-based dynamic awakening mechanism separately. All the wireless sensor nodes available are used for detection in the target vicinity. The awakening mechanisms are compared in Figure 6: (a) Event-driven based on s 3 ; (b) Awakening periodically to s 1 ; (c) Awakening periodically to s 2 ; (d) Prediction-based dynamic awakening. We find that prediction-based dynamic awakening mechanism obtains the lowest energy consumption in both setup and tracking phases. Prediction accuracy of PF is discussed and probability density of position prediction error on X-axis and Y-axis is shown in Figure 6. Moreover, the performance of the proposed algorithm for node selection optimization was evaluated. We analyzed the sensing accuracy and energy consumption during the tracking phase, with selected sensor node detecting and reporting. In each sensing period, PF was employed to predict the target position at the next sensing instant, with which DGASA is implemented to select the optimal wireless sensor node in the vicinity for sensing in the next period. GA and SA were also studied for comparison with the same coding scheme.
To prevent the influence of a target entering and leaving the sensing field, we studied the procedure from 10 s to 50 s. Figure 8 shows the collaborative sensing error and energy consumption of GA, SA and DGASA optimization. In Figure 8(a), the collaborative sensing error of GA and DGASA optimization can satisfy the required sensing accuracy, while part of SA optimization results exceed the required sensing error. As shown in Figure 8(b), energy consumption is compared during tracking, and we can find that DGASA optimization gives the lowest energy consumption, while energy consumption of GA optimization is highest.  A set of network simulations was also performed in the case that forwarding nodes are utilized in communication. The effect of the forwarding node percentage (changing from 0% to 30%) on energy conservation of DGASA optimization was examined, as shown in Figure 8. It can be seen that we have the most energy conservation with this percentage set at 10%. . When the percentage of forwarding nodes is 10%, the collaborative sensing error of DGASA optimization is shown in Figure 10(a), which can satisfy the required sensing accuracy. Energy consumption of WSN during the tracking is presented in Figure 10  Finally, we analyzed energy consumption and conservation ratio of dynamic energy management approaches: dynamic awakening mechanism, node selection optimization and forwarding node routing. Compared to the case that each node keeps in fully active state, total energy conservation of 90.9% can be achieved with all these approaches.

Conclusions
Focusing on the energy-efficiency problem in WSNs, we have proposed a dynamic energy management mechanism based on target prediction. Collaborative sensing model and energy consumption model is established, and PF is applied to predict the target state. With the state of the next sensing instant, each wireless sensor node can update its idle time and schedule its sleep without loss of any event. Meanwhile, as the candidate nodes for sensing are known beforehand, we accomplished the optimization of the sensing process with DGASA, which uses the distributed computing capability of WSNs so that energy consumption can be minimized without degrading the performance accuracy. Moreover, we have discussed the routing scheme for data reporting, and an approach utilizing forwarding nodes is presented to conserve more communication energy. Simulations of target tracking demonstrate that PF target prediction-based dynamic awakening mechanism and DGASA energy management enhance energy efficiency significantly in WSNs target tracking application. The paper gives an adaptive dynamic energy management framework for target monitoring applications in WSNs and has presented details for solving the target tracking problem. The feasibility of prediction-based dynamic energy management mechanisms should be explored on a more practical platform.