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Due to their wide potential applications, wireless sensor networks have recently received tremendous attention. The strict energy constraints of sensor nodes result in the great challenges for energy efficiency. This paper investigates the energy efficiency problem and proposes an energy-efficient organization method with time series forecasting. The organization of wireless sensor networks is formulated for target tracking. Target model, multi-sensor model and energy model are defined accordingly. For the target tracking application, target localization is achieved by collaborative sensing with multi-sensor fusion. The historical localization results are utilized for adaptive target trajectory forecasting. Empirical mode decomposition is implemented to extract the inherent variation modes in the time series of a target trajectory. Future target position is derived from autoregressive moving average (ARMA) models, which forecast the decomposition components, respectively. Moreover, the energy-efficient organization method is presented to enhance the energy efficiency of wireless sensor networks. The sensor nodes implement sensing tasks according to the probability awakening in a distributed manner. When the sensor nodes transfer their observations to achieve data fusion, the routing scheme is obtained by ant colony optimization. Thus, both the operation and communication energy consumption can be minimized. Experimental results verify that the combination of the ARMA model and empirical mode decomposition can estimate the target position efficiently and energy saving is achieved by the proposed organization method in wireless sensor networks.

Ubiquitous computing is emerging as a potential solution for wide sensing applications in the physical world. Thus, wireless sensor networks (WSNs) have become a growing research field. In WSNs, a large number of intelligent sensor nodes are integrated into the environment to accomplish complicated sensing tasks. Sensing, processing and communication capabilities are enabled on each sensor node. As sensor nodes usually work in unsupervised areas, the batteries cannot be easily recharged or replaced. Due to the limited battery life, the energy efficiency of a WSN is an important issue. Sleeping and awakening of sensor nodes are supported in power-aware hardware design [

In this paper, an energy-efficient WSN organization method is proposed utilizing time series forecasting. Equipped with multi-sensors, each sensor node can produce range and bearing measurements of the target within its sensing range. As the target is often detected by a number of sensor nodes, a Fisher information matrix (FIM) [

The rest of this paper is organized as follows. Section 2 gives the preliminaries of the energy-efficient organization for the target tracking problem, where the basic models are introduced. In Section 3, we present the principle of collaborative sensing and adaptive estimation in target tracking. Section 4 describes the approach of energy-efficient organization, including sensor node awakening and dynamic routing scheme. Experimental results are provided by Section 5. Finally, Section 6 presents the conclusions of the paper.

We address energy efficiency in target tracking application of WSN. Focusing on the strict energy constraints of sensor nodes, some researches have referred to the energy optimization approaches in WSN [

Our work mainly includes two parts: collaborative sensing and adaptive estimation of target; energy-efficient organization of sensor nodes. Both the target detection and energy optimization requirements are considered. A novel time series analysis approach is proposed for target forecasting while distributed awakening approach is applied on sensor nodes. Besides, ACO algorithm is introduced for routing optimization during data fusion.

The energy-efficient organization framework for the target tracking application of WSNs is shown in

When the target moves into the sensing field, the corresponding sensor nodes near the trajectory implement collaborative sensing with specified sensing period

Considering the vehicle target which moves though the sensing field, a “current” statistical model is discussed here to describe the target motion [

Here, we assume the maximum target acceleration
_{max}.

It is assumed that each sensor node equips two kinds of sensors, one pyroelectric infra-red (PIR) sensor and one omni-microphone sensor. Sensor nodes obtain the bearing observations of the target with the PIR sensors, while the range observations of the target are produced by the omni-microphone sensors. For each sensor node, it is assumed that the two sensors have the same sensing range _{s}

In _{i}_{i}_{target}_{target}

Both sensors have zero-mean and Gaussian error distribution. The standard deviation of bearing and range observations is _{β}_{r}_{β}_{r}

Basic sensor node architecture consists of the embedded sensors, A/D converter, a processor with memory and the radio frequency (RF) circuits. For the scalability of energy consumption in WSN, all the components of sensor node are supposed to be controlled by an operation system, such as microOperating System (μOS) [

During sensor node operation, four main parts of energy consumption source are considered: processing, sensing, reception and transmission. The processing energy is spent by the processor with memory. It is assumed that when the processor is active it has constant power consumption. The embedded sensors and A/D converter are adopted as there is any sensing task, and the corresponding power consumption is a constant. For wireless communication, the reception and transmission energy is derived from the RF circuits. As radio signal attenuation in the air is related with the distance of propagation, the free space propagation model [_{p}_{s}

When the reception portion is turned on, the sensor node keeps listening to the wireless channel or receiving data. Thus, the power consumption of reception portion is assumed to be constant. For the transmission portion of RF circuits, the transmission amplifier has to achieve an acceptable magnification. Therefore, when sensor nodes _{d}_{1} denotes the electronics energy expended in transmitting one bit of data, _{2} > 0 is a constant related to the transmission amplifier energy consumption, _{i,j}

With the stated basic models, collaborative sensing and adaptive estimation approaches will be exploited for the target tracking problem.

As mentioned in Section 2.2, each sensor node has a sensing range for target detection. Due to the redundancy of sensor node deployment in WSNs, the target can be detected by a group of sensor nodes simultaneously. Thus, the observations of these sensor nodes are merged for higher detection accuracy. The data from multiple sensor nodes, including bearing and range observations, is utilized to localize the target. In this way, collaborative sensing is achieved by maximum likelihood estimation. Moreover, the sink node constructs the forecasting model with the historical target trajectory. Time series analysis is employed for adaptive estimation of target position. Here, a differencing operation and the EMD approach represent the time series of target position by stationary components, which are forecasted by ARMA model respectively.

It is assumed that the coordinates of target is (_{target}_{target}_{s}_{i}_{i}_{s}_{i}_{i}_{s}_{target}_{target}^{T}_{i}_{i}_{i}^{T}_{i}

With the observation of the sensor node

A suitable measure for the information contained in the observations can be derived from the Fisher information matrix (FIM) [

According to _{i}_{,1} = tan^{−1}((_{t}_{arg}_{et}_{i}_{t}_{arg}_{et}_{i}_{i,2}=[(_{t}_{arg}_{et}_{i}^{2}+(_{t}_{arg}_{et}_{i}^{2}]^{1/2}. Then,
_{i}_{target}_{i}_{i}_{target}_{i}

_{i}_{s}

According to the estimation error covariance matrix ^{−1}, the root mean square error (RMSE) _{e}

In this way, the target can be localized by maximum likelihood estimation after gathering the observations from the sensor nodes. The location accuracy is reflected by _{e}

It is assumed that the sink node keeps _{t}_{k}_{t}_{Nt}_{+1} due to its outstanding performance in model fitting and lightweight computational cost. Here, one direction of the target motion {_{k}_{t}

The ARMA model contains two terms, the autoregressive (AR) term and the moving average (MA) term [_{k}_{k}_{−1}, _{k}_{−2}, ⋯, _{k}_{−p}} and a random noise _{k}_{i}_{k}_{k}_{k}_{−1}, ⋯, _{k}_{−q}}. This noise series is constructed from the forecasting errors. This model is defined as a MA process of order _{i}

The backshift operator

Then, the AR process can be written as:

In the autoregressive moving average process, the current value of the time series _{k}_{k}_{−1}, _{k}_{−2}, ⋯ _{k}_{−}_{p}_{k}_{k}_{−1}, ⋯, _{k}_{−}_{q}_{k}

There is an assumption for ARMA process that the time series for analysis should be stationary, that is, the mean of the time series and the covariance among its observations are not time-varied. According to the target model, the process is non-stationary, so the series should be transformed to a stationary process be the model construction. This can be often achieved by a differentiation process. The first-order differencing of the original time series is defined as:
_{k}

For instance, time series is simulated for one direction of target trajectory. As shown in

However, further processing of the time series is performed in order to obtain more stationary time series for forecasting. Here, EMD is introduced to decompose the time series into a set of stationary time series, called intrinsic mode functions (IMFs). More importantly, the IMFs can reflect the inherent variation mode in the time series, including stochastic components and a trend component.

EMD is a general nonlinear, non-stationary signal processing method, first proposed by Huang [

For each IMF, there are two definitive requirements: (1) the numbers of its extrema and zero-crossings are equal or differ at most by one; (2) it is symmetric with respect to local zero mean. The decomposition process is performed as follow:

Identify all the maxima and minima of

Generate its upper and lower envelopes

Calculate the point-by-point mean from upper and lower envelopes as:

Extract the detail as:

Check the properties of _{k}. If it meets the definitive requirements, an IMF is derived and the residual is:
_{k}

Repeat Steps a) to e) until the residual satisfies the stopping criterion.

At the end of this process, the time series can be expressed as:
_{k,i}

Here, the number of IMFs

For the time series in

For time series {_{k}

Taking the IMF1 in

As mentioned earlier, the sink node and a group of sensor nodes maintain the components. Then, the AR(

For any time series {_{k}_{1} = [_{p}_{+1} _{p}_{+2} ⋯ _{N}^{T}_{1} _{2} ⋯ _{p}^{T}_{p}_{+1} _{p}_{+2} ⋯ _{N}^{T}_{i}

Then the least square estimation of coefficients is:

With the constructed AR(

In this way, both directions of the target position can be forecasted adaptively. Since the forecasted target position for the next sensing period is available, related energy-efficient organization will be implemented in WSN.

With the forecasted target position, sensor nodes can be set to sleep when there is no sensing task. Due to the redundancy of sensor node deployment, the WSN performs probability awakening in a distributed manner to enhance the scalability of the energy consumption. Moreover, the routing scheme of data reporting is optimized by ACO for energy efficiency.

According to Section 2.3, sensor nodes can shut down its components if necessary. Thereby, sensor node awakening is considered with the forecasted target position. To prolong the lifetime of WSN, we exploit a sensor node awakening approach, where the mode transition of sensor node is scheduled and probability awakening is considered.

First, five operation modes of sensor node is defined as follow:

Then, sensor node awakening strategy can be exploited according to the defined operation modes.

For a sensor node in

Here, the estimation approach of sleep period number will be discussed. For each sensor nodes, define the shortest distance to the WSN boundary as _{min}. Then, the sleep time can be estimated as:
_{s}_{a}_{max} is the maximum target velocity, and Δ_{target}′_{target}′_{min}, then _{target}_{target}′_{target}_{min}.

Thereby, WSN maintain standby for any new target getting into it. When there is a target in the sensing field, the sensor nodes which are far away from the target will go to sleep. The sleeping sensor nodes are awakened on time when there is potential sensing task.

In addition, the redundancy of sensor node deployment is utilized to prolong the sleep time. For the sensor nodes, the probability of prolonging the sleep time obeys exponential distribution, which is determined by the probability awakening parameter _{sleep}

The sensor node awakening situation around the target is that illustrated in _{s}_{max}_{s}_{max}

With the estimated sleep period number, sensor node can go to

When there is a target in the sensing field, a group of sensor nodes goes into the

The index of sensor nodes with observations is denoted by {1, 2, ⋯, _{a}

The cost measure of edge between sensor node

A optimal path {_{a}_{a}_{a}

In this way, the observations of sensor nodes can be merged step by step on the path and the last sensor node will obtain the final target localization result. This result is then reported to the sink node. As it only includes the coordinates of the target, the communication cost is ignored.

It is assumed that the sink node maintains the awakening information of sensor nodes. Therefore, the optimization of routing scheme can be performed by the sink node. ACO is adopted to find the optimal path, where a society of artificial ants is modeled [_{i,j}_{i,j}_{i,j}_{i,j}_{i,j}_{t}^{k}_{a}

In this section, the efficiency of collaborative sensing, adaptive estimation and energy-efficient organization will be analyzed with simulation experiments.

It is assumed that the sensing field of WSN is 400 m × 400 m, in which 300 wireless sensor nodes are deployed randomly. The sensing period _{max} is set as 8 m/s^{2} and the maximum velocity _{max} is set as 30 m/s.

According to Section 2.2, each sensor node has the sensing range _{s}_{β}_{r}_{1} = 500 nJ/bit, _{2} = 5 nJ/(bit·m^{2}) and _{d}_{tx}

During each sensing period, it is assumed that the time for staying in each mode is _{T}

The target tracking procedure with energy-efficient organization is simulated. As presented in

Utilizing the target trajectory in

First, the efficiency of collaborative sensing is discussed. For sensing performance comparison, we consider the situation that only the closest sensor node for the target acquires the observations. In this situation, the bearing and range observations of single sensor node is available and the related target location error can be derived from

After experimental analysis, the differentiation order

For the time series after differentiation, the forecasting error with and without EMD is compared in

With the distributed target position forecasting, the energy efficiency of the energy-efficient organization can be investigated. The sensor nodes estimate the sleep period number and go to sleep in a distributed manner according to Section 4.1. Thereby, the operation cost of WSN is optimized. In each sensing period, all the sensor nodes which can detect the target wake up. In order to minimize the transmission cost, ACO algorithm is utilized for routing.

According to

With the power consumption curves presented in

In

Moreover, the efficiency of the probability sleep prolonging is discussed in the distributed sensor node awakening. According to

Considering the collaborative sensing accuracy, the cases in which the average number of detecting sensor node exceeds 5 is analyzed. According to

The experiments studied the energy efficiency of target tracking. Collaborative sensing enhances the target localization accuracy. Time series analysis based on EMD approximates the target trajectory well. Besides, the energy-efficient organization achieves energy saving. Moreover, the probabilistic in sensor node awakening leads to extra energy saving.

Considering the energy constraints of target tracking in WSN, this paper proposes an energy-efficient organization method based on collaborative sensing and adaptive target estimation. Sensor nodes which are equipped with bearing and range sensors utilize the maximum likelihood estimation for data fusion. Hence, targets can be localized by collaborative sensing while the localization error is evaluated utilizing FIM. A sink node maintains the historical target positions, with which the target position in the next sensing instant is estimated. The time series of target trajectory is processed by differentiation and EMD. Thereby, the inherent variation modes can be obtained, which are forecasted by the ARMA models. The future target position is derived from the forecasted results and is adopted to organize the sensor nodes for sensing. Here, the energy-efficient organization method includes the distributed sensor node awakening and adaptive routing scheme. Sensor nodes can go to sleep when there is no target in its sensing range and it can be awakened once there is potential sensing task. Besides, probabilistic awakening is introduced to prolong the sleep time of sensor nodes. ACO algorithm is employed to optimize the path of data transmission. Experiments of target tracking verify that target localization accuracy is enhanced by collaborative sensing of the sensor nodes, while the forecasting performance is improved by combining ARMA model with EMD. More importantly, the energy efficiency of WSN is guaranteed by the distributed sensor awakening and dynamic routing. In Section 2, the main contribution of this paper is the energy-efficient organization framework for target tracking as well as the forecasting and awakening approaches. For the future work, we may extend this method to other applications of WSN, such as target classification and environment surveillance. Also, the mobility of wireless sensor node could by investigate for further research.

This paper is supported by the National Grand Fundamental Research 973 Program of China under Grant No.2006CB303000 and the National Natural Science Foundation of China (No.60673176; No.60373014; No.50175056).

Energy-efficient organization framework for target tracking in WSN.

Sensing function of a single sensor node.

Simulated time series of target trajectory: (a) Before differentiation; (b) After differentiation.

Decomposition results for the time series after differentiation.

Analysis of ACF and PACF patterns: (a) ACF; (b) PACF.

Operation mode transition in distributed sensor node awakening approach according to the forecasted target position.

Sensor node awakening when there is a target in WSN sensing field.

Deployment of WSN and the target trajectory.

Comparison of target localization error with collaborative sensing and single sensor node.

Comparison of forecasting error with and without EMD for time series after differentiation: (a) X direction; (b) Y direction.

Target position forecasted results utilizing time series analysis with and without EMD.

Power consumption curves of WSN including operation and transmission cost: (a) Energy-efficient organization; (b) General organization.

Average number of sensor nodes available for target detection in one sensing period with different probability awakening parameter

Patterns in the theoretical ACF and PACF of stationary time series.

ACF | Exponential or sinusoidal decay to zero | Spikes cut off to zero after lag |
Exponential or sinusoidal decay to zero after lag |

PACF | Spikes cut off to zero after lag |
Exponential or sinusoidal decay to zero | Exponential or sinusoidal decay to zero after lag |

Power consumption of the five operation modes for the sensor node

5 | |

25 | |

40 | |

45 | |

45+_{tx} |

Energy consumption comparison of general and energy-efficient organization.

| |||
---|---|---|---|

Operation | 167.4 | 148. 4 | 11.4 |

Transmission | 132.4 | 84.1 | 36.5 |

Total | 299.8 | 232. 5 | 22.4 |

Total energy consumption of WSN with different probability awakening parameter

0.08 | 0.16 | 0.32 | 0.64 | |

189.1 | 201.6 | 217.1 | 229.7 |